Center for Quantum Devices > Research > Publications > Charles Marcus
Publications by Charles M. Marcus
 2019

Selectivearea chemical beam epitaxy of inplane InAs onedimensional
channels grown on InP(001), InP(111)B, and InP(110) surfaces 
Abstract
 We report on the selectivearea chemical beam epitaxial growth of InAs inplane, onedimensional (1D) channels using patterned SiO$_{2}$coated InP(001), InP(111)B, and InP(110) substrates to establish a scalable platform for topological superconductor networks. Topview scanning electron micrographs show excellent surface selectivity and dependence of major facet planes on the substrate orientations and ridge directions, and the ratios of the surface energies of the major facet planes were estimated. Detailed structural properties and defects in the InAs nanowires (NWs) were characterized by transmission electron microscopic analysis of crosssections perpendicular to the NW ridge direction and along the NW ridge direction. Electrical transport properties of the InAs NWs were investigated using Hall bars, a field effect mobility device, a quantum dot, and an AharonovBohm loop device, which reflect the strong spinorbit interaction and phasecoherent transport characteristic in the selectively grown InAs systems. This study demonstrates that selectivearea chemical beam epitaxy is a scalable approach to realize semiconductor 1D channel networks with the excellent surface selectivity and this material system is suitable for quantum transport studies.

Currentphase relations of InAs nanowire Josephson junctions: from
interacting to multimode regimes 
Abstract
 Gatetunable semiconductorsuperconductor nanowires with superconducting leads form exotic Josephson junctions that are a highly desirable platform for two types of qubits: those with topological superconductivity (Majorana qubits) and those based on tunable anharmonicity (gatemon qubits). Controlling their behavior, however, requires understanding their electrostatic environment and electronic structure. Here we study gated InAs nanowires with epitaxial aluminum shells. By measuring currentphase relations (CPR) and comparing them with analytical and numerical calculations, we show that we can tune the number of modes, determine the transparency of each mode, and tune into regimes in which electronelectron interactions are apparent, indicating the presence of a quantum dot. To take into account electrostatic and geometrical effects, we perform microscopic selfconsistent SchrodingerPoisson numerical simulations, revealing the energy spectrum of Andreev states in the junction as well as their spatial distribution. Our work systematically demonstrates the effect of device geometry, gate voltage and phase bias on mode behavior, providing new insights into ongoing experimental efforts and predictive device design.
Sean Hart, Zheng Cui, Gerbold Menard, Mingtang Deng, Andrey Antipov, Roman M. Lutchyn, Peter Krogstrup, Charles M. Marcus, Kathryn A. Moler 1902.07804v1 [pdf]

InPlane Magnetoconductance Mapping of InSb Quantum Wells 
Abstract
 Inplane magnetoconductance of InSb quantum wells (QW) containing a two dimensional electron gas (2DEG) is presented. Using a vector magnet, we created a magnetoconductance map which shows the suppression of weak antilocalization (WAL) as a function of applied field. By fitting the inplane field response of the 2DEG, we estimate material disorder and gfactor as a function of crystal direction. The inplane WAL suppression is found to be dominated by the Zeeman effect and to show a small crystalorientationdependent anistropy in disorder and gfactor. These measurements show the utility of multidirectional measurement of magnetoconductance in analyzing material properties.
J. T. Mlack, K. S. Wickramasinghe, T. D. Mishima, M. B. Santos, C. M. Marcus 1902.07570v1 [pdf]

Interferometry and coherent singleelectron transport through hybrid
superconductorsemiconductor Coulomb islands 
Abstract
 Majorana zero modes are leading candidates for topological quantum computation due to their nonlocal character and nonabelian exchange statistics. Among their attributes, spatially separated Majorana modes are expected to allow coherent singleelectron transport through onedimensional topological superconductors in the Coulomb blockade (CB) regime. We have investigated this feature by patterning an elongated epitaxial InAsAl Coulomb island embedded in an AharonovBohm interferometer. Using a parallel magnetic field to lower the energy of a discrete subgap state in the island below its charging energy, conductance oscillations in the ring were observed with a flux period of h/e (h is Planck's constant and e is the elementary charge), indicating coherent singleelectron transport through the interferometer. Oscillation amplitude was largest when CB conductance peaks in the island were 1e periodic, and suppressed when CB was 2e periodic or when superconductivity was suppressed. Oscillation phase shifts of {\pi} were observed when the charge occupancy of the island was changed by 1e, indicating that the interferometer can detect island parity. Magnetic fields oriented orthogonal to the island reduced the field at which 2e periodic peaks split and where coherent transport could also be observed, suggesting additional nonMajorana mechanisms for 1e transport through these moderately short wires.
A. M. Whiticar, A. Fornieri, E. C. T. O'Farrell, A. C. C. Drachmann, T. Wang, C. Thomas, S. Gronin, R. Kallaher, G. C. Gardner, M. J. Manfra, C. M. Marcus, F. Nichele 1902.07085v1 [pdf]

Suppressing quasiparticle poisoning with a voltagecontrolled filter 
Abstract
 We study singleelectron charging events in an Al/InAs nanowire hybrid system with deliberately introduced gapless regions. The occupancy of a Coulomb island is detected using a nearby radiofrequency quantum dot as a charge sensor. We demonstrate that a 1 micron gapped segment of the wire can be used to efficiently suppress single electron poisoning of the gapless region and therefore protect the parity of the island while maintaining good electrical contact with a normal lead. In the absence of protection by charging energy, the 1e switching rate can be reduced below 200 per second. In the same configuration, we observe strong quantum charge fluctuations due to exchange of electron pairs between the island and the lead. The magnetic field dependence of the poisoning rate yields a zerofield superconducting coherence length of ~ 90 nm.
Gerbold C. Ménard, Filip K. Malinowski, Denise Puglia, Dmitry I. Pikulin, Torsten Karzig, Bela Bauer, Peter Krogstrup, Charles M. Marcus 1902.02689v1 [pdf]

Photon Assisted Tunneling of Zero Modes in a Majorana Wire 
Abstract
 Hybrid nanowires with proximityinduced superconductivity in the topological regime host Majorana zero modes (MZMs) at their ends, and networks of such structures can produce topologically protected qubits. In a doubleisland geometry where each segment hosts a pair of MZMs, interpair coupling mixes the charge parity of the islands and opens an energy gap between the even and odd charge states at the interisland charge degeneracy. Here, we report on the spectroscopic measurement of such an energy gap in an InAs/Al doubleisland device by tracking the position of the microwaveinduced quasiparticle (qp) transitions using a radiofrequency (rf) charge sensor. In zero magnetic field, photon assisted tunneling (PAT) of Cooper pairs gives rise to resonant lines in the 2e2e periodic charge stability diagram. In the presence of a magnetic field aligned along the nanowire, resonance lines are observed parallel to the interisland charge degeneracy of the 1e1e periodic charge stability diagram, where the 1e periodicity results from a zeroenergy subgap state that emerges in magnetic field. Resonant lines in the charge stability diagram indicate coherent photon assisted tunneling of singleelectron states, changing the parity of the two islands. The dependence of resonant frequency on detuning indicates a sizable (GHzscale) hybridization of zero modes across the junction separating islands.

Radiofrequency methods for Majoranabased quantum devices: fast charge
sensing and phase diagram mapping 
Abstract
 Radiofrequency (RF) reflectometry is implemented in hybrid semiconductorsuperconductor nanowire systems designed to probe Majorana zero modes. Two approaches are presented. In the first, hybrid nanowirebased devices are part of a resonant circuit, allowing conductance to be measured as a function of several gate voltages ~40 times faster than using conventional lowfrequency lockin methods. In the second, nanowire devices are capacitively coupled to a nearby RF singleelectron transistor made from a separate nanowire, allowing RF detection of charge, including chargeonly measurement of the crossover from 2e interisland charge transitions at zero magnetic field to 1e transitions at axial magnetic fields above 0.6 T, where a topological state is expected. Singleelectron sensing yields signaltonoise exceeding 3 and visibility 99.8% for a measurement time of 1 {\mu}s.

Selectivearea chemical beam epitaxy of inplane InAs onedimensional
channels grown on InP(001), InP(111)B, and InP(110) surfaces 
Abstract
 2018

Effective gfactor in Majorana Wires 
Abstract
 We use the effective gfactor of subgap states, g*, in hybrid InAs nanowires with an epitaxial Al shell to investigate how the superconducting density of states is distributed between the semiconductor core and the metallic shell. We find a steplike reduction of g* and improved hard gap with reduced carrier density in the nanowire, controlled by gate voltage. These observations are relevant for Majorana devices, which require tunable carrier density and g* exceeding the gfactor of the proximitizing superconductor. Additionally, we observe the closing and reopening of a gap in the subgap spectrum coincident with the appearance of a zerobias conductance peak.
S. Vaitiekėnas, M. T. Deng, J. Nygård, P. Krogstrup, C. M. Marcus Journal reference: Phys. Rev. Lett. 121, 037703 (2018) [pdf] DOI: 10.1103/PhysRevLett.121.037703

Fluxinduced Majorana modes in fullshell nanowires 
Abstract
 We demonstrate a novel means of creating Majorana zero modes using magnetic flux applied to a full superconducting shell surrounding a semiconducting nanowire core, unifying approaches based on proximitized nanowires and vortices in topological superconductors. In the destructive LittleParks regime, reentrant regions of superconductivity are associated with integer number of phase windings in the shell. Tunneling into the core reveals a hard induced gap near zero applied flux, corresponding to zero phase winding, and a gapped region with a discrete zeroenergy state for flux around {\Phi}_0 = h/2e, corresponding to 2{\pi} phase winding. Coulomb peak spacing in fullshell islands around one applied flux shows exponentially decreasing deviation from 1e periodicity with device length, consistent with the picture of Majorana modes located at the ends of the wire.
S. Vaitiekėnas, M. T. Deng, P. Krogstrup, C. M. Marcus 1809.05513v1 [pdf]

SelectiveAreaGrown SemiconductorSuperconductor Hybrids: A Basis for Topological Networks 
Abstract
 We introduce selective area grown hybrid InAs/Al nanowires based on molecular beam epitaxy, allowing arbitrary semiconductorsuperconductor networks containing loops and branches. Transport reveals a hard induced gap and unpoisoned 2eperiodic Coulomb blockade, with temperature dependent 1e features in agreement with theory. Coulomb peak spacing in parallel magnetic field displays overshoot, indicating an oscillating discrete nearzero subgap state consistent with device length. Finally, we investigate a loop network, finding strong spinorbit coupling and a coherence length of several microns. These results demonstrate the potential of this platform for scalable topological networks among other applications.
S. Vaitiekėnas, A. M. Whiticar, M. T. Deng, F. Krizek, J. E. Sestoft, C. J. Palmstrøm, S. MartiSanchez, J. Arbiol, P. Krogstrup, L. Casparis, C. M. Marcus Journal reference: Phys. Rev. Lett. 121, 147701 (2018) [ 1802.04210v3 ] DOI: 10.1103/PhysRevLett.121.147701

Evidence of topological superconductivity in planar Josephson junctions 
Abstract
 Majorana zero modes are quasiparticle states localized at the boundaries of topological superconductors that are expected to be ideal building blocks for faulttolerant quantum computing. Several observations of zerobias conductance peaks measured in tunneling spectroscopy above a critical magnetic field have been reported as experimental indications of Majorana zero modes in superconductor/semiconductor nanowires. On the other hand, two dimensional systems offer the alternative approach to confine Ma jorana channels within planar Josephson junctions, in which the phase difference {\phi} between the superconducting leads represents an additional tuning knob predicted to drive the system into the topological phase at lower magnetic fields. Here, we report the observation of phasedependent zerobias conductance peaks measured by tunneling spectroscopy at the end of Josephson junctions realized on a InAs/Al heterostructure. Biasing the junction to {\phi} ~ {\pi} significantly reduces the critical field at which the zerobias peak appears, with respect to {\phi} = 0. The phase and magnetic field dependence of the zeroenergy states is consistent with a model of Majorana zero modes in finitesize Josephson junctions. Besides providing experimental evidence of phasetuned topological superconductivity, our devices are compatible with superconducting quantum electrodynamics architectures and scalable to complex geometries needed for topological quantum computing.
Antonio Fornieri, Alexander M. Whiticar, F. Setiawan, Elías Portolés Marín, Asbjørn C. C. Drachmann, Anna Keselman, Sergei Gronin, Candice Thomas, Tian Wang, Ray Kallaher, Geoffrey C. Gardner, Erez Berg, Michael J. Manfra, Ady Stern, Charles M. Marcus, Fabrizio Nichele Journal reference: Nature 569, 8992 (2019) [ 1809.03037v1 ] DOI: 10.1038/s4158601910688

Fast spin exchange across a multielectron mediator 
Abstract
 The Heisenberg exchange interaction between neighboring quantum dots allows precise voltage control over spin dynamics, due to the ability to precisely control the overlap of orbital wavefunctions by gate electrodes. This allows the study of fundamental electronic phenomena and finds applications in quantum information processing. Although spinbased quantum circuits based on shortrange exchange interactions are possible, the development of scalable, longerrange coupling schemes constitutes a critical challenge within the spinqubit community. Approaches based on capacitative coupling and cavitymediated interactions effectively couple spin qubits to the charge degree of freedom, making them susceptible to electricallyinduced decoherence. The alternative is to extend the range of the Heisenberg exchange interaction by means of a quantum mediator. Here, we show that a multielectron quantum dot with 50100 electrons serves as an excellent mediator, preserving speed and coherence of the resulting spinspin coupling while providing several functionalities that are of practical importance. These include speed (mediated twoqubit rates up to several gigahertz), distance (of order of a micrometer), voltage control, possibility of sweet spot operation (reducing susceptibility to charge noise), and reversal of the interaction sign (useful for dynamical decoupling from noise).
Filip K. Malinowski, Frederico Martins, Thomas B. Smith, Stephen D. Bartlett, Andrew C. Doherty, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Nature Communications 10, 1196 (2019) [ 1808.09736v1 ] DOI: 10.1038/s4146701909194x

Parity effect does not mean a superconductor free of quasiparticles 
Abstract
 We show that a superconducting device can show a clear parity effect in the number of electrons even when there is, on average, a single nonequilibrium quasiparticle present, by monitoring in real time the charge state of a superconducting island connected to normal leads by tunnel junctions. The quasiparticles are created by Cooper pairs breaking on the island at a rate of a few kHz. We demonstrate that the pair breaking is caused by the backaction of the singleelectron transistor used as a charge detector. With sufficiently low probing currents, our superconducting island is free of quasiparticles 97% of the time.
E. T. Mannila, V. F. Maisi, H. Q. Nguyen, C. M. Marcus, J. P. Pekola 1807.01733v1 [pdf]

Hybridization of Subgap States in OneDimensional SuperconductorSemiconductor Coulomb Islands 
Abstract
 We present measurements of onedimensional superconductorsemiconductor Coulomb islands, fabricated by gate confinement of a twodimensional InAs heterostructure with an epitaxial Al layer. When tuned via electrostatic side gates to regimes without subgap states, Coulomb blockade reveals Cooperpair mediated transport. When subgap states are present, Coulomb peak positions and heights oscillate in a correlated way with magnetic field and gate voltage, as predicted theoretically, with (anti) crossings in (parallel) transverse magnetic field indicating Rashbatype spinorbit coupling. Overall results are consistent with a picture of overlapping Majorana zero modes in finite wires.
E. C. T. O'Farrell, A. C. C. Drachmann, M. Hell, A. Fornieri, A. M. Whiticar, E. B. Hansen, S. Gronin, G. C. Gardener, C. Thomas, M. J. Manfra, K. Flensberg, C. M. Marcus, F. Nichele Journal reference: Phys. Rev. Lett. 121, 256803 (2018) [ 1804.09676v1 ] DOI: 10.1103/PhysRevLett.121.256803

Field effect enhancement in buffered quantum nanowire networks 
Abstract
 IIIV semiconductor nanowires have shown great potential in various quantum transport experiments. However, realizing a scalable highquality nanowirebased platform that could lead to quantum information applications has been challenging. Here, we study the potential of selective area growth by molecular beam epitaxy of InAs nanowire networks grown on GaAsbased buffer layers. The buffered geometry allows for substantial elastic strain relaxation and a strong enhancement of field effect mobility. We show that the networks possess strong spinorbit interaction and long phase coherence lengths with a temperature dependence indicating ballistic transport. With these findings, and the compatibility of the growth method with hybrid epitaxy, we conclude that the material platform fulfills the requirements for a wide range of quantum experiments and applications.
Filip Krizek, Joachim E. Sestoft, Pavel Aseev, Sara MartiSanchez, Saulius Vaitiekenas, Lucas Casparis, Sabbir A. Khan, Yu Liu, Tomas Stankevic, Alexander M. Whiticar, Alexandra Fursina, Frenk Boekhout, Rene Koops, Emanuele Uccelli, Leo P. Kouwenhoven, Charles M. Marcus, Jordi Arbiol, Peter Krogstrup Journal reference: Phys. Rev. Materials 2, 093401 (2018) [ 1802.07808v2 ] DOI: 10.1103/PhysRevMaterials.2.093401

Majorana zero modes in superconductor–semiconductor heterostructures 
Abstract
 Realizing topological superconductivity and Majorana zero modes in the laboratory is one of the major goals in condensed matter physics. We review the current status of this rapidlydeveloping field, focusing on semiconductorsuperconductor proposals for topological superconductivity. Material science progress and robust signatures of Majorana zero modes in recent experiments are discussed. After a brief introduction to the subject, we outline several nextgeneration experiments probing exotic properties of Majorana zero modes, including fusion rules and nonAbelian exchange statistics. Finally, we discuss prospects for implementing Majoranabased topological quantum computation in these systems.
R. M. Lutchyn, E. P. A. M. Bakkers, L. P. Kouwenhoven, P. Krogstrup, C. M. Marcus, Y. Oreg Journal reference: Nat Rev Mater 3, 52  68 (2018) [ 1707.04899v2 ] DOI: 10.1038/s4157801800031

Voltagecontrolled superconducting quantum bus 
Abstract
 We demonstrate the ability of an epitaxial semiconductorsuperconductor nanowire to serve as a fieldeffect switch to tune a superconducting cavity. Two superconducting gatemon qubits are coupled to the cavity, which acts as a quantum bus. Using a gate voltage to control the superconducting switch yields up to a factor of 8 change in qubitqubit coupling between the on and off states without detrimental effect on qubit coherence. Highbandwidth operation of the coupling switch on nanosecond timescales degrades qubit coherence.
L. Casparis, N. J. Pearson, A. Kringhøj, T. W. Larsen, F. Kuemmeth, J. Nygård, P. Krogstrup, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. B 99, 085434 (2019) [ 1802.01327v1 ] DOI: 10.1103/PhysRevB.99.085434

Effective gfactor in Majorana Wires 
Abstract
 2017

Engineering hybrid epitaxial InAsSb/Al nanowires for stronger topological protection 
Abstract
 The combination of strong spinorbit coupling, large $g$factors, and the coupling to a superconductor can be used to create a topologically protected state in a semiconductor nanowire. Here we report on growth and characterization of hybrid epitaxial InAsSb/Al nanowires, with varying composition and crystal structure. We find the strongest spinorbit interaction at intermediate compositions in zincblende InAs$_{1x}$Sb$_{x}$ nanowires, exceeding that of both InAs and InSb materials, confirming recent theoretical studies \cite{winkler2016topological}. We show that the epitaxial InAsSb/Al interfaces allows for a hard induced superconducting gap and 2$e$ transport in Coulomb charging experiments, similar to experiments on InAs/Al and InSb/Al materials, and find measurements consistent with topological phase transitions at low magnetic fields due to large effective $g$factors. Finally we present a method to grow pure wurtzite InAsSb nanowires which are predicted to exhibit even stronger spinorbit coupling than the zincblende structure.
Joachim E. Sestoft, Thomas Kanne, Aske Nørskov Gejl, Merlin von Soosten, Jeremy S. Yodh, Daniel Sherman, Brian Tarasinski, Michael Wimmer, Erik Johnson, Mingtang Deng, Jesper Nygård, Thomas Sand Jespersen, Charles M. Marcus, Peter Krogstrup Journal reference: Phys. Rev. Materials 2, 044202 (2018) [ 1711.06864v2 ] DOI: 10.1103/PhysRevMaterials.2.044202

Superconducting, Insulating, and Anomalous Metallic Regimes in a Gated
TwoDimensional SemiconductorSuperconductor Array 
Abstract
 The superconductorinsulator transition in two dimensions has been widely investigated as a paradigmatic quantum phase transition. The topic remains controversial, however, because many experiments exhibit a metallic regime with saturating lowtemperature resistance, at odds with conventional theory. Here, we explore this transition in a novel, highly controllable system, a semiconductor heterostructure with epitaxial Al, patterned to form a regular array of superconducting islands connected by a gateable quantum well. Spanning nine orders of magnitude in resistance, the system exhibits regimes of superconducting, metallic, and insulating behavior, along with signatures of flux commensurability and vortex penetration. An inplane magnetic field eliminates the metallic regime, restoring the direct superconductorinsulator transition, and improves scaling, while strongly altering the scaling exponent.
C. G. L. Bøttcher, F. Nichele, M. Kjaergaard, H. J. Suominen, J. Shabani, C. J. Palmstrøm, C. M. Marcus DOI: 10.1038/s4156701802599 1711.01451v2 [pdf]

Nonlocality of Majorana modes in hybrid nanowires 
Abstract
 Emergent Majorana bound states (MBSs) in topological superconductors appear capable of providing a naturally faulttolerant basis for quantum computing. Key to topological protection is the separation, or nonlocality, of MBSs, which makes Majorana qubits immune to decoherence by a local disturbance. While a number of experiments have reported signatures of MBSs based on zerobias peaks in tunneling conductance, the nonlocal character of Majorana modes  in contrast to Andreev bound states at zero energy  has not been previously demonstrated. Here, we experimentally demonstrate nonlocality of Majorana modes in epitaxial semiconductorsuperconducting nanowires. This is achieved using recent theory showing that nonlocality can be measured via the interaction of the zeroenergy state in the nanowire with a quantumdot state at one end. By comparing coupling to even versus odd occupied quantum dots states, we measure a high degree of nonlocality, consistent with topological MBSs, as well as the spin canting angles of the Majorana modes.
M. T. Deng, S. Vaitiekénas, E. Prada, P. SanJose, J. Nygård, P. Krogstrup, R. Aguado, C. M. Marcus Journal reference: Phys. Rev. B 98, 085125 (2018) [ 1712.03536v1 ] DOI: 10.1103/PhysRevB.98.085125

Superconducting gatemon qubit based on a proximitized twodimensional electron gas 
Abstract
 The coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconducting circuits, from setting qubit transition frequencies and interqubit coupling strengths, to the gain of parametric amplifiers for quantumlimited readout. The inductance is either set by tailoring the metaloxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices (SQUIDs) with local currentbiased flux lines. JJs based on superconductorsemiconductor hybrids represent a tantalizing allelectric alternative. The gatemon is a recently developed transmon variant which employs locally gated nanowire (NW) superconductorsemiconductor JJs for qubit control. Here, we go beyond proofofconcept and demonstrate that semiconducting channels etched from a waferscale twodimensional electron gas (2DEG) are a suitable platform for building a scalable gatemonbased quantum computer. We show 2DEG gatemons meet the requirements by performing voltagecontrolled single qubit rotations and twoqubit swap operations. We measure qubit coherence times up to ~2 us, limited by dielectric loss in the 2DEG host substrate.
Lucas Casparis, Malcolm R. Connolly, Morten Kjaergaard, Natalie J. Pearson, Anders Kringhøj, Thorvald W. Larsen, Ferdinand Kuemmeth, Tiantian Wang, Candice Thomas, Sergei Gronin, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Karl D. Petersson Journal reference: Nature Nanotechnology 13, 915 (2018) [ 1711.07665v3 ] DOI: 10.1038/s415650180207y

ZeroEnergy Modes from Coalescing Andreev States in a TwoDimensional SemiconductorSuperconductor Hybrid Platform 
Abstract
 We investigate zerobias conductance peaks that arise from coalescing subgap Andreev states, consistent with emerging Majorana zero modes, in hybrid semiconductorsuperconductor wires defined in a twodimensional InAs/Al heterostructure using topdown lithography and gating. The measurements indicate a hard superconducting gap, ballistic tunneling contact, and inplane critical fields up to $3$~T. Topdown lithography allows complex geometries, branched structures, and straightforward scaling to multicomponent devices compared to structures made from assembled nanowires.
Henri J. Suominen, Morten Kjaergaard, Alexander R. Hamilton, Javad Shabani, Chris J. Palmstrøm, Charles M. Marcus, Fabrizio Nichele Journal reference: Phys. Rev. Lett. 119, 176805 (2017) [ 1703.03699v2 ] DOI: 10.1103/PhysRevLett.119.176805

Spin of a Multielectron Quantum Dot and Its Interaction with a Neighboring Electron 
Abstract
 We investigate the spin of a multielectron GaAs quantum dot in a sequence of nine charge occupancies, by exchange coupling the multielectron dot to a neighboring twoelectron double quantum dot. For all nine occupancies, we make use of a leakage spectroscopy technique to reconstruct the spectrum of spin states in the vicinity of the interdot charge transition between a single and a multielectron quantum dot. In the same regime we also perform timeresolved measurements of coherent exchange oscillations between the single and multielectron quantum dot. With these measurements, we identify distinct characteristics of the multielectron spin state, depending on whether the dot's occupancy is even or odd. For three out of four even occupancies we do not observe any exchange interaction with the single quantum dot, indicating a spin0 ground state. For the one remaining even occupancy, we observe an exchange interaction that we associate with a spin1 multielectron quantum dot ground state. For all five of the odd occupancies, we observe an exchange interaction associated with a spin1/2 ground state. For three of these odd occupancies, we clearly demonstrate that the exchange interaction changes sign in the vicinity of the charge transition. For one of these, the exchange interaction is negative (i.e. tripletpreferring) beyond the interdot charge transition, consistent with the observed spin1 for the next (even) occupancy. Our experimental results are interpreted through the use of a Hubbard model involving two orbitals of the multielectron quantum dot. Allowing for the spin correlation energy (i.e. including a term favoring Hund's rules) and different tunnel coupling to different orbitals, we qualitatively reproduce the measured exchange profiles for all occupancies.
Filip K. Malinowski, Frederico Martins, Thomas B. Smith, Stephen D. Bartlett, Andrew C. Doherty, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. X 8, 011045 (2018) [ 1710.10012v1 ] DOI: 10.1103/PhysRevX.8.011045

Conduction channels of an InAsAl nanowire Josephson weak link 
Abstract
 We present a quantitative characterization of an electrically tunable Josephson junction defined in an InAs nanowire proximitized by an epitaxiallygrown superconducting Al shell. The gatedependence of the number of conduction channels and of the set of transmission coefficients are extracted from the highly nonlinear currentvoltage characteristics. Although the transmissions evolve nonmonotonically, the number of independent channels can be tuned, and configurations with a single quasiballistic channel achieved.
M. F. Goffman, C. Urbina, H. Pothier, J. Nygård, C. M. Marcus, P. Krogstrup Journal reference: New Journal of Physics, Institute of Physics: Open Access Journals, 2017, 19, pp.092002 [ 1706.09150v2 ] DOI: 10.1088/13672630/aa7641

$h/e$ superconducting quantum interference through trivial edge states
in InAs 
Abstract
 Josephson junctions defined in strong spin orbit semiconductors are highly interesting for the search for topological systems. However, next to topological edge states that emerge in a sufficient magnetic field, trivial edge states can also occur. We study the trivial edge states with superconducting quantum interference measurements on nontopological InAs Josephson junctions. We observe a SQUID pattern, an indication of superconducting edge transport. Also, a remarkable $h/e$ SQUID signal is observed that, as we find, stems from crossed Andreev states.
Folkert K. de Vries, Tom Timmerman, Viacheslav P. Ostroukh, Jasper van Veen, Arjan J. A. Beukman, Fanming Qu, Michael Wimmer, BinhMinh Nguyen, Andrey A. Kiselev, Wei Yi, Marko Sokolich, Michael J. Manfra, Charles M. Marcus, Leo P. Kouwenhoven Journal reference: Phys. Rev. Lett. 120, 047702 (2018) [ 1709.03727v2 ] DOI: 10.1103/PhysRevLett.120.047702

Scaling of Majorana ZeroBias Conductance Peaks 
Abstract
 We report an experimental study of the scaling of zerobias conductance peaks compatible with Majorana zero modes as a function of magnetic field, tunnel coupling, and temperature in onedimensional structures fabricated from an epitaxial semiconductorsuperconductor heterostructure. Results are consistent with theory, including a peak conductance that is proportional to tunnel coupling, saturates at $2e^2/h$, decreases as expected with fielddependent gap, and collapses onto a simple scaling function in the dimensionless ratio of temperature and tunnel coupling.
Fabrizio Nichele, Asbjorn C. C. Drachmann, Alexander M. Whiticar, Eoin C. T. O'Farrell, Henri J. Suominen, Antonio Fornieri, Tian Wang, Geoffrey C. Gardner, Candice Thomas, Anthony T. Hatke, Peter Krogstrup, Michael J. Manfra, Karsten Flensberg, Charles M. Marcus Journal reference: Phys. Rev. Lett. 119, 136803 (2017) [ 1706.07033v2 ] DOI: 10.1103/PhysRevLett.119.136803

Scalable designs for quasiparticlepoisoningprotected topological quantum computation with Majorana zero modes 
Abstract
 We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurementonly protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological $T$junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.
Torsten Karzig, Christina Knapp, Roman M. Lutchyn, Parsa Bonderson, Matthew B. Hastings, Chetan Nayak, Jason Alicea, Karsten Flensberg, Stephan Plugge, Yuval Oreg, Charles M. Marcus, Michael H. Freedman Journal reference: Phys. Rev. B 95, 235305 (2017) [ 1610.05289v4 ] DOI: 10.1103/PhysRevB.95.235305

Negative Spin Exchange in a Multielectron Quantum Dot 
Abstract
 By operating a oneelectron quantum dot (fabricated between a multielectron dot and a oneelectron reference dot) as a spectroscopic probe, we study the spin properties of a gatecontrolled multielectron GaAs quantum dot at the transition between odd and even occupation number. We observe that the multielectron groundstate transitions from spin1/2like to singletlike to tripletlike as we increase the detuning towards the next higher charge state. The sign reversal in the inferred exchange energy persists at zero magnetic field, and the exchange strength is tunable by gate voltages and inplane magnetic fields. Complementing spin leakage spectroscopy data, the inspection of coherent multielectron spin exchange oscillations provides further evidence for the sign reversal and, inferentially, for the importance of nontrivial multielectron spin exchange correlations.
Frederico Martins, Filip K. Malinowski, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. Lett. 119, 227701 (2017) [ 1706.01007v1 ] DOI: 10.1103/PhysRevLett.119.227701

Transport studies of epiAl/InAs 2DEG systems for required
buildingblocks in topological superconductor networks 
Abstract
 Onedimensional (1D) electronic transport and induced superconductivity in semiconductor nanostructures are crucial ingredients to realize topological superconductivity. Our approach for topological superconductivity employs a twodimensional electron gas (2DEG) formed by an InAs quantum well, cleanly interfaced with a superconductor (epitaxial Al). This epiAl/InAs quantum well heterostructure is advantageous for fabricating largescale nanostructures consisting of multiple Majorana zero modes. Here, we demonstrate buildingblock transport studies using a highquality epiAl/InAs 2DEG heterostructure, which could be put together to realize the proposed 1D nanowirebased nanostructures and 2DEGbased networks that could host multiple Majorana zero modes: 1D transport using 1) quantum point contacts and 2) gatedefined quasi1D channels in the InAs 2DEG as well as induced superconductivity in 3) a ballistic AlInAs 2DEGAl Josephson junction. From 1D transport, systematic evolution of conductance plateaus in halfinteger conductance quanta are observed as a result of strong spinorbit coupling in the InAs 2DEG. Large IcRn, a product of critical current and normal state resistance from the Josephson junction, indicates that the interface between the epitaxial Al and the InAs 2DEG is highly transparent. Our results of electronic transport studies based on the 2D approach suggest that the epitaxial superconductor/2D semiconductor system is suitable for realizing largescale nanostructures for quantum computing applications.
Joon Sue Lee, Borzoyeh Shojaei, Mihir Pendharkar, Anthony P. McFadden, Younghyun Kim, Henri J. Suominen, Morten Kjaergaard, Fabrizio Nichele, Charles M. Marcus, Chris J. Palmstrøm 1705.05049v1 [pdf]

Spectrum of the Nuclear Environment for GaAs Spin Qubits 
Abstract
 Using a singlettriplet spin qubit as a sensitive spectrometer of the GaAs nuclear spin bath, we demonstrate that the spectrum of Overhauser noise agrees with a classical spin diffusion model over six orders of magnitude in frequency, from 1 mHz to 1 kHz, is flat below 10 mHz, and falls as $1/f^2$ for frequency $f \! \gtrsim \! 1$ Hz. Increasing the applied magnetic field from 0.1 T to 0.75 T suppresses electronmediated spin diffusion, which decreases spectral content in the $1/f^2$ region and lowers the saturation frequency, each by an order of magnitude, consistent with a numerical model. Spectral content at megahertz frequencies is accessed using dynamical decoupling, which shows a crossover from the fewpulse regime ($\lesssim \! 16$ $\pi$pulses), where transverse Overhauser fluctuations dominate dephasing, to the manypulse regime ($\gtrsim \! 32$ $\pi$pulses), where longitudinal Overhauser fluctuations with a $1/f$ spectrum dominate.
Filip K. Malinowski, Frederico Martins, Łukasz Cywiński, Mark S. Rudner, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. Lett. 118, 177702 (2017) [ 1701.01855v2 ] DOI: 10.1103/PhysRevLett.118.177702

Spinorbit interaction in a dual gated InAs/GaSb quantum well 
Abstract
 Spinorbit interaction is investigated in a dual gated InAs/GaSb quantum well. Using an electric field the quantum well can be tuned between a single carrier regime with exclusively electrons as carriers and a twocarriers regime where electrons and holes coexist. Spinorbit interaction in both regimes manifests itself as a beating in the Shubnikovde Haas oscillations. In the single carrier regime the linear Dresselhaus strength is characterized by $\beta =$ 28.5 meV$\AA$ and the Rashba coefficient $\alpha$ is tuned from 75 to 53 meV$\AA$ by changing the electric field. In the twocarriers regime the spin splitting shows a nonmonotonic behavior with gate voltage, which is consistent with our band structure calculations.
Arjan J. A. Beukman, Folkert K. de Vries, Jasper van Veen, Rafal Skolasinski, Michael Wimmer, Fanming Qu, David T. de Vries, BinhMinh Nguyen, Wei Yi, Andrey A. Kiselev, Marko Sokolich, Michael J. Manfra, Fabrizio Nichele, Charles M. Marcus, Leo P. Kouwenhoven Journal reference: Phys. Rev. B 96, 241401 (2017) [ 1704.03482v1 ] DOI: 10.1103/PhysRevB.96.241401

Symmetric operation of the resonant exchange qubit 
Abstract
 We operate a resonant exchange qubit in a highly symmetric tripledot configuration using IQmodulated RF pulses. At the resulting threedimensional sweet spot the qubit splitting is an order of magnitude less sensitive to all relevant control voltages, compared to the conventional operating point, but we observe no significant improvement in the quality of Rabi oscillations. For weak driving this is consistent with Overhauser field fluctuations modulating the qubit splitting. For strong driving we infer that effective voltage noise modulates the coupling strength between RF drive and the qubit, thereby quickening Rabi decay. Application of CPMG dynamical decoupling sequences consisting of up to n = 32 {\pi} pulses significantly prolongs qubit coherence, leading to marginally longer dephasing times in the symmetric configuration. This is consistent with dynamical decoupling from low frequency noise, but quantitatively cannot be explained by effective gate voltage noise and Overhauser field fluctuations alone. Our results inform recent strategies for the utilization of partial sweet spots in the operation and longdistance coupling of tripledot qubits.
Filip K. Malinowski, Frederico Martins, Peter D. Nissen, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. B 96, 045443 (2017) [ 1704.01298v1 ] DOI: 10.1103/PhysRevB.96.045443

Anharmonicity of a superconducting qubit with a fewmode Josephson junction 
Abstract
 Coherent operation of gatevoltagecontrolled hybrid transmon qubits (gatemons) based on semiconductor nanowires was recently demonstrated. Here we experimentally investigate the anharmonicity in epitaxial InAsAl Josephson junctions, a key parameter for their use as a qubit. Anharmonicity is found to be reduced by roughly a factor of two compared to conventional metallic junctions, and dependent on gate voltage. Experimental results are consistent with a theoretical model, indicating that Josephson coupling is mediated by a small number of highly transmitting modes in the semiconductor junction.
A. Kringhøj, L. Casparis, M. Hell, T. W. Larsen, F. Kuemmeth, M. Leijnse, K. Flensberg, P. Krogstrup, J. Nygård, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. B 97, 060508 (2018) [ 1703.05643v1 ] DOI: 10.1103/PhysRevB.97.060508

Notch filtering the nuclear environment of a spin qubit 
Abstract
 Electron spins in gatedefined quantum dots provide a promising platform for quantum computation. In particular, spinbased quantum computing in gallium arsenide takes advantage of the high quality of semiconducting materials, reliability in fabricating arrays of quantum dots, and accurate qubit operations. However, the effective magnetic noise arising from the hyperfine interaction with uncontrolled nuclear spins in the host lattice constitutes a major source of decoherence. Low frequency nuclear noise, responsible for fast (10 ns) inhomogeneous dephasing, can be removed by echo techniques. High frequency nuclear noise, recently studied via echo revivals, occurs in narrow frequency bands related to differences in Larmor precession of the three isotopes $\mathbf{^{69}Ga}$, $\mathbf{^{71}Ga}$, and $\mathbf{^{75}As}$. Here we show that both low and high frequency nuclear noise can be filtered by appropriate dynamical decoupling sequences, resulting in a substantial enhancement of spin qubit coherence times. Using nuclear notch filtering, we demonstrate a spin coherence time ($\mathbf{T_{2}}$) of 0.87 ms, five orders of magnitude longer than typical exchange gate times, and exceeding the longest coherence times reported to date in Si/SiGe gatedefined quantum dots.
F. K. Malinowski, F. Martins, P. D. Nissen, E. Barnes, Ł. Cywiński, M. S. Rudner, S. Fallahi, G. C. Gardner, M. J. Manfra, C. M. Marcus, F. Kuemmeth Journal reference: Nat. Nanotechnol. 12, 1620 (2017) [ 1601.06677v3 ] DOI: 10.1038/nnano.2016.170

Current–phase relations of fewmode InAs nanowire Josephson junctions 
Abstract
 Gatetunable semiconductor nanowires with superconducting leads have great potential for quantum computation and as model systems for mesoscopic Josephson junctions. The supercurrent, $I$, versus the phase, $\phi$, across the junction is called the currentphase relation (CPR). It can reveal not only the amplitude of the critical current, but also the number of modes and their transmission. We measured the CPR of many individual InAs nanowire Josephson junctions, one junction at a time. Both the amplitude and shape of the CPR varied between junctions, with small critical currents and skewed CPRs indicating fewmode junctions with high transmissions. In a gatetunable junction, we found that the CPR varied with gate voltage: Near the onset of supercurrent, we observed behavior consistent with resonant tunneling through a single, highly transmitting mode. The gate dependence is consistent with modeled subband structure that includes an effective tunneling barrier due to an abrupt change in the Fermi level at the boundary of the gatetuned region. These measurements of skewed, tunable, fewmode CPRs are promising both for applications that require anharmonic junctions and for Majorana readout proposals.
Eric M. Spanton, Mingtang Deng, Saulius Vaitiekėnas, Peter Krogstrup, Jesper Nygård, Charles M. Marcus, Kathryn A. Moler Journal reference: Nature Physics (2017) [ 1701.01188v1 ] DOI: 10.1038/nphys4224

Majorana bound state in a coupled quantumdot hybridnanowire system 
Abstract
 Hybrid nanowires combining semiconductor and superconductor materials appear well suited for the creation, detection, and control of Majorana bound states (MBSs). We demonstrate the emergence of MBSs from coalescing Andreev bound states (ABSs) in a hybrid InAs nanowire with epitaxial Al, using a quantum dot at the end of the nanowire as a spectrometer. Electrostatic gating tuned the nanowire density to a regime of one or a few ABSs. In an applied axial magnetic field, a topological phase emerges in which ABSs move to zero energy and remain there, forming MBSs. We observed hybridization of the MBS with the enddot bound state, which is in agreement with a numerical model. The ABS/MBS spectra provide parameters that are useful for understanding topological superconductivity in this system.
M. T. Deng, S. Vaitiekenas, E. B. Hansen, J. Danon, M. Leijnse, K. Flensberg, J. Nygård, P. Krogstrup, C. M. Marcus Journal reference: Science 354, 15571562 (2016) [ 1612.07989v2 ] DOI: 10.1126/science.aaf3961

Engineering hybrid epitaxial InAsSb/Al nanowires for stronger topological protection 
Abstract
 2016

Transport Signatures of Quasiparticle Poisoning in a Majorana Island 
Abstract
 We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normalmetal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (~ 1 {\mu}s) and sets a bound for a weakly coupled island (> 10 {\mu}s). Fluctuations in the gatevoltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. In energy units, fluctuations are consistent with previous measurements.
S. M. Albrecht, E. B. Hansen, A. P. Higginbotham, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, J. Danon, K. Flensberg, C. M. Marcus Journal reference: Phys. Rev. Lett. 118, 137701 (2017) [ 1612.05748v1 ] DOI: 10.1103/PhysRevLett.118.137701

Proximity Effect Transfer from NbTi into a Semiconductor Heterostructure via Epitaxial Aluminum 
Abstract
 We demonstrate the transfer of the superconducting properties of NbTia largegap highcriticalfield superconductorinto an InAs heterostructure via a thin intermediate layer of epitaxial Al. Two device geometries, a Josephson junction and a gatedefined quantum point contact, are used to characterize interface transparency and the twostep proximity effect. In the Josephson junction, multiple Andreev reflection reveal nearunity transparency, with an induced gap $\Delta^*=0.50~\mathrm{meV}$ and a critical temperature of $7.8~\mathrm{K}$. Tunneling spectroscopy yields a hard induced gap in the InAs adjacent to the superconductor of $\Delta^*=0.43~\mathrm{meV}$ with substructure characteristic of both Al and NbTi.
A. C. C. Drachmann, H. J. Suominen, M. Kjaergaard, B. Shojaei, C. J. Palmstrøm, C. M. Marcus, F. Nichele Journal reference: Nano Lett. 17, 1200 (2017) [ 1611.10166v1 ] DOI: 10.1021/acs.nanolett.6b04964

Quantized conductance doubling and hard gap in a twodimensional semiconductor–superconductor heterostructure 
Abstract
 The prospect of coupling a twodimensional (2D) semiconductor heterostructure to a superconductor opens new research and technology opportunities, including fundamental problems in mesoscopic superconductivity, scalable superconducting electronics, and new topological states of matter. For instance, one route toward realizing topological matter is by coupling a 2D electron gas (2DEG) with strong spinorbit interaction to an swave superconductor. Previous efforts along these lines have been hindered by interface disorder and unstable gating. Here, we report measurements on a gateable InGaAs/InAs 2DEG with patterned epitaxial Al, yielding multilayer devices with atomically pristine interfaces between semiconductor and superconductor. Using surface gates to form a quantum point contact (QPC), we find a hard superconducting gap in the tunneling regime, overcoming the softgap problem in 2D superconductorsemiconductor hybrid systems. With the QPC in the open regime, we observe a first conductance plateau at 4e^2/h, as expected theoretically for a normalQPCsuperconductor structure. The realization of a hardgap semiconductorsuperconductor system that is amenable to topdown processing provides a means of fabricating scalable multicomponent hybrid systems for applications in lowdissipation electronics and topological quantum information.
M. Kjaergaard, F. Nichele, H. J. Suominen, M. P. Nowak, M. Wimmer, A. R. Akhmerov, J. A. Folk, K. Flensberg, J. Shabani, C. J. Palmstrom, C. M. Marcus Journal reference: Nat. Commun. 7, 12841 (2016) [ 1603.01852v2 ] DOI: 10.1038/ncomms12841

InAs Nanowire with Epitaxial Aluminum as a SingleElectron Transistor with Fixed Tunnel Barriers 
Abstract
 We report on fabrication of singleelectron transistors using InAs nanowires with epitaxial aluminium with fixed tunnel barriers made of aluminium oxide. The devices exhibit a hard superconducting gap induced by the proximized aluminium cover shell and they behave as metallic singleelectron transistors. In contrast to the typical few channel contacts in semiconducting devices, our approach forms opaque multichannel contacts to a semiconducting wire and thus provides a complementary way to study them. In addition, we confirm that unwanted extra quantum dots can appear at the surface of the nanowire. Their presence is prevented in our devices, and also by inserting a protective layer of GaAs between the InAs and Al, the latter being suitable for standard measurement methods.
M. Taupin, E. Mannila, P. Krogstrup, V. F. Maisi, H. Nguyen, S. M. Albrecht, J. Nygard, C. M. Marcus, J. P. Pekola Journal reference: Phys. Rev. Applied 6, 054017 (2016) [ 1601.01149v4 ] DOI: 10.1103/PhysRevApplied.6.054017

Giant spinorbit splitting in inverted InAs/GaSb double quantum wells 
Abstract
 Transport measurements in inverted InAs/GaSb quantum wells reveal a giant spinorbit splitting of the energy bands close to the hybridization gap. The splitting results from the interplay of electronhole mixing and spinorbit coupling, and can exceed the hybridization gap. We experimentally investigate the band splitting as a function of top gate voltage for both electronlike and holelike states. Unlike conventional, noninverted twodimensional electron gases, the Fermi energy in InAs/GaSb can cross a single spinresolved band, resulting in full spinorbit polarization. In the fully polarized regime we observe exotic transport phenomena such as quantum Hall plateaus evolving in $e^2/h$ steps and a nontrivial Berry phase.
Fabrizio Nichele, Morten Kjaergaard, Henri J. Suominen, Rafal Skolasinski, Michael Wimmer, BinhMinh Nguyen, Andrey A. Kiselev, Wei Yi, Marko Sokolich, Michael J. Manfra, Fanming Qu, Arjan J. A. Beukman, Leo P. Kouwenhoven, Charles M. Marcus Journal reference: Phys. Rev. Lett. 118, 016801 (2017) [ 1605.01241v2 ] DOI: 10.1103/PhysRevLett.118.016801

Anomalous Fraunhofer interference in epitaxial superconductorsemiconductor Josephson junctions 
Abstract
 We investigate patterns of critical current as a function of perpendicular and inplane magnetic fields in superconductorsemiconductorsuperconductor (SNS) junctions based on InAs/InGaAs heterostructures with an epitaxial Al layer. This material system is of interest due to its exceptionally good superconductorsemiconductor coupling, as well as large spinorbit interaction and gfactor in the semiconductor. Thin epitaxial Al allows the application of large inplane field without destroying superconductivity. For fields perpendicular to the junction, flux focusing results in aperiodic node spacings in the pattern of critical currents known as Fraunhofer patterns by analogy to the related interference effect in optics. Adding an inplane field yields two further anomalies in the pattern. First, higher order nodes are systematically strengthened, indicating current flow along the edges of the device, as a result of confinement of Andreev states driven by an induced flux dipole; second, asymmetries in the interference appear that depend on the field direction and magnitude. A model is presented, showing good agreement with experiment, elucidating the roles of flux focusing, Zeeman and spinorbit coupling, and disorder in producing these effects.
H. J. Suominen, J. Danon, M. Kjaergaard, K. Flensberg, J. Shabani, C. J. Palmstrøm, F. Nichele, C. M. Marcus Journal reference: Phys. Rev. B 95, 035307 (2017) [ 1611.00190v1 ] DOI: 10.1103/PhysRevB.95.035307

Limits to mobility in InAs quantum wells with nearly latticematched barriers 
Abstract
 The growth and the density dependence of the low temperature mobility of a series of twodimensional electron systems confined to unintentionally doped, low extended defect density InAs quantum wells with Al$_{1x}$Ga$_{x}$Sb barriers are reported. The electron mobility limiting scattering mechanisms were determined by utilizing dualgated devices to study the dependence of mobility on carrier density and electric field independently. Analysis of the possible scattering mechanisms indicate the mobility was limited primarily by rough interfaces in narrow quantum wells and a combination of alloy disorder and interface roughness in wide wells at high carrier density within the first occupied electronic subband. At low carrier density the functional dependence of the mobility on carrier density provided evidence of coulombic scattering from charged defects. A gatetuned electron mobility exceeding 750,000 cm$^{2}$/Vs was achieved at a sample temperature of 2 K.
B. Shojaei, A. C. C. Drachmann, M. Pendharkar, D. J. Pennachio, M. P. Echlin, P. G. Callahan, S. Kraemer, T. M. Pollock, C. M. Marcus, C. J. Palmstrøm Journal reference: Phys. Rev. B 94, 245306 (2016) [ 1610.03785v2 ] DOI: 10.1103/PhysRevB.94.245306

Quantized conductance and large gfactor anisotropy in InSb quantum
point contacts 
Abstract
 Due to a strong spinorbit interaction and a large Land\'e gfactor, InSb plays an important role in research on Majorana fermions. To further explore novel properties of Majorana fermions, hybrid devices based on quantum wells are conceived as an alternative approach to nanowires. In this work, we report a pronounced conductance quantization of quantum point contact devices in InSb/InAlSb quantum wells. Using a rotating magnetic field, we observe a large inplane (g1=26) and outofplane (g1=52) gfactor anisotropy. Additionally, we investigate crossings of subbands with opposite spins and extract the electron effective mass from magnetic depopulation of onedimensional subbands.
Fanming Qu, Jasper van Veen, Folkert K. de Vries, Arjan J. A. Beukman, Michael Wimmer, Wei Yi, Andrey A. Kiselev, BinhMinh Nguyen, Marko Sokolich, Michael J. Manfra, Fabrizio Nichele, Charles M. Marcus, Leo P. Kouwenhoven Journal reference: Nano Lett., 2016, 16, 7509 [ 1608.05478v1 ] DOI: 10.1021/acs.nanolett.6b03297

Edge transport in the trivial phase of InAs/GaSb 
Abstract
 We present transport and scanning SQUID measurements on InAs/GaSb double quantum wells, a system predicted to be a twodimensional topological insulator. Top and back gates allow independent control of density and band offset, allowing tuning from the trivial to the topological regime. In the trivial regime, bulk conductivity is quenched but transport persists along the edges, superficially resembling the predicted helical edgechannels in the topological regime. We characterize edge conduction in the trivial regime in a wide variety of sample geometries and measurement configurations, as a function of temperature, magnetic field, and edge length. Despite similarities to studies claiming measurements of helical edge channels, our characterization points to a nontopological origin for these observations.
Fabrizio Nichele, Henri J. Suominen, Morten Kjaergaard, Charles M. Marcus, Ebrahim Sajadi, Joshua A. Folk, Fanming Qu, Arjan J. A. Beukman, Folkert K. de Vries, Jasper van Veen, Stevan NadjPerge, Leo P. Kouwenhoven, BinhMinh Nguyen, Andrey A. Kiselev, Wei Yi, Marko Sokolich, Michael J. Manfra, Eric M. Spanton, Kathryn A. Moler Journal reference: New J. Phys. 18, 083005 (2016) [ 1511.01728v4 ] DOI: 10.1088/13672630/18/8/083005

Transparent SemiconductorSuperconductor Interface and Induced Gap in an Epitaxial Heterostructure Josephson Junction 
Abstract
 Measurement of multiple Andreev reflection (MAR) in a Josephson junction made from an InAs heterostructure with epitaxial aluminum is used to quantify the highly transparent semiconductorsuperconductor interface, indicating nearunity transmission. The observed temperature dependence of MAR does not follow a conventional BCS form, but instead agrees with a model in which the density of states in the quantum well acquires an effective induced gap, in our case 180 {\mu}eV, close to that of the epitaxial superconductor. Carrier density dependence of MAR is investigated using a depletion gate, revealing the subband structure of the semiconductor quantum well, consistent with magnetotransport experiment of the bare InAs performed on the same wafer.
M. Kjaergaard, H. J. Suominen, M. P. Nowak, A. R. Akhmerov, J. Shabani, C. J. Palmstrøm, F. Nichele, C. M. Marcus Journal reference: Phys. Rev. Applied 7, 034029 (2017) [ 1607.04164v2 ] DOI: 10.1103/PhysRevApplied.7.034029

Decoupling edge versus bulk conductance in the trivial regime of an
InAs/GaSb double quantum well using Corbino ring geometry 
Abstract
 A Corbino ring geometry is utilized to analyze edge and bulk conductance of InAs/GaSb quantum well structures. We show that edge conductance exists in the trivial regime of this theoreticallypredicted topological system with a temperature insensitive linear resistivity per unit length in the range of 2 kOhm/um. A resistor network model of the device is developed to decouple the edge conductance from the bulk conductance, providing a quantitative technique to further investigate the nature of this trivial edge conductance, conclusively identified here as being of ntype.
BinhMinh Nguyen, Andrey A. Kiselev, Ramsey Noah, Wei Yi, Fanming Qu, Arjan J. A. Beukman, Folkert K. de Vries, Jasper van Veen, Stevan NadjPerge, Leo P. Kouwenhoven, Morten Kjaergaard, Henri J. Suominen, Fabrizio Nichele, Charles M. Marcus, Michael J. Manfra, Marko Sokolich Journal reference: Phys. Rev. Lett. 117, 077701 (2016) [ 1605.04818v1 ] DOI: 10.1103/PhysRevLett.117.077701

Normal, superconducting and topological regimes of hybrid double quantum dots 
Abstract
 Epitaxial semiconductorsuperconductor hybrid materials are an excellent basis for studying mesoscopic and topological superconductivity, as the semiconductor inherits a hard superconducting gap while retaining tunable carrier density. Here, we investigate doublequantumdot devices made from InAs nanowires with a patterned epitaxial Al twofacet shell that proximitizes two gatedefined segments along the nanowire. We follow the evolution of mesoscopic superconductivity and charging energy in this system as a function of magnetic field and voltagetuned barriers. Interdot coupling is varied from strong to weak using side gates, and the ground state is varied between normal, superconducting, and topological regimes by applying a magnetic field. We identify the topological transition by tracking the spacing between successive cotunneling peaks as a function of axial magnetic field and show that the individual dots host weakly hybridized Majorana modes.
D. Sherman, J. S. Yodh, S. M. Albrecht, J. Nygård, P. Krogstrup, C. M. Marcus Journal reference: Nature Nanotechnology 12, 212 (2017) [ 1605.01865v1 ] DOI: 10.1038/nnano.2016.227

Milestones Toward MajoranaBased Quantum Computing 
Abstract
 We introduce a scheme for preparation, manipulation, and readout of Majorana zero modes in semiconducting wires with mesoscopic superconducting islands. Our approach synthesizes recent advances in materials growth with tools commonly used in quantumdot experiments, including gatecontrol of tunnel barriers and Coulomb effects, charge sensing, and charge pumping. We outline a sequence of milestones interpolating between zeromode detection and quantum computing that includes (1) detection of fusion rules for nonAbelian anyons using either proximal charge sensors or pumped current; (2) validation of a prototype topological qubit; and (3) demonstration of nonAbelian statistics by braiding in a branched geometry. The first two milestones require only a single wire with two islands, and additionally enable sensitive measurements of the system's excitation gap, quasiparticle poisoning rates, residual Majorana zeromode splittings, and topologicalqubit coherence times. These prebraiding experiments can be adapted to other manipulation and readout schemes as well.
David Aasen, Michael Hell, Ryan V. Mishmash, Andrew Higginbotham, Jeroen Danon, Martin Leijnse, Thomas S. Jespersen, Joshua A. Folk, Charles M. Marcus, Karsten Flensberg, Jason Alicea Journal reference: Phys. Rev. X 6, 031016 (2016) [ 1511.05153v2 ] DOI: 10.1103/PhysRevX.6.031016

Filter function formalism beyond pure dephasing and nonMarkovian noise in singlettriplet qubits 
Abstract
 The filter function formalism quantitatively describes the dephasing of a qubit by a bath that causes Gaussian fluctuations in the qubit energies with an arbitrary noise power spectrum. Here, we extend this formalism to account for more general types of noise that couple to the qubit through terms that do not commute with the qubit's bare Hamiltonian. Our approach applies to any power spectrum that generates slow noise fluctuations in the qubit's evolution. We demonstrate our formalism in the case of singlettriplet qubits subject to both quasistatic nuclear noise and $1/\omega^\alpha$ charge noise and find good agreement with recent experimental findings. This comparison shows the efficacy of our approach in describing real systems and additionally highlights the challenges with distinguishing different types of noise in free induction decay experiments.
Edwin Barnes, Mark S. Rudner, Frederico Martins, Filip K. Malinowski, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. B 93, 121407 (2016) [pdf] DOI: 10.1103/PhysRevB.93.121407

Exponential protection of zero modes in Majorana islands 
Abstract
 Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of faulttolerant quantum computers [1]. They are expected to exhibit nonAbelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, and the pinning is predicted to be exponential as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in proximitized nanowires and atomic chains, with small modesplitting potentially explained by hybridization of Majoranas. Here, we use Coulombblockade spectroscopy in an InAs nanowire segment with epitaxial aluminum, which forms a proximityinduced superconducting Coulomb island (a Majorana island) that is isolated from normalmetal leads by tunnel barriers, to measure the splitting of nearzeroenergy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometers, subgap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half micrometer of increased wire length. For devices longer than about one micrometer, transport in strong magnetic fields occurs through a zeroenergy state that is energetically isolated from a continuum, yielding uniformly spaced Coulombblockade conductance peaks, consistent with teleportation via Majorana modes. Our results help explain the trivialtotopological transition in finite systems and to quantify the scaling of topological protection with endmode separation.
S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, C. M. Marcus Journal reference: Nature 531, 206 (2016) [pdf] DOI: 10.1038/nature17162

Noise Suppression Using Symmetric Exchange Gates in Spin Qubits 
Abstract
 We demonstrate a substantial improvement in the spinexchange gate using symmetric control instead of conventional detuning in GaAs spin qubits, up to a factorofsix increase in the quality factor of the gate. For symmetric operation, nanosecond voltage pulses are applied to the barrier that controls the interdot potential between quantum dots, modulating the exchange interaction while maintaining symmetry between the dots. Excellent agreement is found with a model that separately includes electrical and nuclear noise sources for both detuning and symmetric gating schemes. Unlike exchange control via detuning, the decoherence of symmetric exchange rotations is dominated by rotationaxis fluctuations due to nuclear field noise rather than direct exchange noise.
Frederico Martins, Filip K. Malinowski, Peter D. Nissen, Edwin Barnes, Saeed Fallahi, Geoffrey C. Gardner, Michael J. Manfra, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Phys. Rev. Lett. 116, 116801 (2016) [pdf] DOI: 10.1103/PhysRevLett.116.116801

Transport Signatures of Quasiparticle Poisoning in a Majorana Island 
Abstract
 2015

Gatemon Benchmarking and TwoQubit Operations 
Abstract
 Recent experiments have demonstrated superconducting transmon qubits with semiconductor nanowire Josephson junctions. These hybrid gatemon qubits utilize field effect tunability characteristic for semiconductors to allow complete qubit control using gate voltages, potentially a technological advantage over conventional fluxcontrolled transmons. Here, we present experiments with a twoqubit gatemon circuit. We characterize qubit coherence and stability and use randomized benchmarking to demonstrate singlequbit gate errors below 0.7% for all gates, including voltagecontrolled $Z$ rotations. We show coherent capacitive coupling between two gatemons and coherent swap operations. Finally, we perform a twoqubit controlledphase gate with an estimated fidelity of 91%, demonstrating the potential of gatemon qubits for building scalable quantum processors.
L. Casparis, T. W. Larsen, M. S. Olsen, F. Kuemmeth, P. Krogstrup, J. Nygård, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. Lett. 116, 150505 (2016) [ 1512.09195v1 ] DOI: 10.1103/PhysRevLett.116.150505

Twodimensional epitaxial superconductorsemiconductor heterostructures: A platform for topological superconducting networks 
Abstract
 Progress in the emergent field of topological superconductivity relies on synthesis of new material combinations, combining superconductivity, low density, and spinorbit coupling (SOC). For example, theory [14] indicates that the interface between a onedimensional (1D) semiconductor (Sm) with strong SOC and a superconductor (S) hosts Majorana modes with nontrivial topological properties [58]. Recently, epitaxial growth of Al on InAs nanowires was shown to yield a high quality SSm system with uniformly transparent interfaces [9] and a hard induced gap, indicted by strongly suppressed sub gap tunneling conductance [10]. Here we report the realization of a twodimensional (2D) InAs/InGaAs heterostructure with epitaxial Al, yielding a planar SSm system with structural and transport characteristics as good as the epitaxial wires. The realization of 2D epitaxial SSm systems represent a significant advance over wires, allowing extended networks via topdown processing. Among numerous potential applications, this new material system can serve as a platform for complex networks of topological superconductors with gatecontrolled Majorana zero modes [14]. We demonstrate gateable Josephson junctions and a highly transparent 2D SSm interface based on the product of excess current and normal state resistance.
J. Shabani, M. Kjaergaard, H. J. Suominen, Younghyun Kim, F. Nichele, K. Pakrouski, T. Stankevic, R. M. Lutchyn, P. Krogstrup, R. Feidenhans'l, S. Kraemer, C. Nayak, M. Troyer, C. M. Marcus, C. J. Palmstrøm Journal reference: Phys. Rev. B 93, 155402 (2016) [pdf] DOI: 10.1103/PhysRevB.93.155402

SemiconductorNanowireBased Superconducting Qubit 
Abstract
 We introduce a hybrid qubit based on a semiconductor nanowire with an epitaxially grown superconductor layer. Josephson energy of the transmonlike device ("gatemon") is controlled by an electrostatic gate that depletes carriers in a semiconducting weak link region. Strong coupling to an onchip microwave cavity and coherent qubit control via gate voltage pulses is demonstrated, yielding reasonably long relaxation times (0.8 {\mu}s) and dephasing times (1 {\mu}s), exceeding gate operation times by two orders of magnitude, in these firstgeneration devices. Because qubit control relies on voltages rather than fluxes, dissipation in resistive control lines is reduced, screening reduces crosstalk, and the absence of flux control allows operation in a magnetic field, relevant for topological quantum information.
T. W. Larsen, K. D. Petersson, F. Kuemmeth, T. S. Jespersen, P. Krogstrup, J. Nygard, C. M. Marcus Journal reference: Phys. Rev. Lett. 115, 127001 (2015) [pdf] DOI: 10.1103/PhysRevLett.115.127001

Gatetunable high mobility remotedoped InSb/In_{1x}Al_{x}Sb quantum
well heterostructures 
Abstract
 Gatetunable highmobility InSb/In_{1x}Al_{x}Sb quantum wells (QWs) grown on GaAs substrates are reported. The QW twodimensional electron gas (2DEG) channel mobility in excess of 200,000 cm^{2}/Vs is measured at T=1.8K. In asymmetrically remotedoped samples with an HfO_{2} gate dielectric formed by atomic layer deposition, parallel conduction is eliminated and complete 2DEG channel depletion is reached with minimal hysteresis in gate bias response of the 2DEG electron density. The integer quantum Hall effect with Landau level filling factor down to 1 is observed. A hightransparency nonalloyed Ohmic contact to the 2DEG with contact resistance below 1{\Omega} \cdot mm is achieved at 1.8K.
Wei Yi, Andrey A. Kiselev, Jacob Thorp, Ramsey Noah, BinhMinh Nguyen, Steven Bui, Rajesh D. Rajavel, Tahir Hussain, Mark Gyure, Philip Kratz, Qi Qian, Michael J. Manfra, Vlad S. Pribiag, Leo P. Kouwenhoven, Charles M. Marcus, Marko Sokolich Journal reference: Appl. Phys. Lett. 106, 142103 (2015) [pdf] DOI: 10.1063/1.4917027

Electric and Magnetic Tuning Between the Trivial and Topological Phases in InAs/GaSb Double Quantum Wells 
Abstract
 Among the theoretically predicted twodimensional topological insulators, InAs/GaSb double quantum wells (DQWs) have a unique doublelayered structure with electron and hole gases separated in two layers, which enables tuning of the band alignment via electric and magnetic fields. However, the rich trivialtopological phase diagram has yet to be experimentally explored. We present an in situ and continuous tuning between the trivial and topological insulating phases in InAs/GaSb DQWs through electrical dualgating. Furthermore, we show that an inplane magnetic field shifts the electron and hole bands relatively to each other in momentum space, functioning as a powerful tool to discriminate between the topologically distinct states.
Fanming Qu, Arjan J. A. Beukman, Stevan NadjPerge, Michael Wimmer, BinhMinh Nguyen, Wei Yi, Jacob Thorp, Marko Sokolich, Andrey A. Kiselev, Michael J. Manfra, Charles M. Marcus, Leo P. Kouwenhoven Journal reference: Phys. Rev. Lett. 115, 036803 (2015) [pdf] DOI: 10.1103/PhysRevLett.115.036803

Hard gap in epitaxial semiconductor–superconductor nanowires 
Abstract
 Many present and future applications of superconductivity would benefit from electrostatic control of carrier density and tunneling rates, the hallmark of semiconductor devices. One particularly exciting application is the realization of topological superconductivity as a basis for quantum information processing. Proposals in this direction based on proximity effect in semiconductor nanowires are appealing because the key ingredients are currently in hand. However, previous instances of proximitized semiconductors show significant tunneling conductance below the superconducting gap, suggesting a continuum of subgap statesa situation that nullifies topological protection. Here, we report a hard superconducting gap induced by proximity effect in a semiconductor, using epitaxial AlInAs superconductorsemiconductor nanowires. The hard gap, along with favorable material properties and gatetunability, makes this new hybrid system attractive for a number of applications, as well as fundamental studies of mesoscopic superconductivity.
W. Chang, S. M. Albrecht, T. S. Jespersen, F. Kuemmeth, P. Krogstrup, J. Nygård, C. M. Marcus Journal reference: Nature Nanotechnology 10, 232 (2015) [pdf] DOI: 10.1038/nnano.2014.306

Parity lifetime of bound states in a proximitized semiconductor nanowire 
Abstract
 Quasiparticle excitations can compromise the performance of superconducting devices, causing high frequency dissipation, decoherence in Josephson qubits, and braiding errors in proposed Majoranabased topological quantum computers. Quasiparticle dynamics have been studied in detail in metallic superconductors but remain relatively unexplored in semiconductorsuperconductor structures, which are now being intensely pursued in the context of topological superconductivity. To this end, we introduce a new physical system comprised of a gateconfined semiconductor nanowire with an epitaxially grown superconductor layer, yielding an isolated, proximitized nanowire segment. We identify Andreevlike bound states in the semiconductor via bias spectroscopy, determine the characteristic temperatures and magnetic fields for quasiparticle excitations, and extract a parity lifetime (poisoning time) of the bound state in the semiconductor exceeding 10 ms.
A. P. Higginbotham, S. M. Albrecht, G. Kirsanskas, W. Chang, F. Kuemmeth, P. Krogstrup, T. S. Jespersen, J. Nygard, K. Flensberg, C. M. Marcus Journal reference: Nature Physics 11, 1017 (2015) [pdf] DOI: 10.1038/nphys3461

Gatemon Benchmarking and TwoQubit Operations 
Abstract
 2014

Epitaxy of semiconductor–superconductor nanowires 
Abstract
 Controlling the properties of semiconductor/metal interfaces is a powerful method for designing functionality and improving the performance of electrical devices. Recently semiconductor/superconductor hybrids have appeared as an important example where the atomic scale uniformity of the interface plays a key role for the quality of the induced superconducting gap. Here we present epitaxial growth of semiconductormetal coreshell nanowires by molecular beam epitaxy, a method that provides a conceptually new route to controlled electrical contacting of nanostructures and for designing devices for specialized applications such as topological and gatecontrolled superconducting electronics. Our materials of choice, InAs/Al, are grown with epitaxially matched single plane interfaces, and alternative semiconductor/metal combinations allowing epitaxial interface matching in nanowires are discussed. We formulate the grain growth kinetics of the metal phase in general terms of continuum parameters and bicrystal symmetries. The method realizes the ultimate limit of uniform interfaces and appears to solve the softgap problem in superconducting hybrid structures.
P. Krogstrup, N. L. B. Ziino, W. Chang, S. M. Albrecht, M. H. Madsen, E. Johnson, J. Nygård, C. M. Marcus, T. S. Jespersen Journal reference: Nature Materials 14, 400 (2015) [pdf] DOI: 10.1038/nmat4176

Hole Spin Coherence in a Ge/Si Heterostructure Nanowire 
Abstract
 Relaxation and dephasing of hole spins are measured in a gatedefined Ge/Si nanowire double quantum dot using a fast pulsedgate method and dispersive readout. An inhomogeneous dephasing time $T_2^* \sim 0.18~\mathrm{\mu s}$ exceeds corresponding measurements in IIIV semiconductors by more than an order of magnitude, as expected for predominately nuclearspinfree materials. Dephasing is observed to be exponential in time, indicating the presence of a broadband noise source, rather than Gaussian, previously seen in systems with nuclearspindominated dephasing.
A. P. Higginbotham, T. W. Larsen, J. Yao, H. Yan, C. M. Lieber, C. M. Marcus, F. Kuemmeth Journal reference: Nano Letters 14, 3582 (2014) [pdf] DOI: 10.1021/nl501242b

Antilocalization of Coulomb Blockade in a Ge/Si Nanowire 
Abstract
 The distribution of Coulomb blockade peak heights as a function of magnetic field is investigated experimentally in a GeSi nanowire quantum dot. Strong spinorbit coupling in this holegas system leads to antilocalization of Coulomb blockade peaks, consistent with theory. In particular, the peak height distribution has its maximum away from zero at zero magnetic field, with an average that decreases with increasing field. Magnetoconductance in the openwire regime places a bound on the spinorbit length ($l_{so}$ < 20 nm), consistent with values extracted in the Coulomb blockade regime ($l_{so}$ < 25 nm).
A. P. Higginbotham, F. Kuemmeth, T. W. Larsen, M. Fitzpatrick, J. Yao, H. Yan, C. M. Lieber, C. M. Marcus Journal reference: Phys. Rev. Lett. 112, 216806 (2014) [pdf] DOI: 10.1103/PhysRevLett.112.216806

Epitaxy of semiconductor–superconductor nanowires 
Abstract
 2013

Epitaxial aluminum contacts to InAs nanowires 
Abstract
 We report a method for making epitaxial superconducting contacts to semiconducting nanowires. The temperature and gate characteristics demonstrate barrierfree electrical contact, and the properties in the superconducting state are investigated at low temperature. Halfcovering aluminum contacts are realized without the need of lithography and we demonstrate how to controllably insert highband gap layers in the interface region. These developments are relevant to hybrid superconductornanowire devices that support Majorana zero energy states.
N. L. B. Ziino, P. Krogstrup, M. H. Madsen, E. Johnson, J. B. Wagner, C. M. Marcus, J. Nygård, T. S. Jespersen 1309.4569v1 [pdf]

Singlelayer graphene on silicon nitride micromembrane resonators 
Abstract
 Due to their exceptional mechanical and optical properties, dielectric silicon nitride (SiN) micromembrane resonators have become the centerpiece of many optomechanical experiments. Efficient capacitive coupling of the membrane to an electrical system would facilitate exciting hybrid optoelectromechanical devices. However, capacitive coupling of such dielectric membranes is rather weak. Here we add a single layer of graphene on SiN micromembranes and compare electromechanical coupling and mechanical properties to bare dielectric membranes and to membranes metallized with an aluminium layer. The electrostatic coupling of graphene coated membranes is found to be equal to a perfectly conductive membrane. Our results show that a single layer of graphene substantially enhances the electromechanical capacitive coupling without significantly adding mass, decreasing the superior mechanical quality factor or affecting the optical properties of SiN micromembrane resonators.
Silvan Schmid, Tolga Bagci, Emil Zeuthen, Jacob M. Taylor, Patrick K. Herring, Maja C. Cassidy, Charles M. Marcus, Luis Guillermo Villanueva, Bartolo Amato, Anja Boisen, Yong Cheol Shin, Jing Kong, Anders S. Sørensen, Koji Usami, Eugene S. Polzik Journal reference: J. Appl. Phys. 115, 054513 (2014) [pdf] DOI: 10.1063/1.4862296

Coherent Operations and Screening in Multielectron Spin Qubits 
Abstract
 The performance of multielectron spin qubits is examined by comparing exchange oscillations in coupled singleelectron and multielectron quantum dots in the same device. Fast (> 1 GHz) exchange oscillations with a quality factor Q > 15 are found for the multielectron case, compared to Q ~ 2 for the singleelectron case, the latter consistent with previous experiments. A model of dephasing that includes voltage and hyperfine noise is developed that is in good agreement with both single and multielectron data, though in both cases additional exchangeindependent dephasing is needed to obtain quantitative agreement across a broad parameter range.
A. P. Higginbotham, F. Kuemmeth, M. P. Hanson, A. C. Gossard, C. M. Marcus Journal reference: Phys. Rev. Lett. 112, 026801 (2014) [pdf] DOI: 10.1103/PhysRevLett.112.026801

In vivo magnetic resonance imaging of hyperpolarized silicon particles 
Abstract
 Siliconbased micro and nanoparticles have gained popularity in a wide range of biomedical applications due to their biocompatibility and biodegradability invivo, as well as a flexible surface chemistry, which allows drug loading, functionalization and targeting. Here we report direct invivo imaging of hyperpolarized 29Si nuclei in silicon microparticles by MRI. Natural physical properties of silicon provide surface electronic states for dynamic nuclear polarization (DNP), extremely long depolarization times, insensitivity to the invivo environment or particle tumbling, and surfaces favorable for functionalization. Potential applications to gastrointestinal, intravascular, and tumor perfusion imaging at subpicomolar concentrations are presented. These results demonstrate a new backgroundfree imaging modality applicable to a range of inexpensive, readily available, and biocompatible Si particles.
M. C. Cassidy, H. R. Chan, B. D. Ross, P. K. Bhattacharya, C. M. Marcus Journal reference: Nature Nanotechnology 8, 363 (2013) [pdf] DOI: 10.1038/nnano.2013.65

Synthesis of LongT1 Silicon Nanoparticles for Hyperpolarized 29Si
Magnetic Resonance Imaging 
Abstract
 We describe the synthesis, materials characterization and dynamic nuclear polarization (DNP) of amorphous and crystalline silicon nanoparticles for use as hyperpolarized magnetic resonance imaging (MRI) agents. The particles were synthesized by means of a metathesis reaction between sodium silicide (Na4Si4) and silicon tetrachloride (SiCl4) and were surface functionalized with a variety of passivating ligands. The synthesis scheme results in particles of diameter ~10 nm with long sizeadjusted 29Si spin lattice relaxation (T1) times (> 600 s), which are retained after hyperpolarization by low temperature DNP.
Tonya M. Atkins, Maja C. Cassidy, Menyoung Lee, Shreyashi Ganguly, Charles M. Marcus, Susan M. Kauzlarich Journal reference: ACS Nano 7, 1609 (2013) [pdf] DOI: 10.1021/nn305462y

QuantumDotBased Resonant Exchange Qubit 
Abstract
 We introduce a solidstate qubit in which exchange interactions among confined electrons provide both the static longitudinal field and the oscillatory transverse field, allowing rapid and full qubit control via rf gatevoltage pulses. We demonstrate twoaxis control at a detuning sweetspot, where leakage due to hyperfine coupling is suppressed by the large exchange gap. A {\pi}/2gate time of 2.5 ns and a coherence time of 19 {\mu}s, using multipulse echo, are also demonstrated. Model calculations that include effects of hyperfine noise are in excellent quantitative agreement with experiment.
J. Medford, J. Beil, J. M. Taylor, E. I. Rashba, H. Lu, A. C. Gossard, C. M. Marcus Journal reference: Phys. Rev. Lett. 111, 050501 (2013) [pdf] DOI: 10.1103/PhysRevLett.111.050501

Superconductornanowire devices from tunneling to the multichannel regime: Zerobias oscillations and magnetoconductance crossover 
Abstract
 We present transport measurements in superconductornanowire devices with a gated constriction forming a quantum point contact. Zerobias features in tunneling spectroscopy appear at finite magnetic fields, and oscillate in amplitude and split away from zero bias as a function of magnetic field and gate voltage. A crossover in magnetoconductance is observed: Magnetic fields above ~ 0.5 T enhance conductance in the lowconductance (tunneling) regime but suppress conductance in the highconductance (multichannel) regime. We consider these results in the context of Majorana zero modes as well as alternatives, including Kondo effect and analogs of 0.7 structure in a disordered nanowire.
H. O. H. Churchill, V. Fatemi, K. GroveRasmussen, M. T. Deng, P. Caroff, H. Q. Xu, C. M. Marcus Journal reference: Phys. Rev. B 87, 241401(R) (2013) [pdf] DOI: 10.1103/PhysRevB.87.241401

Selfconsistent measurement and state tomography of an exchangeonly spin qubit 
Abstract
 We report initialization, complete electrical control, and singleshot readout of an exchangeonly spin qubit. Full control via the exchange interaction is fast, yielding a demonstrated 75 qubit rotations in under 2 ns. Measurement and state tomography are performed using a maximumlikelihood estimator method, allowing decoherence, leakage out of the qubit state space, and measurement fidelity to be quantified. The methods developed here are generally applicable to systems with state leakage, noisy measurements, and nonorthogonal control axes.
J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, C. M. Marcus Journal reference: Nature Nanotechnology 8, 654 (2013) [pdf] DOI: 10.1038/nnano.2013.168

Epitaxial aluminum contacts to InAs nanowires 
Abstract
 2012

Tunneling Spectroscopy of Quasiparticle Bound States in a Spinful Josephson Junction 
Abstract
 The spectrum of a segment of InAs nanowire, confined between two superconducting leads, was measured as function of gate voltage and superconducting phase difference using a third normalmetal tunnel probe. Subgap resonances for odd electron occupancyinterpreted as bound states involving a confined electron and a quasiparticle from the superconducting leads, reminiscent of YuShibaRusinov statesevolve into Kondorelated resonances at higher magnetic fields. An additional zero bias peak of unknown origin is observed to coexist with the quasiparticle bound states.
W. Chang, V. E. Manucharyan, T. S. Jespersen, J. Nygard, C. M. Marcus Journal reference: Phys. Rev. Lett. 110, 217005 (2013) [pdf] DOI: 10.1103/PhysRevLett.110.217005

gTensor Control in Bent Carbon Nanotube Quantum Dots 
Abstract
 We demonstrate gate control of the electronic gtensor in single and double quantum dots formed along a bend in a carbon nanotube. From the dependence of the singledot excitation spectrum on magnetic field magnitude and direction, we extract spinorbit coupling, valley coupling, spin and orbital magnetic moments. Gate control of the gtensor is measured using the splitting of the Kondo peak in conductance as a sensitive probe of Zeeman energy. In the double quantum dot regime, the magnetic field dependence of the position of cotunneling lines in the two dimensional charge stability diagram is used to infer the positions of the two dots along the nanotube.
R. A. Lai, H. O. H. Churchill, C. M. Marcus Journal reference: Physical Review B 89, 121303(R) 2014 [pdf] DOI: 10.1103/PhysRevB.89.121303

Radicalfree dynamic nuclear polarization using electronic defects in silicon 
Abstract
 Direct dynamic nuclear polarization of 1H nuclei in frozen water and waterethanol mixtures is demonstrated using silicon nanoparticles as the polarizing agent. Electron spins at danglingbond sites near the silicon surface are identified as the source of the nuclear hyperpolarization. This novel polarization method open new avenues for the fabrication of surface engineered nanostructures to create high nuclearspin polarized solutions without introducing contaminating radicals, and for the study of molecules adsorbed onto surfaces.
M. C. Cassidy, C. Ramanathan, D. G. Cory, J. W. Ager, C. M. Marcus Journal reference: Phys. Rev. B 87, 161306(R) (2013) [pdf] DOI: 10.1103/PhysRevB.87.161306

Scaling of Dynamical Decoupling for Spin Qubits 
Abstract
 We investigate scaling of coherence time, T2, with the number of {\pi}pulses, n_{\pi}, in a singlet triplet spin qubit using CarrPurcellMeiboomGill (CPMG) and concatenated dynamical decoupling (CDD) pulse sequences. For an even numbers of CPMG pulses, we find a power law, T2 = (n_{\pi})^({\gamma}_e), with {\gamma}_e = 0.72\pm0.01, essentially independent of the envelope function used to extract T2. From this surprisingly robust value, a powerlaw model of the noise spectrum of the environment, S({\omega}) ~ {\omega}^({\beta}), yields {\beta} = {\gamma}_e/(1  {\gamma}_e) = 2.6 \pm 0.1. Model values for T2(n_{\pi}) using {\beta} = 2.6 for CPMG with both even and odd n_{\pi} up to 32 and CDD orders 3 through 6 compare very well with experiment.
J. Medford, L. Cywinski, C. Barthel, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 108, 086802 (2012) [pdf] DOI: 10.1103/PhysRevLett.108.086802

Coulomb Oscillations in Antidots in the Integer and Fractional Quantum Hall Regimes 
Abstract
 We report measurements of resistance oscillations in micronscale antidots in both the integer and fractional quantum Hall regimes. In the integer regime, we conclude that oscillations are of the Coulomb type from the scaling of magnetic field period with the number of edges bound to the antidot. Based on both gatevoltage and field periods, we find at filling factor {\nu} = 2 a tunneling charge of e and two charged edges. Generalizing this picture to the fractional regime, we find (again, based on field and gatevoltage periods) at {\nu} = 2/3 a tunneling charge of (2/3)e and a single charged edge.
A. Kou, C. M. Marcus, L. N. Pfeiffer, K. W. West Journal reference: PRL 108, 256803 (2012) [pdf] DOI: 10.1103/PhysRevLett.108.256803

Tunneling Spectroscopy of Quasiparticle Bound States in a Spinful Josephson Junction 
Abstract
 2011

FabryPerot Interferometry with Fractional Charges 
Abstract
 Resistance oscillations in electronic FabryPerot interferometers near fractional quantum Hall (FQH) filling factors 1/3, 2/3, 4/3 and 5/3 in the constrictions are compared to corresponding oscillations near integer quantum Hall (IQH) filling factors in the constrictions, appearing in the same devices and at the same gate voltages. Twodimensional plots of resistance versus gate voltage and magnetic field indicate that all oscillations are Coulomb dominated. Applying a Coulomb charging model yields an effective tunneling charge e* \approx e/3 for all FQH constrictions and e* \approx e for IQH constrictions. Surprisingly, we find a common characteristic temperature for FQH oscillations and a different common characteristic temperature for IQH oscillations.
D. T. McClure, W. Chang, C. M. Marcus, L. N. Pfeiffer, K. W. West Journal reference: PRL 108, 256804 (2012) [pdf] DOI: 10.1103/PhysRevLett.108.256804

Magnetic field dependence of Pauli spin blockade: A window into the sources of spin relaxation in silicon quantum dots 
Abstract
 We investigate spin relaxation in a silicon double quantum dot via leakage current through Pauli blockade as a function of interdot detuning and magnetic field. A dip in leakage current as a function of magnetic field on a \sim 40 mT field scale is attributed to spinorbit mediated spin relaxation. On a larger (\sim 400 mT) field scale, a peak in leakage current is seen in some, but not all, Pauliblocked transitions, and is attributed to spinflip cotunneling. Both dip and peak structure show good agreement between theory and experiment.
G. Yamahata, T. Kodera, H. O. H. Churchill, K. Uchida, C. M. Marcus, S. Oda Journal reference: Phys Rev. B 86, 115322 (2012) [pdf] DOI: 10.1103/PhysRevB.86.115322

Hole spin relaxation in Ge–Si core–shell nanowire qubits 
Abstract
 Controlling decoherence is the most challenging task in realizing quantum information hardware. Single electron spins in gallium arsenide are a leading candidate among solid state implementations, however strong coupling to nuclear spins in the substrate hinders this approach. To realize spin qubits in a nuclearspinfree system, intensive studies based on groupIV semiconductor are being pursued. In this case, the challenge is primarily control of materials and interfaces, and device nanofabrication. We report important steps toward implementing spin qubits in a predominantly nuclearspinfree system by demonstrating state preparation, pulsed gate control, and chargesensing spin readout of confined hole spins in a onedimensional Ge/Si nanowire. With fast gating, we measure T1 spin relaxation times in coupled quantum dots approaching 1 ms, increasing with lower magnetic field, consistent with a spinorbit mechanism that is usually masked by hyperfine contributions.
Yongjie Hu, Ferdinand Kuemmeth, Charles M. Lieber, Charles M. Marcus Journal reference: Nature Nanotechnology 7, 4750 (2012) [pdf] DOI: 10.1038/nnano.2011.234

Hot Carrier Transport and Photocurrent Response in Graphene 
Abstract
 Strong electronelectron interactions in graphene are expected to result in multipleexcitation generation by the absorption of a single photon. We show that the impact of carrier multiplication on photocurrent response is enhanced by very inefficient electron cooling, resulting in an abundance of hot carriers. The hotcarriermediated energy transport dominates the photoresponse and manifests itself in quantum efficiencies that can exceed unity, as well as in a characteristic dependence of the photocurrent on gate voltages. The pattern of multiple photocurrent sign changes as a function of gate voltage provides a fingerprint of hotcarrierdominated transport and carrier multiplication.
Justin C. W. Song, Mark S. Rudner, Charles M. Marcus, Leonid S. Levitov Journal reference: Nano Lett., 11 (11), pp 46884692 (2011) [pdf] DOI: 10.1021/nl202318u

GateActivated Photoresponse in a Graphene p–n Junction 
Abstract
 We study photodetection in graphene near a local electrostatic gate, which enables active control of the potential landscape and carrier polarity. We find that a strong photoresponse only appears when and where a pn junction is formed, allowing onoff control of photodetection. Photocurrents generated near pn junctions do not require biasing and can be realized using submicron gates. Locally modulated photoresponse enables a new range of applications for graphenebased photodetectors including, for example, pixilated infrared imaging with control of response on subwavelength dimensions.
M. C. Lemme, F. H. L. Koppens, A. L. Falk, M. S. Rudner, H. Park, L. S. Levitov, C. M. Marcus Journal reference: Nano Letters 11, 4134 (2011) [pdf] DOI: 10.1021/nl2019068

Relaxation and readout visibility of a singlettriplet qubit in an Overhauser field gradient 
Abstract
 Using singleshot charge detection in a GaAs double quantum dot, we investigate spin relaxation time T_1 and readout visibility of a twoelectron singlettriplet qubit following singleelectron dynamic nuclear polarization (DNP). For magnetic fields up to 2 T, the DNP cycle is in all cases found to increase Overhauser field gradients, which in turn decrease T_1 and consequently reduce readout visibility. This effect was previously attributed to a suppression of singlettriplet dephasing under a similar DNP cycle. A model describing relaxation after singlettriplet mixing agrees well with experiment. Effects of pulse bandwidth on visibility are also investigated.
C. Barthel, J. Medford, H. Bluhm, A. Yacoby, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. B 85, 035306 (2012) [pdf] DOI: 10.1103/PhysRevB.85.035306

Laser cooling and optical detection of excitations in a LC electrical
circuit 
Abstract
 We explore a method for laser cooling and optical detection of excitations in a LC electrical circuit. Our approach uses a nanomechanical oscillator as a transducer between optical and electronic excitations. An experimentally feasible system with the oscillator capacitively coupled to the LC and at the same time interacting with light via an optomechanical force is shown to provide strong electromechanical coupling. Conditions for improved sensitivity and quantum limited readout of electrical signals with such an "optical loud speaker" are outlined.
J. M. Taylor, A. S. Sørensen, C. M. Marcus, E. S. Polzik Journal reference: Phys. Rev. Lett. 107, 273601 (2011) [pdf] DOI: 10.1103/PhysRevLett.107.273601

Direct graphene growth on insulator 
Abstract
 Fabrication of graphene devices is often hindered by incompatibility between the silicon technology and the methods of graphene growth. Exfoliation from graphite yields excellent films but is good mainly for research. Graphene grown on metal has a technological potential but requires mechanical transfer. Growth by SiC decomposition requires a temperature budget exceeding the technological limits. These issues could be circumvented by growing graphene directly on insulator, implying Van der Waals growth. During growth, the insulator acts as a support defining the growth plane. In the device, it insulates graphene from the Si substrate. We demonstrate planar growth of graphene on mica surface. This was achieved by molecular beam deposition above 600{\deg}C. High resolution Raman scans illustrate the effect of growth parameters and substrate topography on the film perfection. Ab initio calculations suggest a growth model. Data analysis highlights the competition between nucleation at surface steps and flat surface. As a proof of concept, we show the evidence of electric field effect in a transistor with a directly grown channel.
Gunther Lippert, Jarek Dabrowski, Max C. Lemme, Charles M. Marcus, Olaf Seifarth, Grzegorz Lupina Journal reference: Phys. Status Solidi B, 248, No. 11, 26192622 (2011) [pdf] DOI: 10.1002/pssb.201100052

Decay of nuclear hyperpolarization in silicon microparticles 
Abstract
 We investigate the lowfield relaxation of nuclear hyperpolarization in undoped and highly doped silicon microparticles at room temperature following removal from high field. For nominally undoped particles, two relaxation time scales are identified for ambient fields above 0.2 mT. The slower, T_1s, is roughly independent of ambient field; the faster, T_1f, decreases with increasing ambient field. A model in which nuclear spin relaxation occurs at the particle surface via a twoelectron mechanism is shown to be in good agreement with the experimental data, particularly the fieldindependence of T_1s. For borondoped particles, a single relaxation time scale is observed. This suggests that for doped particles, mobile carriers and bulk ionized acceptor sites, rather than paramagnetic surface states, are the dominant relaxation mechanisms. Relaxation times for the undoped particles are not affected by tumbling in a liquid solution.
M. Lee, M. C. Cassidy, C. Ramanathan, C. M. Marcus Journal reference: Phys. Rev. B 84 035304 (2011) [pdf] DOI: 10.1103/PhysRevB.84.035304

ChargeState Conditional Operation of a Spin Qubit 
Abstract
 We report coherent operation of a singlettriplet qubit controlled by the arrangement of two electrons in an adjacent double quantum dot. The system we investigate consists of two pairs of capacitively coupled double quantum dots fabricated by electrostatic gates on the surface of a GaAs heterostructure. We extract the strength of the capacitive coupling between qubit and double quantum dot and show that the present geometry allows fast conditional gate operation, opening pathways to multiqubit control and implementation of quantum algorithms with spin qubits.
I. van Weperen, B. D. Armstrong, E. A. Laird, J. Medford, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 107 030506 (2011) [pdf] DOI: 10.1103/PhysRevLett.107.030506

FabryPerot Interferometry with Fractional Charges 
Abstract
 2010

Gatecontrolled guiding of electrons in graphene 
Abstract
 Ballistic semiconductor structures have allowed the realization of opticslike phenomena in electronics, including magnetic focusing and lensing. An extension that appears unique to graphene is to use both n and p carrier types to create electronic analogs of optical devices having both positive and negative indices of refraction. Here, we use gatecontrolled density with both p and n carrier types to demonstrate the analog of the fiberoptic guiding in graphene. Two basic effects are investigated: (1) bipolar pn junction guiding, based on the principle of angleselective transmission though the graphene pn interface, and (2) unipolar fiberoptic guiding, using total internal reflection controlled by carrier density. Modulation of guiding efficiency through gating is demonstrated and compared to numerical simulations, which indicates that interface roughness limits guiding performance, with fewnanometer effective roughness extracted. The development of pn and fiberoptic guiding in graphene may lead to electrically reconfigurable wiring in highmobility devices.
J. R. Williams, Tony Low, M. S. Lundstrom, C. M. Marcus Journal reference: Nature Nanotechnology 6, 222225 (2011) [pdf] DOI: 10.1038/nnano.2011.3

Interlaced Dynamical Decoupling and Coherent Operation of a SingletTriplet Qubit 
Abstract
 We experimentally demonstrate coherence recovery of singlettriplet superpositions by interlacing qubit rotations between CarrPurcell (CP) echo sequences. We then compare performance of Hahn, CP, concatenated dynamical decoupling (CDD) and Uhrig dynamical decoupling (UDD) for singlet recovery. In the present case, where gate noise and drift combined with spatially varying hyperfine coupling contribute significantly to dephasing, and pulses have limited bandwidth, CP and CDD yield comparable results, with T2 ~ 80 microseconds.
C. Barthel, J. Medford, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 105 266808 (2010) [pdf] DOI: 10.1103/PhysRevLett.105.266808

Snake States in Graphene pn Junctions 
Abstract
 We investigate transport in locallygated graphene devices, where carriers are injected and collected along, rather than across, the gate edge. Tuning densities into the pn regime significantly reduces resistance along the pn interface, while resistance across the interface increases. This provides an experimental signature of snake states, which zigzag along the pn interface and remain stable as applied perpendicular magnetic field approaches zero. Snake states appear as a peak in transverse resistance measured along the pn interface. The generic role of snake states disordered graphene is also discussed.
J. R. Williams, C. M. Marcus Journal reference: Phys. Rev. Lett. 107, 046602 (2011) [pdf] DOI: 10.1103/PhysRevLett.107.046602

GateDefined Graphene Quantum Point Contact in the Quantum Hall Regime 
Abstract
 We investigate transport in a gatedefined graphene quantum point contact in the quantum Hall regime. Edge states confined to the interface of p and n regions in the graphene sheet are controllably brought together from opposite sides of the sample and allowed to mix in this splitgate geometry. Among the expected quantum Hall features, an unexpected additional plateau at 0.5 h/e^2 is observed. We propose that chaotic mixing of edge channels gives rise to the extra plateau.
S. Nakaharai, J. R. Williams, C. M. Marcus Journal reference: Phys. Rev. Lett. 107 036602 (2011) [pdf] DOI: 10.1103/PhysRevLett.107.036602

Dynamic Nuclear Polarization in Double Quantum Dots 
Abstract
 We theoretically investigate the controlled dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. Three regimes of longterm dynamics are identified, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of socalled "dark states," and the elimination of the difference field. We show that in the case of unequal dots, build up of difference fields generally accompanies the nuclear polarization process, whereas for nearly identical dots, build up of difference fields competes with polarization saturation in dark states. The elimination of the difference field does not, in general, correspond to a stable steady state of the polarization process.
M. Gullans, J. J. Krich, J. M. Taylor, H. Bluhm, B. I. Halperin, C. M. Marcus, M. Stopa, A. Yacoby, M. D. Lukin Journal reference: Phys. Rev. Lett. 104, 226807 (2010) [pdf] DOI: 10.1103/PhysRevLett.104.226807

Bends in nanotubes allow electric spin control and coupling 
Abstract
 We investigate combined effects of spinorbit coupling and magnetic field in carbon nanotubes containing one or more bends along their length. We show how bends can be used to provide electrical control of confined spins, while spins confined in straight segments remain insensitive to electric fields. Device geometries that allow general rotation of single spins are presented and analyzed. In addition, capacitive coupling along bends provides coherent spinspin interaction, including between otherwise disconnected nanotubes, completing a universal set of one and twoqubit gates.
K. Flensberg, C. M. Marcus Journal reference: Phys. Rev. B 81, 195418 (2010) [pdf] DOI: 10.1103/PhysRevB.81.195418

Coherent spin manipulation in an exchangeonly qubit 
Abstract
 Initialization, manipulation, and measurement of a threespin qubit are demonstrated using a fewelectron triple quantum dot, where all operations can be driven by tuning the nearestneighbor exchange interaction. Multiplexed reflectometry, applied to two nearby charge sensors, allows for qubit readout. Decoherence is found to be consistent with predictions based on gate voltage noise with a uniform power spectrum. The theory of the exchangeonly qubit is developed and it is shown that initialization of only two spins suffices for operation. Requirements for full multiqubit control using only exchange and electrostatic interactions are outlined.
E. A. Laird, J. M. Taylor, D. P. DiVincenzo, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. B 82 075403 (2010) [pdf] DOI: 10.1103/PhysRevB.82.075403

Dynamic Nuclear Polarization in the Fractional Quantum Hall Regime 
Abstract
 We investigate dynamic nuclear polarization in quantum point contacts (QPCs) in the integer and fractional quantum Hall regimes. Following the application of a dc bias, fractional plateaus in the QPC shift symmetrically about half filling of the lowest Landau level, \nu=1/2, suggesting an interpretation in terms of composite fermions. Polarizing and detecting at different filling factors indicates that Zeeman energy is reduced by the induced nuclear polarization. Mapping effects from integer to fractional regimes extends the composite fermion picture to include hyperfine coupling.
A. Kou, D. T. McClure, C. M. Marcus, L. N. Pfeiffer, K. W. West Journal reference: Phys.Rev.Lett.105:056804,2010 [pdf] DOI: 10.1103/PhysRevLett.105.056804

Fast sensing of doubledot charge arrangement and spin state with a radiofrequency sensor quantum dot 
Abstract
 Singleshot measurement of the charge arrangement and spin state of a double quantum dot are reported, with measurement times down to ~ 100 ns. Sensing uses radiofrequency reflectometry of a proximal quantum dot in the Coulomb blockade regime. The sensor quantum dot is up to 30 times more sensitive than a comparable quantum point contact sensor, and yields three times greater signal to noise in rf singleshot measurements. Numerical modeling is qualitatively consistent with experiment and shows that the improved sensitivity of the sensor quantum dot results from reduced screening and lifetime broadening.
C. Barthel, M. Kjaergaard, J. Medford, M. Stopa, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Physical Review B 81 161308(R), 2010 [pdf] DOI: 10.1103/PhysRevB.81.161308

Gatecontrolled guiding of electrons in graphene 
Abstract
 2009

Carbon nanotubes for coherent spintronics 
Abstract
 Carbon nanotubes bridge the molecular and crystalline quantum worlds, and their extraordinary electronic, mechanical and optical properties have attracted enormous attention from a broad scientific community. We review the basic principles of fabricating spinelectronic devices based on individual, electricallygated carbon nanotubes, and present experimental efforts to understand their electronic and nuclear spin degrees of freedom, which in the future may enable quantum applications.
F. Kuemmeth, H. O. H. Churchill, P. K. Herring, C. M. Marcus Journal reference: Materials Today 13, 18 (2010) [pdf] DOI: 10.1016/S13697021(10)700304

Rapid SingleShot Measurement of a SingletTriplet Qubit 
Abstract
 We report repeated singleshot measurements of the twoelectron spin state in a GaAs double quantum dot. The readout scheme allows measurement with fidelity above 90% with a 7 microsecond cycle time. Hyperfineinduced precession between singlet and triplet states of the twoelectron system are directly observed, as nuclear Overhauser fields are quasistatic on the time scale of the measurement cycle. Repeated measurements on millisecond to second time scales reveal evolution of the nuclear environment.
C. Barthel, D. J. Reilly, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 103 160503 (2009) [pdf] DOI: 10.1103/PhysRevLett.103.160503

Precision cutting and patterning of graphene with helium ions 
Abstract
 We report nanoscale patterning of graphene using a helium ion microscope configured for lithography. Helium ion lithography is a directwrite lithography process, comparable to conventional focused ion beam patterning, with no resist or other material contacting the sample surface. In the present application, graphene samples on Si/SiO2 substrates are cut using helium ions, with computer controlled alignment, patterning, and exposure. Once suitable beam doses are determined, sharp edge profiles and clean etching are obtained, with little evident damage or doping to the sample. This technique provides fast lithography compatible with graphene, with ~15 nm feature sizes.
D. C. Bell, M. C. Lemme, L. A. Stern, J. R. Williams, C. M. Marcus Journal reference: Nanotechnology 20, 455301 (2009) [pdf] DOI: 10.1088/09574484/20/45/455301

Etching of Graphene Devices with a Helium Ion Beam 
Abstract
 We report on the etching of graphene devices with a helium ion beam, including in situ electrical measurement during lithography. The etching process can be used to nanostructure and electrically isolate different regions in a graphene device, as demonstrated by etching a channel in a suspended graphene device with etched gaps down to about 10 nm. Graphene devices on silicon dioxide (SiO2) substrates etch with lower He ion doses and are found to have a residual conductivity after etching, which we attribute to contamination by hydrocarbons.
M. C. Lemme, D. C. Bell, J. R. Williams, L. A. Stern, B. W. H. Baugher, P. JarilloHerrero, C. M. Marcus Journal reference: ACSNano 3, 2674 (2009) [pdf] DOI: 10.1021/nn900744z

EdgeState Velocity and Coherence in a Quantum Hall FabryPérot Interferometer 
Abstract
 We investigate nonlinear transport in electronic FabryPerot interferometers in the integer quantum Hall regime. For interferometers sufficiently large that Coulomb blockade effects are absent, a checkerboardlike pattern of conductance oscillations as a function of dc bias and perpendicular magnetic field is observed. Edgestate velocities extracted from the checkerboard data are compared to model calculations and found to be consistent with a crossover from skipping orbits at low fields to E x B drift at high fields. Suppression of visibility as a function of bias and magnetic field is accounted for by including energy and fielddependent dephasing of edge electrons.
D. T. McClure, Yiming Zhang, B. Rosenow, E. M. LevensonFalk, C. M. Marcus, L. N. Pfeiffer, K. W. West Journal reference: Phys. Rev. Lett. 103 206806 (2009). [pdf] DOI: 10.1103/PhysRevLett.103.206806

Silicon Nanoparticles as Hyperpolarized Magnetic Resonance Imaging Agents 
Abstract
 Silicon nanoparticles are experimentally investigated as a potential hyperpolarized, targetable MRI imaging agent. Nuclear T_1 times at room temperature for a variety of Si nanoparticles are found to be remarkably long (10^2 to 10^4 s)  roughly consistent with predictions of a coreshell diffusion model  allowing them to be transported, administered and imaged on practical time scales without significant loss of polarization. We also report surface functionalization of Si nanoparticles, comparable to approaches used in other biologically targeted nanoparticle systems.
J. W. Aptekar, M. C. Cassidy, A. C. Johnson, R. A. Barton, M. Y. Lee, A. C. Ogier, C. Vo, M. N. Anahtar, Y. Ren, S. N. Bhatia, C. Ramanathan, D. G. Cory, A. L. Hill, R. W. Mair, M. S. Rosen, R. L. Walsworth, C. M. Marcus Journal reference: ACS Nano 3, 4003 (2009) [pdf] DOI: 10.1021/nn900996p

Carbon nanotubes for coherent spintronics 
Abstract
 2008

Distinct signatures for Coulomb blockade and AharonovBohm interference in electronic FabryPerot interferometers 
Abstract
 Two distinct types of magnetoresistance oscillations are observed in two electronic FabryPerot interferometers of different sizes in the integer quantum Hall regime. Measuring these oscillations as a function of magnetic field and gate voltages, we observe three signatures that distinguish the two types. The oscillations observed in a 2.0 square micron device are understood to arise from the Coulomb blockade mechanism, and those observed in an 18 square micron device from the AharonovBohm mechanism. This work clarifies, provides ways to distinguish, and demonstrates control over, these distinct physical origins of resistance oscillations seen in electronic FabryPerot interferometers.
Yiming Zhang, D. T. McClure, E. M. LevensonFalk, C. M. Marcus, L. N. Pfeiffer, K. W. West Journal reference: Phys. Rev. B (RC) 79, 241304 (2009) [pdf] DOI: 10.1103/PhysRevB.79.241304

A new mechanism of electric dipole spin resonance: hyperfine coupling in quantum dots 
Abstract
 A recently discovered mechanism of electric dipole spin resonance, mediated by the hyperfine interaction, is investigated experimentally and theoretically. The effect is studied using a spinselective transition in a GaAs double quantum dot. The resonant frequency is sensitive to the instantaneous hyperfine effective field, revealing a nuclear polarization created by driving the resonance. A device incorporating a micromagnet exhibits a magnetic field difference between dots, allowing electrons in either dot to be addressed selectively. An unexplained additional signal at half the resonant frequency is presented.
E. A. Laird, C. Barthel, E. I. Rashba, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Semicond. Sci. Technol. 24 (2009) 064004. [pdf] DOI: 10.1088/02681242/24/6/064004

Electron–nuclear interaction in 13C nanotube double quantum dots 
Abstract
 For coherent electron spins, hyperfine coupling to nuclei in the host material can either be a dominant source of unwanted spin decoherence or, if controlled effectively, a resource allowing storage and retrieval of quantum information. To investigate the effect of a controllable nuclear environment on the evolution of confined electron spins, we have fabricated and measured gatedefined double quantum dots with integrated charge sensors made from singlewalled carbon nanotubes with a variable concentration of 13C (nuclear spin I=1/2) among the majority zeronuclearspin 12C atoms. Spinsensitive transport in doubledot devices grown using methane with the natural abundance (~ 1%) of 13C is compared with similar devices grown using an enhanced (~99%) concentration of 13C. We observe strong isotope effects in spinblockaded transport, and from the dependence on external magnetic field, estimate the hyperfine coupling in 13C nanotubes to be on the order of 100 microeV, two orders of magnitude larger than anticipated theoretically. 13Cenhanced nanotubes are an interesting new system for spinbased quantum information processing and memory, with nuclei that are strongly coupled to gatecontrolled electrons, differ from nuclei in the substrate, are naturally confined to one dimension, lack quadrupolar coupling, and have a readily controllable concentration from less than one to 10^5 per electron.
H. O. H. Churchill, A. J. Bestwick, J. W. Harlow, F. Kuemmeth, D. Marcos, C. H. Stwertka, S. K. Watson, C. M. Marcus Journal reference: Nature Physics 5, 321 (2009) [pdf] DOI: 10.1038/nphys1247

Relaxation and Dephasing in a Twoelectron 13C Nanotube Double Quantum
Dot 
Abstract
 We use charge sensing of Pauli blockade (including spin and isospin) in a twoelectron 13C nanotube double quantum dot to measure relaxation and dephasing times. The relaxation time, T1, first decreases with parallel magnetic field then goes through a minimum in a field of 1.4 T. We attribute both results to the spinorbitmodified electronic spectrum of carbon nanotubes, which suppresses hyperfine mediated relaxation and enhances relaxation due to soft phonons. The inhomogeneous dephasing time, T2*, is consistent with previous data on hyperfine coupling strength in 13C nanotubes.
H. O. H. Churchill, F. Kuemmeth, J. W. Harlow, A. J. Bestwick, E. I. Rashba, K. Flensberg, C. H. Stwertka, T. Taychatanapat, S. K. Watson, C. M. Marcus Journal reference: Phys. Rev. Lett. 102, 166802 (2009). [pdf] DOI: 10.1103/PhysRevLett.102.166802

Quantum Hall conductance of twoterminal graphene devices 
Abstract
 Measurement and theory of the twoterminal conductance of monolayer and bilayer graphene in the quantum Hall regime are compared. We examine features of conductance as a function of gate voltage that allow monolayer, bilayer, and gapped samples to be distinguished, including Nshaped distortions of quantum Hall plateaus and conductance peaks and dips at the charge neutrality point. Generally good agreement is found between measurement and theory. Possible origins of discrepancies are discussed.
J. R. Williams, D. A. Abanin, L. DiCarlo, L. S. Levitov, C. M. Marcus Journal reference: Phys. Rev. B 80, 045408 (2009) [pdf] DOI: 10.1103/PhysRevB.80.045408

Measurement of Temporal Correlations of the Overhauser Field in a Double Quantum Dot 
Abstract
 In quantum dots made from materials with nonzero nuclear spins, hyperfine coupling creates a fluctuating effective Zeeman field (Overhauser field) felt by electrons, which can be a dominant source of spin qubit decoherence. We characterize the spectral properties of the fluctuating Overhauser field in a GaAs double quantum dot by measuring correlation functions and power spectra of the rate of singlettriplet mixing of two separated electrons. Away from zero field, spectral weight is concentrated below 10 Hz, with 1/f^2 dependence on frequency, f. This is consistent with a model of nuclear spin diffusion, and indicates that decoherence can be largely suppressed by echo techniques.
D. J. Reilly, J. M. Taylor, E. A. Laird, J. R. Petta, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 101, 236803 (2008). [pdf] DOI: 10.1103/PhysRevLett.101.236803

Suppressing Spin Qubit Dephasing by Nuclear State Preparation 
Abstract
 Coherent spin states in semiconductor quantum dots offer promise as electrically controllable quantum bits (qubits) with scalable fabrication. For fewelectron quantum dots made from gallium arsenide (GaAs), fluctuating nuclear spins in the host lattice are the dominant source of spin decoherence. We report a method of preparing the nuclear spin environment that suppresses the relevant component of nuclear spin fluctuations below its equilibrium value by a factor of ~ 70, extending the inhomogeneous dephasing time for the twoelectron spin state beyond 1 microsecond. The nuclear state can be readily prepared by electrical gate manipulation and persists for > 10 seconds.
D. J. Reilly, J. M. Taylor, J. R. Petta, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Science 321, 817 (2008) [pdf] DOI: 10.1126/science.1159221

Quasiparticle Tunneling in the Fractional Quantum Hall State at ν=
5/2 
Abstract
 Theory predicts that quasiparticle tunneling between the counterpropagating edges in a fractional quantum Hall state can be used to measure the effective quasiparticle charge e* and dimensionless interaction parameter g, and thereby characterize the manybody wavefunction describing the state. We report measurements of quasiparticle tunneling in a high mobility GaAs two dimensional electron system in the fractional quantum Hall state at nu=5/2 using a gatedefined constriction to bring the edges close together. We find the dcbias peaks in the tunneling conductance at different temperatures collapse onto a single curve when scaled, in agreement with weak tunneling theory. Various models for the \nu=5/2 state predict different values for g. Among these models, the nonabelian states with e*=1/4 and g=1/2 are most consistent with the data.
Iuliana P. Radu, J. B. Miller, C. M. Marcus, M. A. Kastner, L. N. Pfeiffer, K. W. West Journal reference: Science 320, 899 (2008). [pdf]

Exchange Control of Nuclear Spin Diffusion in a Double Quantum Dot 
Abstract
 Coherent twolevel systems, or qubits, based on electron spins in GaAs quantum dots are strongly coupled to the nuclear spins of the host lattice via the hyperfine interaction. Realizing nuclear spin control would likely improve electron spin coherence and potentially enable the nuclear environment to be harnessed for the longterm storage of quantum information. Toward this goal, we report experimental control of the relaxation of nuclear spin polarization in a gatedefined twoelectron GaAs double quantum dot. A cyclic gatepulse sequence transfers the spin of an electron pair to the host nuclear system, establishing a local nuclear polarization that relaxes on a time scale of seconds. We find nuclear relaxation depends on magnetic field and gatecontrolled twoelectron exchange, consistent with a model of electron mediated nuclear spin diffusion.
D. J. Reilly, J. M. Taylor, J. R. Petta, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Physical Review Letters 104, 236802 (2010) [pdf] DOI: 10.1103/PhysRevLett.104.236802

Shot Noise in Graphene 
Abstract
 We report measurements of current noise in single and multilayer graphene devices. In four singlelayer devices, including a pn junction, the Fano factor remains constant to within +/10% upon varying carrier type and density, and averages between 0.35 and 0.38. The Fano factor in a multilayer device is found to decrease from a maximal value of 0.33 at the chargeneutrality point to 0.25 at high carrier density. These results are compared to theoretical predictions for shot noise in ballistic and disordered graphene.
L. DiCarlo, J. R. Williams, Yiming Zhang, D. T. McClure, C. M. Marcus Journal reference: Phys. Rev. Lett. 100, 156801 (2008). [pdf] DOI: 10.1103/PhysRevLett.100.156801

Distinct signatures for Coulomb blockade and AharonovBohm interference in electronic FabryPerot interferometers 
Abstract
 2007

HyperfineMediated GateDriven Electron Spin Resonance 
Abstract
 An allelectrical spin resonance effect in a GaAs fewelectron double quantum dot is investigated experimentally and theoretically. The magnetic field dependence and absence of associated Rabi oscillations are consistent with a novel hyperfine mechanism. The resonant frequency is sensitive to the instantaneous hyperfine effective field, and the effect can be used to detect and create sizable nuclear polarizations. A device incorporating a micromagnet exhibits a magnetic field difference between dots, allowing electrons in either dot to be addressed selectively.
E. A. Laird, C. Barthel, E. I. Rashba, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 99 246601 (2007) [pdf] DOI: 10.1103/PhysRevLett.99.246601

Dynamic Nuclear Polarization with Single Electron Spins 
Abstract
 We polarize nuclear spins in a GaAs double quantum dot by controlling twoelectron spin states near the anticrossing of the singlet (S) and m_S=+1 triplet (T+) using pulsed gates. An initialized S state is cyclically brought into resonance with the T+ state, where hyperfine fields drive rapid rotations between S and T+, 'flipping' an electron spin and 'flopping' a nuclear spin. The resulting Overhauser field approaches 80 mT, in agreement with a simple rateequation model. A selflimiting pulse sequence is developed that allows the steadystate nuclear polarization to be set using a gate voltage.
J. R. Petta, J. M. Taylor, A. C. Johnson, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 100, 067601 (2008). [pdf] DOI: 10.1103/PhysRevLett.100.067601

Quantum Hall Effect in a Graphene pn Junction 
Abstract
 We report on the fabrication and transport studies of a singlelayer graphene pn junction. Carrier type and density in two adjacent regions are individually controlled by electrostatic gating using a local top gate and a global back gate. A functionalized Al203 oxide that adheres to graphene and does not significantly affect its electronic properties is described. Measurements in the quantum Hall regime reveal new plateaus of twoterminal conductance across the junction at 1 and 3/2 times the quantum of conductance, e2/h, consistent with theory.
J. R. Williams, L. DiCarlo, C. M. Marcus Journal reference: Science 317, 638 (2007) [pdf]

Fast singlecharge sensing with a rf quantum point contact 
Abstract
 We report highbandwidth charge sensing measurements using a GaAs quantum point contact embedded in a radio frequency impedance matching circuit (rfQPC). With the rfQPC biased near pinchoff where it is most sensitive to charge, we demonstrate a conductance sensitivity of 5x10^(6) e^(2)/h Hz^(1/2) with a bandwidth of 8 MHz. Singleshot readout of a proximal fewelectron double quantum dot is investigated in a mode where the rfQPC backaction is rapidly switched.
D. J. Reilly, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Appl. Phys. Lett. 91, 162101 (2007) [pdf] DOI: 10.1063/1.2794995

A Ge/Si heterostructure nanowirebased double quantum dot with integrated charge sensor 
Abstract
 Coupled electron spins in semiconductor double quantum dots hold promise as the basis for solidstate qubits. To date, most experiments have used IIIV materials, in which coherence is limited by hyperfine interactions. Ge/Si heterostructure nanowires seem ideally suited to overcome this limitation: the predominance of spinzero nuclei suppresses the hyperfine interaction and chemical synthesis creates a clean and defectfree system with highly controllable properties. Here we present a top gatedefined double quantum dot based on Ge/Si heterostructure nanowires with fully tunable coupling between the dots and to the leads. We also demonstrate a novel approach to charge sensing in a onedimensional nanostructure by capacitively coupling the double dot to a single dot on an adjacent nanowire. The double quantum dot and integrated charge sensor serve as an essential building block required to form a solidstate spin qubit free of nuclear spin.
Yongjie Hu, Hugh H. O. Churchill, David J. Reilly, Jie Xiang, Charles M. Lieber, Charles M. Marcus Journal reference: Nature Nanotechnology 2, 622 (2007). [pdf] DOI: 10.1038/nnano.2007.302

Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2 
Abstract
 Recent theories suggest that the excitations of certain quantum Hall states may have exotic braiding statistics which could be used to build topological quantum gates. This has prompted an experimental push to study such states using confined geometries where the statistics can be tested. We study the transport properties of quantum point contacts (QPCs) fabricated on a GaAs/AlGaAs two dimensional electron gas that exhibits welldeveloped fractional quantum Hall effect, including at bulk filling fraction 5/2. We find that a plateau at effective QPC filling factor 5/2 is identifiable in point contacts with lithographic widths of 1.2 microns and 0.8 microns, but not 0.5 microns. We study the temperature and dccurrentbias dependence of the 5/2 plateau in the QPC, as well as neighboring fractional and integer plateaus in the QPC while keeping the bulk at filling factor 3. Transport near QPC filling factor 5/2 is consistent with a picture of chiral Luttinger liquid edgestates with interedge tunneling, suggesting that an incompressible state at 5/2 forms in this confined geometry.
J. B. Miller, I. P. Radu, D. M. Zumbuhl, E. M. LevensonFalk, M. A. Kastner, C. M. Marcus, L. N. Pfeiffer, K. W. West Journal reference: Nature Physics 3, 561 (2007). [ condmat/0703161v2 ] DOI: 10.1038/nphys658

Current Noise in Quantum Point Contacts 
Abstract
 We present measurements of current noise in quantum point contacts as a function of sourcedrain bias, gate voltage, and inplane magnetic field. At zero bias, Johnson noise provides a measure of the electron temperature. At finite bias, shot noise at zero field exhibits an asymmetry related to the 0.7 structure in conductance. The asymmetry in noise evolves smoothly into the symmetric signature of spinresolved electron transmission at high field. Comparison to a phenomenological model with densitydependent level splitting yields quantitative agreement. Additionally, a devicespecific contribution to the finitebias noise, particularly visible on conductance plateaus (where shot noise vanishes), agrees quantitatively with a model of biasdependent electron heating.
L. DiCarlo, Yiming Zhang, D. T. McClure, D. J. Reilly, C. M. Marcus, L. N. Pfeiffer, K. W. West, M. P. Hanson, A. C. Gossard 0704.3892v1 [pdf]

Noise Correlations in a CoulombBlockaded Quantum Dot 
Abstract
 We report measurements of current noise auto and crosscorrelation in a tunable quantum dot with two or three leads. As the Coulomb blockade is lifted at finite sourcedrain bias, the autocorrelation evolves from superPoissonian to subPoissonian in the twolead case, and the crosscorrelation evolves from positive to negative in the threelead case, consistent with transport through multiple levels. Crosscorrelations in the threelead dot are found to be proportional to the noise in excess of the Poissonian value in the limit of weak output tunneling.
Y. Zhang, L. DiCarlo, D. T. McClure, M. Yamamoto, S. Tarucha, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 99, 036603 (2007). [ condmat/0703419v1 ] DOI: 10.1103/PhysRevLett.99.036603

Relaxation, dephasing, and quantum control of electron spins in double quantum dots 
Abstract
 Recent experiments have demonstrated quantum manipulation of twoelectron spin states in double quantum dots using electrically controlled exchange interactions. Here, we present a detailed theory for electron spin dynamics in twoelectron double dot systems that was used to guide these experiments and analyze experimental results. The theory treats both charge and spin degrees of freedom on an equal basis. Specifically, we analyze the relaxation and dephasing mechanisms that are relevant to experiments and discuss practical approaches for quantum control of twoelectron system. We show that both charge and spin dephasing play important roles in the dynamics of the twospin system, but neither represents a fundamental limit for electrical control of spin degrees of freedom in semiconductor quantum bits.
J. M. Taylor, J. R. Petta, A. C. Johnson, A. Yacoby, C. M. Marcus, M. D. Lukin Journal reference: Phys. Rev. B 76, 035315 (2007) [ condmat/0602470v2 ] DOI: 10.1103/PhysRevB.76.035315

HyperfineMediated GateDriven Electron Spin Resonance 
Abstract
 2006

Tunable Noise Cross Correlations in a Double Quantum Dot 
Abstract
 We report measurements of the crosscorrelation between current noise fluctuations in two capacitively coupled quantum dots in the Coulomb blockade regime. The sign of the crossspectral density is found to be tunable by gate voltage and sourcedrain bias. Good agreement is found with a model of sequential tunneling through the dots in the presence of interdot capacitive coupling.
D. T. McClure, L. DiCarlo, Y. Zhang, H. A. Engel, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 98, 056801 (2007) [ condmat/0607280v1 ] DOI: 10.1103/PhysRevLett.98.056801

Effect of Exchange Interaction on Spin Dephasing in a Double Quantum Dot 
Abstract
 We measure singlettriplet dephasing in a twoelectron double quantum dot in the presence of an exchange interaction which can be electrically tuned from much smaller to much larger than the hyperfine energy. Saturation of dephasing and damped oscillations of the spin correlator as a function of time are observed when the two interaction strengths are comparable. Both features of the data are compared with predictions from a quasistatic model of the hyperfine field.
E. A. Laird, J. R. Petta, A. C. Johnson, C. M. Marcus, A. Yacoby, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 97, 056801 (2006). [ condmat/0512077v3 ] DOI: 10.1103/PhysRevLett.97.056801

System for measuring auto and cross correlation of current noise at low temperatures 
Abstract
 We describe the construction and operation of a twochannel noise detection system for measuring power and cross spectral densities of current fluctuations near 2 MHz in electronic devices at low temperatures. The system employs cryogenic amplification and fastFouriertransform based spectral measurement. The gain and electron temperature are calibrated using Johnson noise thermometry. Full shot noise of 100 pA can be resolved with an integration time of 10 s. We report a demonstration measurement of biasdependent current noise in a gate defined GaAs/AlGaAs quantum point contact.
L. DiCarlo, Y. Zhang, D. T. McClure, C. M. Marcus, L. N. Pfeiffer, K. W. West Journal reference: Rev. Sci. Instru. 77, 073906 (2006). [ condmat/0604018v2 ] DOI: 10.1063/1.2221541

ShotNoise Signatures of 0.7 Structure and Spin in a Quantum Point Contact 
Abstract
 We report simultaneous measurement of shot noise and dc transport in a quantum point contact as a function of sourcedrain bias, gate voltage, and inplane magnetic field. Shot noise at zero field exhibits an asymmetry related to the 0.7 structure in conductance. The asymmetry in noise evolves smoothly into the symmetric signature of spinresolved electron transmission at high field. Comparison to a phenomenological model with densitydependent level splitting yields good quantitative agreement.
L. DiCarlo, Y. Zhang, D. T. McClure, D. J. Reilly, C. M. Marcus, L. N. Pfeiffer, K. W. West Journal reference: Phys. Rev. Lett. 97, 036810 (2006) [ condmat/0604019v2 ] DOI: 10.1103/PhysRevLett.97.036810

Magnetic Field Control of Exchange and Noise Immunity in Double Quantum
Dots 
Abstract
 We employ density functional calculated eigenstates as a basis for exact diagonalization studies of semiconductor double quantum dots, with two electrons, through the transition from the symmetric bias regime to the regime where both electrons occupy the same dot. We calculate the singlettriplet splitting $J(\epsilon)$ as a function of bias detuning $\epsilon$ and explain its functional shape with a simple, double anticrossing model. A voltage noise suppression "sweet spot," where $dJ(\epsilon)/d\epsilon=0$ with nonzero $J(\epsilon)$, is predicted and shown to be tunable with a magnetic field $B$.
M. Stopa, C. M. Marcus condmat/0604008v1 [pdf]

Nonequilibrium singlet–triplet Kondo effect in carbon nanotubes 
Abstract
 The Kondoeffect is a manybody phenomenon arising due to conduction electrons scattering off a localized spin. Coherent spinflip scattering off such a quantum impurity correlates the conduction electrons and at low temperature this leads to a zerobias conductance anomaly. This has become a common signature in biasspectroscopy of singleelectron transistors, observed in GaAs quantum dots as well as in various singlemolecule transistors. While the zerobias Kondo effect is well established it remains uncertain to what extent Kondo correlations persist in nonequilibrium situations where inelastic processes induce decoherence. Here we report on a pronounced conductance peak observed at finite biasvoltage in a carbon nanotube quantum dot in the spin singlet ground state. We explain this finitebias conductance anomaly by a nonequilibrium Kondoeffect involving excitations into a spin triplet state. Excellent agreement between calculated and measured nonlinear conductance is obtained, thus strongly supporting the correlated nature of this nonequilibrium resonance.
J. Paaske, A. Rosch, P. Woelfle, N. Mason, C. M. Marcus, J. Nygard Journal reference: Nature Physics, vol. 2, p.460  464 (2006) [ condmat/0602581v1 ] DOI: 10.1038/nphys340

Tunable Noise Cross Correlations in a Double Quantum Dot 
Abstract
 2005

Charge sensing in carbon nanotube quantum dots on microsecond timescales 
Abstract
 We report fast, simultaneous charge sensing and transport measurements of gatedefined carbon nanotube quantum dots. Aluminum radio frequency single electron transistors (rfSETs) capacitively coupled to the nanotube dot provide singleelectron charge sensing on microsecond timescales. Simultaneously, rf reflectometry allows fast measurement of transport through the nanotube dot. Charge stability diagrams for the nanotube dot in the Coulomb blockade regime show extended Coulomb diamonds into the highbias regime, as well as evenodd filling effects, revealed in charge sensing data.
M. J. Biercuk, D. J. Reilly, T. M. Buehler, V. C. Chan, J. M. Chow, R. G. Clark, C. M. Marcus DOI: 10.1103/PhysRevB.73.201402 condmat/0510550v1 [pdf]

Charge and spin manipulation in a fewelectron double dot 
Abstract
 We demonstrate high speed manipulation of a fewelectron double quantum dot. In the oneelectron regime, the double dot forms a charge qubit. Microwaves are used drive transitions between the (1,0) and (0,1) charge states of the double dot. A local quantum point contact charge detector measures the photoninduced change in occupancy of the charge states. Charge detection is used to measure T1~16 ns and also provides a lower bound estimate for T2* of 400 ps for the charge qubit. In the twoelectron regime we use pulsedgate techniques to measure the singlettriplet relaxation time for nearlydegenerate spin states. These experiments demonstrate that the hyperfine interaction leads to fast spin relaxation at low magnetic fields. Finally, we discuss how twoelectron spin states can be used to form a logical spin qubit.
J. R. Petta, A. C. Johnson, J. M. Taylor, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Physica E 34, 42 (2006) [ condmat/0510151v1 ] DOI: 10.1016/j.physe.2006.02.033

Asymmetry of Nonlinear Transport and Electron Interactions in Quantum Dots 
Abstract
 The symmetry properties of transport beyond the linear regime in chaotic quantum dots are investigated experimentally. A component of differential conductance that is antisymmetric in both applied sourcedrain bias V and magnetic field B, absent in linear transport, is found to exhibit mesoscopic fluctuations around a zero average. Typical values of this component allow a measurement of the electron interaction strength.
D. M. Zumbuhl, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 96, 206802 (2006) [ condmat/0508766v1 ] DOI: 10.1103/PhysRevLett.96.206802

Triplet–singlet spin relaxation via nuclei in a double quantum dot 
Abstract
 The spin of a confined electron, when oriented originally in some direction, will lose memory of that orientation after some time. Physical mechanisms leading to this relaxation of spin memory typically involve either coupling of the electron spin to its orbital motion or to nuclear spins. Relaxation of confined electron spin has been previously measured only for Zeeman or exchange split spin states, where spinorbit effects dominate relaxation, while spin flips due to nuclei have been observed in optical spectroscopy studies. Using an isolated GaAs double quantum dot defined by electrostatic gates and direct time domain measurements, we investigate in detail spin relaxation for arbitrary splitting of spin states. Results demonstrate that electron spin flips are dominated by nuclear interactions and are slowed by several orders of magnitude when a magnetic field of a few millitesla is applied. These results have significant implications for spinbased information processing.
A. C. Johnson, J. R. Petta, J. M. Taylor, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Nature 435, 925 (2005) [ condmat/0503687v3 ] DOI: 10.1038/nature03815

GateDefined Quantum Dots on Carbon Nanotubes 
Abstract
 We report the realization of nanotubebased quantum dot structures that use local electrostatic gating to produce individually controllable dots in series along a nanotube. Electrostatic topgates produce depletion regions in the underlying tube; a pair of such depletion regions defines a quantum dot. Transparencies of tunnel barriers as well as the electrostatic energies, within single and multiple dots, can be tuned by gate voltages. The approach allows accurate control over multiple devices on a single tube, and serves as a design paradigm for nanotubebased electronics and quantum systems.
M. J. Biercuk, S. Garaj, N. Mason, J. M. Chow, C. M. Marcus Journal reference: Nano Letters 5, 1267 (2005) [ condmat/0502634v2 ] DOI: 10.1021/nl050364v

Conductance fluctuations and partially broken spin symmetries in quantum dots 
Abstract
 Conductance fluctuations in GaAs quantum dots with spinorbit and Zeeman coupling are investigated experimentally and compared to a random matrix theory formulation that defines a number of regimes of spin symmetry depending on experimental parameters. Accounting for orbital coupling of the inplane magnetic field, which can break timereversal symmetry, yields excellent overall agreement between experiment and theory.
D. M. Zumbuhl, J. B. Miller, D. GoldhaberGordon, C. M. Marcus, J. S. Harris, Jr., K. Campman, A. C. Gossard Journal reference: Phys. Rev. B 72, 081305 (2005) [ condmat/0501622v2 ] DOI: 10.1103/PhysRevB.72.081305

Solidstate circuit for spin entanglement generation and purification 
Abstract
 We show how realistic charge manipulation and measurement techniques, combined with the exchange interaction, allow for the robust generation and purification of fourparticle spin entangled states in electrically controlled semiconductor quantum dots. The generated states are immunized to the dominant sources of noise via a dynamical decoherencefree subspace; all additional errors are corrected by a purification protocol. This approach may find application in quantum computation, communication, and metrology.
J. M. Taylor, W. Dür, P. Zoller, A. Yacoby, C. M. Marcus, M. D. Lukin DOI: 10.1103/PhysRevLett.94.236803 condmat/0503255v2 [pdf]

Charge sensing in carbon nanotube quantum dots on microsecond timescales 
Abstract
 2004

Pulsedgate measurements of the singlettriplet relaxation time in a twoelectron double quantum dot 
Abstract
 A pulsedgate technique with charge sensing is used to measure the singlettriplet relaxation time for nearlydegenerate spin states in a twoelectron double quantum dot. Transitions from the (1,1) charge occupancy state to the (0,2) state, measured as a function of pulse cycle duration and magnetic field, allow the (1,1) singlettriplet relaxation time (~70 microseconds) and the (0,2) singlettriplet splitting to be measured. The use of charge sensing rather than current measurement allows long relaxation times to be readily probed.
J. R. Petta, A. C. Johnson, A. Yacoby, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. B (RC) 72, 161301 (2005) [ condmat/0412048v2 ] DOI: 10.1103/PhysRevB.72.161301

Singlettriplet spin blockade and charge sensing in a fewelectron double quantum dot 
Abstract
 Singlettriplet spin blockade in a fewelectron lateral double quantum dot is investigated using simultaneous transport and chargesensing measurements. Transport from the (1,1) to the (0,2) electron occupancy states is strongly suppressed relative to the opposite bias [(0,2) to (1,1)]. At large bias, spin blockade ceases as the (0,2) triplet state enters the transport window, giving a direct measure of exchange splitting as a function of magnetic field. A simple model for current and steadystate charge distribution in spinblockade conditions is developed and found to be in excellent agreement with experiment.
A. C. Johnson, J. R. Petta, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. B 72, 165308 (2005). [ condmat/0410679v1 ] DOI: 10.1103/PhysRevB.72.165308

Zerofield splitting of Kondo resonances in a carbon nanotube quantum
dot 
Abstract
 We present lowtemperature electron transport measurements on a singlewall carbon nanotube quantum dot exhibiting Kondo resonances at low temperature. Contrary to the usual behavior for the spin1/2 Kondo effect we find that the temperature dependence of the zero bias conductance is nonmonotonic. In nonlinear transport measurements lowenergy splittings of the Kondo resonances are observed at zero magnetic field. We suggest that these anomalies reflect interactions between the nanotube and a magnetic (catalyst) particle. The nanotube device may effectively act as a ferromagnetically contacted Kondo dot.
J. Nygard, W. F. Koehl, N. Mason, L. DiCarlo, C. M. Marcus condmat/0410467v2 [pdf]

Photovoltaic and rectification currents in quantum dots 
Abstract
 We investigate theoretically and experimentally the statistical properties of dc current through an open quantum dot subject to ac excitation of a shapedefining gate. The symmetries of rectification current and photovoltaic current with respect to applied magnetic field are examined. Theory and experiment are found to be in good agreement throughout a broad range of frequency and ac power, ranging from adiabatic to nonadiabatic regimes.
M. G. Vavilov, L. DiCarlo, C. M. Marcus Journal reference: Phys. Rev. B 71, 241309(R) (2005) [ condmat/0410042v1 ] DOI: 10.1103/PhysRevB.71.241309

Controlling Spin Qubits in Quantum Dots 
Abstract
 We review progress on the spintronics proposal for quantum computing where the quantum bits (qubits) are implemented with electron spins. We calculate the exchange interaction of coupled quantum dots and present experiments, where the exchange coupling is measured via transport. Then, experiments on single spins on dots are described, where long spin relaxation times, on the order of a millisecond, are observed. We consider spinorbit interaction as sources of spin decoherence and find theoretically that also long decoherence times are expected. Further, we describe the concept of spin filtering using quantum dots and show data of successful experiments. We also show an implementation of a read out scheme for spin qubits and define how qubits can be measured with high precision. Then, we propose new experiments, where the spin decoherence time and the Rabi oscillations of single electrons can be measured via charge transport through quantum dots. Finally, all these achievements have promising applications both in conventional and quantum information processing.
HansAndreas Engel, L. P. Kouwenhoven, Daniel Loss, C. M. Marcus Journal reference: Quantum Information Processing 3, 115 (2004) [ condmat/0409294v1 ] DOI: 10.1007/s1112800431033

Anomalous Conductance Quantization in Carbon Nanotubes 
Abstract
 Conductance measurements of carbon nanotubes containing gated local depletion regions exhibit plateaus as a function of gate voltage, spaced by approximately e2/h, the quantum of conductance for a single (nondegenerate) mode. Plateau structure is investigated as a function of bias voltage, temperature, and magnetic field. We speculate on the origin of this surprising quantization, which appears to lack band and spin degeneracy.
M. J. Biercuk, N. Mason, J. Martin, A. Yacoby, C. M. Marcus Journal reference: Phys. Rev. Lett. 94, 026801 (2005). [ condmat/0406652v2 ] DOI: 10.1103/PhysRevLett.94.026801

Cotunneling Spectroscopy in FewElectron Quantum Dots 
Abstract
 Fewelectron quantum dots are investigated in the regime of strong tunneling to the leads. Inelastic cotunneling is used to measure the twoelectron singlettriplet splitting above and below a magnetic field driven singlettriplet transition. Evidence for a nonequilibrium twoelectron singlettriplet Kondo effect is presented. Cotunneling allows orbital correlations and parameters characterizing entanglement of the twoelectron singlet ground state to be extracted from dc transport.
D. M. Zumbuhl, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 93, 256801 (2004) [ condmat/0408276v1 ] DOI: 10.1103/PhysRevLett.93.256801

Manipulation of a Single Charge in a Double Quantum Dot 
Abstract
 We manipulate a single electron in a fully tunable double quantum dot using microwave excitation. Under resonant conditions, microwaves drive transitions between the (1,0) and (0,1) charge states of the double dot. Local quantum point contact charge detectors enable a direct measurement of the photoninduced change in occupancy of the charge states. From charge sensing measurements, we find T1~16 ns and a lower bound estimate for T2* of 400 ps for the charge twolevel system.
J. R. Petta, A. C. Johnson, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 93, 186802 (2004) [ condmat/0408139v1 ] DOI: 10.1103/PhysRevLett.93.186802

Voltage Dependence of Spin Polarized Tunneling 
Abstract
 A mesoscopic spin valve is used to determine the effective spin polarization of electrons tunneling from and into ferromagnetic transition metals at finite voltages. The tunneling spin polarization from the ferromagnet (FM) slowly decreases with bias, but drops faster and even inverts with voltage when electrons tunnel into it. A biasdependent free electron model shows that in the former case electrons originate near the Fermi level of the FM with large polarization whereas in the latter, electrons tunnel into hot electron states for which the polarization is significantly reduced. The change in sign is ascribed to the detailed matching of the electron wave function through the tunnel barrier.
S. O. Valenzuela, D. J. Monsma, C. M. Marcus, V. Narayanamurti, M. Tinkham condmat/0407489v1 [pdf]

Tunable Nonlocal Spin Control in a CoupledQuantum Dot System 
Abstract
 The effective interaction between magnetic impurities in metals that can lead to various magnetic ground states often competes with a tendency for electrons near impurities to screen the local moment (Kondo effect). The simplest system exhibiting the richness of this competition, the twoimpurity Kondo system, is here realized experimentally in the form of two quantum dots coupled through an open conducting region. We demonstrate nonlocal spin control by suppressing and splitting Kondo resonances in one quantum dot by changing electron number and coupling of the other dot. Results suggest an approach to nonlocal spin control relevant to quantum information processing.
N. J. Craig, J. M. Taylor, E. A. Lester, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Science 304, 565 (2004) [ condmat/0404213v2 ] DOI: 10.1126/science.1095452

Differential Charge Sensing and Charge Delocalization in a Tunable Double Quantum Dot 
Abstract
 We report measurements of a tunable double quantum dot, operating in the quantum regime, with integrated local charge sensors. The spatial resolution of the sensors is sufficient to allow the charge distribution within the double dot system to be resolved at fixed total charge. We use this readout scheme to investigate charge delocalization as a function of temperature and strength of tunnel coupling, showing that local charge sensing allows an accurate determination of interdot tunnel coupling in the absence of transport.
L. DiCarlo, H. J. Lynch, A. C. Johnson, L. I. Childress, K. Crockett, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 92, 226801 (2004) [ condmat/0311308v4 ] DOI: 10.1103/PhysRevLett.92.226801

CoulombModified Fano Resonance in a OneLead Quantum Dot 
Abstract
 We investigate a tunable Fano interferometer consisting of a quantum dot coupled via tunneling to a onedimensional channel. In addition to Fano resonance, the channel shows strong Coulomb response to the dot, with a single electron modulating channel conductance by factors of up to 100. Where these effects coexist, lineshapes with up to four extrema are found. A model of Coulombmodified Fano resonance is developed and gives excellent agreement with experiment.
A. C. Johnson, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 93, 106803 (2004). [ condmat/0312571v2 ] DOI: 10.1103/PhysRevLett.93.106803

Charge sensing of excited states in an isolated double quantum dot 
Abstract
 Pulsed electrostatic gating combined with capacitive charge sensing is used to perform excited state spectroscopy of an electrically isolated doublequantumdot system. The tunneling rate of a single charge moving between the two dots is affected by the alignment of quantized energy levels; measured tunneling probabilities thereby reveal spectral features. Two pulse sequences are investigated, one of which, termed latched detection, allows measurement of a single tunneling event without repetition. Both provide excitedstate spectroscopy without electrical contact to the doubledot system.
A. C. Johnson, C. M. Marcus, M. P. Hanson, A. C. Gossard Journal reference: Phys. Rev. B 71, 115333 (2005) [ condmat/0312717v2 ] DOI: 10.1103/PhysRevB.71.115333

Pulsedgate measurements of the singlettriplet relaxation time in a twoelectron double quantum dot 
Abstract
 2003

Orbital effects of inplane magnetic fields probed by mesoscopic conductance fluctuations 
Abstract
 We use the high sensitivity to magnetic flux of mesoscopic conductance fluctuations in large quantum dots to investigate changes in the twodimensional electron dispersion caused by an inplane magnetic field. In particular, changes in effective mass and the breaking of momentum reversal symmetry in the electron dispersion are extracted quantitatively from correlations of conductance fluctuations. New theory is presented, and good agreement between theory and experiment is found.
D. M. Zumbuhl, J. B. Miller, C. M. Marcus, V. I. Fal'ko, T. Jungwirth, J. S. Harris Jr Journal reference: Phys. Rev. B 69, 121305(R) (2004) [ condmat/0304404v2 ] DOI: 10.1103/PhysRevB.69.121305

Locally addressable tunnel barriers within a carbon nanotube 
Abstract
 We report the realization and characterization of independently controllable tunnel barriers within a carbon nanotube. The nanotubes are mechanically bent or kinked using an atomic force microscope, and top gates are subsequently placed near each kink. Transport measurements indicate that the kinks form gatecontrolled tunnel barriers, and that gates placed away from the kinks have little or no effect on conductance. The overall conductance of the nanotube can be controlled by tuning the transmissions of either the kinks or the metalnanotube contacts.
M. J. Biercuk, N. Mason, J. M. Chow, C. M. Marcus DOI: 10.1021/nl0486721 condmat/0312276v1 [pdf]

NATO Science Series II: Mathematics, Physics and ChemistryFundamental Problems of Mesoscopic PhysicsEntanglement Production in a Chaotic Quantum Dot 
Abstract
 It has recently been shown theoretically that elastic scattering in the Fermi sea produces quantum mechanically entangled states. The mechanism is similar to entanglement by a beam splitter in optics, but a key distinction is that the electronic mechanism works even if the source is in local thermal equilibrium. An experimental realization was proposed using tunneling between two edge channels in a strong magnetic field. Here we investigate a lowmagnetic field alternative, using multiple scattering in a quantum dot. Two pairs of singlechannel point contacts define a pair of qubits. If the scattering is chaotic, a universal statistical description of the entanglement production (quantified by the concurrence) is possible. The mean concurrence turns out to be almost independent on whether timereversal symmetry is broken or not. We show how the concurrence can be extracted from a Bell inequality using lowfrequency noise measurements, without requiring the tunneling assumption of earlier work.
C. W. J. Beenakker, M. Kindermann, C. M. Marcus, A. Yacoby Journal reference: Fundamental Problems of Mesoscopic Physics, eds. I.V. Lerner, B.L. Altshuler, and Y. Gefen, NATO Science Series II. Vol. 154 (Kluwer, Dordrecht, 2004) [ condmat/0310199v1 ] DOI: 10.1007/1402021933_10

Local Gating of Carbon Nanotubes 
Abstract
 Local effects of multiple electrostatic gates placed beneath carbon nanotubes grown by chemical vapor deposition (CVD) are reported. Singlewalled carbon nanotubes were grown by CVD from Fe catalyst islands across thin Mo "finger gates" (150 x 10nm). Prior to tube growth, several finger gates were patterned lithogrpahically and subsequently coated with a patterned highk dielectric using lowtemperature atomic layer deposition. Transport measurements demonstrate that local finger gates have a distinct effect from a global backgate.
M. J. Biercuk, N. Mason, C. M. Marcus Journal reference: Nano Letters 4, 1 (2004). [ condmat/0308477v1 ] DOI: 10.1021/nl034696g

Lowtemperature atomiclayerdeposition liftoff method for microelectronic and nanoelectronic applications 
Abstract
 We report a novel method for depositing patterned dielectric layers with submicron features using atomic layer deposition (ALD). The patterned films are superior to sputtered or evaporated films in continuity, smoothness, conformality, and minimum feature size. Films were deposited at 100150C using several different precursors and patterned using either PMMA or photoresist. The low deposition temperature permits uniform film growth without significant outgassing or hardbaking of resist layers. A liftoff technique presented here gives sharp step edges with edge roughness as low as ~10 nm. We also measure dielectric constants (k) and breakdown fields for the highk materials aluminum oxide (k ~ 89), hafnium oxide (k ~ 1619) and zirconium oxide (k ~ 2029), grown under similar low temperature conditions.
M. J. Biercuk, D. J. Monsma, C. M. Marcus, J. S. Becker, R. G. Gordon Journal reference: Appl. Phys. Lett. 83, 2405 (2003) [ condmat/0305711v2 ] DOI: 10.1063/1.1612904

Experimental Realization of a Quantum Spin Pump 
Abstract
 We demonstrate the operation of a quantum spin pump based on cyclic radiofrequency excitation of a GaAs quantum dot, including the ability to pump pure spin without pumping charge. The device takes advantage of bidirectional mesoscopic fluctuations of pumped current, made spindependent by the application of an inplane Zeeman field. Spin currents are measured by placing the pump in a focusing geometry with a spinselective collector.
Susan K. Watson, R. M. Potok, C. M. Marcus, V. Umansky Journal reference: Phys. Rev. Lett. 91, 258301 (2003) [ condmat/0302492v2 ] DOI: 10.1103/PhysRevLett.91.258301

Photocurrent, Rectification, and Magnetic Field Symmetry of Induced Current through Quantum Dots 
Abstract
 We report mesoscopic dc current generation in an open chaotic quantum dot with ac excitation applied to one of the shapedefining gates. For excitation frequencies large compared to the inverse dwell time of electrons in the dot (i.e., GHz), we find mesoscopic fluctuations of induced current that are fully asymmetric in the applied perpendicular magnetic field, as predicted by recent theory. Conductance, measured simultaneously, is found to be symmetric in field. In the adiabatic (i.e., MHz) regime, in contrast, the induced current is always symmetric in field, suggesting its origin is mesoscopic rectification.
L. DiCarlo, C. M. Marcus, J. S. Harris Jr Journal reference: Phys. Rev. Lett. 91, 246804 (2003) [ condmat/0304397v1 ] DOI: 10.1103/PhysRevLett.91.246804

GateControlled SpinOrbit Quantum Interference Effects in Lateral Transport 
Abstract
 In situ control of spinorbit coupling in coherent transport using a clean GaAs/AlGaAs 2DEG is realized, leading to a gatetunable crossover from weak localization to antilocalization. The necessary theory of 2D magnetotransport in the presence of spinorbit coupling beyond the diffusive approximation is developed and used to analyze experimental data. With this theory the Rashba contribution and linear and cubic Dresselhaus contributions to spinorbit coupling are separately estimated, allowing the angular dependence of spinorbit precession to be extracted at various gate voltages.
J. B. Miller, D. M. Zumbuhl, C. M. Marcus, Y. B. LyandaGeller, D. GoldhaberGordon, K. Campman, A. C. Gossard Journal reference: Phys. Rev. Lett. 90, 076807 (2003) [ condmat/0206375v4 ] DOI: 10.1103/PhysRevLett.90.076807

Spin and Polarized Current from Coulomb Blockaded Quantum Dots 
Abstract
 We report measurements of spin transitions for GaAs quantum dots in the Coulomb blockade regime, and compare ground and excited state transport spectroscopy to direct measurements of the spin polarization of emitted current. Transport spectroscopy reveals both spinincreasing and spindecreasing transitions as well as higherspin ground states, and allows gfactors to be measured down to a single electron. The spin of emitted current in the Coulomb blockade regime, measured using spinsensitive electron focusing, is found to be polarized along the direction of the applied magnetic field regardless of the ground state spin transition.
R. M. Potok, J. A. Folk, C. M. Marcus, V. Umansky, M. Hanson, A. C. Gossard Journal reference: Phys. Rev. Lett. 91, 016802 (2003) [ condmat/0303152v1 ] DOI: 10.1103/PhysRevLett.91.016802

LongLived Memory for Mesoscopic Quantum Bits 
Abstract
 We describe a technique to create longlived quantum memory for quantum bits in mesoscopic systems. Specifically we show that electronic spin coherence can be reversibly mapped onto the collective state of the surrounding nuclei. The coherent transfer can be efficient and fast and it can be used, when combined with standard resonance techniques, to reversibly store coherent superpositions on the time scale of seconds. This method can also allow for ``engineering'' entangled states of nuclear ensembles and efficiently manipulating the stored states. We investigate the feasibility of this method through a detailed analysis of the coherence properties of the system.
J. M. Taylor, C. M. Marcus, M. D. Lukin Journal reference: Phys. Rev. Lett. 90, 206803 (2003) [ condmat/0301323v1 ] DOI: 10.1103/PhysRevLett.90.206803

Orbital effects of inplane magnetic fields probed by mesoscopic conductance fluctuations 
Abstract
 2002

SpinOrbit Coupling, Antilocalization, and Parallel Magnetic Fields in Quantum Dots 
Abstract
 We investigate antilocalization due to spinorbit coupling in ballistic GaAs quantum dots. Antilocalization that is prominent in large dots is suppressed in small dots, as anticipated theoretically. Parallel magnetic fields suppress both antilocalization and also, at larger fields, weak localization, consistent with random matrix theory results once orbital coupling of the parallel field is included. In situ control of spinorbit coupling in dots is demonstrated as a gatecontrolled crossover from weak localization to antilocalization.
D. M. Zumbuhl, J. B. Miller, C. M. Marcus, K. Campman, A. C. Gossard Journal reference: Phys. Rev. Lett. 89, 276803 (2002). [ condmat/0208436v2 ] DOI: 10.1103/PhysRevLett.89.276803

Detecting SpinPolarized Currents in Ballistic Nanostructures 
Abstract
 We demonstrate a mesoscopic spin polarizer/analyzer system that allows the spin polarization of current from a quantum point contact in an inplane magnetic field to be measured. A transverse focusing geometry is used to couple current from an emitter point contact into a collector point contact. At large inplane fields, with the point contacts biased to transmit only a single spin (g < e^2/h), the voltage across the collector depends on the spin polarization of the current incident on it. Spin polarizations of greater than 80% are found for both emitter and collector at 300mK and 7T inplane field.
R. M. Potok, J. A. Folk, C. M. Marcus, V. Umansky Journal reference: Phys. Rev. Lett. 89, 266602 (2002). [ condmat/0206379v1 ] DOI: 10.1103/PhysRevLett.89.266602

LowTemperature Fate of the 0.7 Structure in a Point Contact: A Kondolike Correlated State in an Open System 
Abstract
 Besides the usual conductance plateaus at multiples of 2e2/h, quantum point contacts typically show an extra plateau at ~ 0.7(2e2/h), believed to arise from electronelectron interactions that prohibit the two spin channels from being simultaneously occupied. We present evidence that the disappearance of the 0.7 structure at very low temperature signals the formation of a Kondolike correlated spin state. Evidence includes a zerobias conductance peak that splits in a parallel field, scaling of conductance to a modified Kondo form, and consistency between peak width and the Kondo temperature.
S. M. Cronenwett, H. J. Lynch, D. GoldhaberGordon, L. P. Kouwenhoven, C. M. Marcus, K. Hirose, N. S. Wingreen, V. Umansky Journal reference: Phys. Rev. Lett. 88, 226805 (2002). [ condmat/0201577v1 ] DOI: 10.1103/PhysRevLett.88.226805

SpinOrbit Coupling, Antilocalization, and Parallel Magnetic Fields in Quantum Dots 
Abstract
 2001

Adiabatic Quantum Pump of SpinPolarized Current 
Abstract
 We propose a mechanism by which an open quantum dot driven by two ac (radio frequency) gate voltages in the presence of a moderate inplane magnetic field generates a spin polarized, phase coherent dc current. The idea combines adiabatic, nonquantized (but coherent) pumping through periodically modulated external parameters and the strong fluctuations of the electron wave function existent in chaotic cavities. We estimate that the spin polarization of the current can be observed for temperatures and Zeeman splitting energies of the order of the singleparticle mean level spacing.
Eduardo R. Mucciolo, Claudio Chamon, Charles M. Marcus Journal reference: Phys. Rev. Lett. 89, 146802 (2002) [ condmat/0112157v1 ] DOI: 10.1103/PhysRevLett.89.146802

Decoherence in Nearly Isolated Quantum Dots 
Abstract
 Decoherence in nearlyisolated GaAs quantum dots is investigated using the change in average Coulomb blockade peak height upon breaking timereversal symmetry. The normalized change in average peak height approaches the predicted universal value of 1/4 at temperatures well below the singleparticle level spacing, but is greatly suppressed for temperature greater than the level spacing, suggesting that inelastic scattering or other dephasing mechanisms dominate in this regime.
J. A. Folk, C. M. Marcus, J. S. Harris Jr Journal reference: Phys. Rev. Lett. 87, 206802 (2001) [ condmat/0008052v2 ] DOI: 10.1103/PhysRevLett.87.206802

Adiabatic Quantum Pump of SpinPolarized Current 
Abstract
 2000

Spin Degeneracy and Conductance Fluctuations in Open Quantum Dots 
Abstract
 The dependence of mesoscopic conductance fluctuations on parallel magnetic field is used as a probe of spin degeneracy in open GaAs quantum dots. The variance of fluctuations at high parallel field is reduced from the lowfield variance (with broken timereversal symmetry) by factors ranging from roughly two in a 1 squaremicron dot at low temperature, to four or greater in 8 squaremicron dots. The factor of two is expected for simple Zeeman splitting of spin degenerate channels. A possible explanation for the unexpected larger factors in terms of fielddependent spin orbit scattering is proposed.
J. A. Folk, S. R. Patel, K. M. Birnbaum, C. M. Marcus, C. I. Duruoz, J. S. Harris Jr Journal reference: Phys. Rev. Lett. 86, 2102 (2001) [ condmat/0005066v3 ] DOI: 10.1103/PhysRevLett.86.2102

Ground state spin and Coulomb blockade peak motion in chaotic quantum
dots 
Abstract
 We investigate experimentally and theoretically the behavior of Coulomb blockade (CB) peaks in a magnetic field that couples principally to the groundstate spin (rather than the orbital moment) of a chaotic quantum dot. In the first part, we discuss numerically observed features in the magnetic field dependence of CB peak and spacings that unambiguously identify changes in spin S of each ground state for successive numbers of electrons on the dot, N. We next evaluate the probability that the ground state of the dot has a particular spin S, as a function of the exchange strength, J, and external magnetic field, B. In the second part, we describe recent experiments on gatedefined GaAs quantum dots in which Coulomb peak motion and spacing are measured as a function of inplane magnetic field, allowing changes in spin between N and N+1 electron ground states to be inferred.
J. A. Folk, C. M. Marcus, R. Berkovits, I. L. Kurland, I. L. Aleiner, B. L. Altshuler DOI: 10.1238/Physica.Topical.090a00026 condmat/0010441v1 [pdf]

Spin orbit effects in a GaAs quantum dot in a parallel magnetic field 
Abstract
 We analyze the effects of spinorbit coupling on fluctuations of the conductance of a quantum dot fabricated in a GaAs heterostructure. We argue that spinorbit effects may become important in the presence of a large parallel magnetic field B_{}, even if they are negligble for B_{}=0. This should be manifest in the level repulsion of a closed dot, and in reduced conductance fluctuations in dots with a small number of open channels in each lead, for large B_{}. Our picture is consistent with the experimental observations of Folk et al.
B. I. Halperin, Ady Stern, Y. Oreg, J. H. Cremers, J. Folk, C. M. Marcus DOI: 10.1103/PhysRevLett.86.2106 condmat/0010064v1 [pdf]

Spin Degeneracy and Conductance Fluctuations in Open Quantum Dots 
Abstract
 1999

LowTemperature Saturation of the Dephasing Time and Effects of Microwave Radiation on Open Quantum Dots 
Abstract
 The dephasing time of electrons in open semiconductor quantum dots, measured using ballistic weak localization, is found to saturate below ~ 100 mK, roughly twice the electron base temperature, independent of dot size. Microwave radiation deliberately coupled to the dots affects quantum interference indistinguishably from elevated temperature, suggesting that direct dephasing due to radiation is not the cause of the observed saturation. Coulomb blockade measurements show that the applied microwaves create sufficient source drain voltages to account for dephasing due to Joule heating.
A. G. Huibers, J. A. Folk, S. R. Patel, C. M. Marcus, C. I. Duruoz, J. S. Harris, Jr Journal reference: Phys. Rev. Lett 83, 5090 (1999) [ condmat/9904274v1 ] DOI: 10.1103/PhysRevLett.83.5090

Coulomb Blockade Fluctuations in Strongly Coupled Quantum Dots 
Abstract
 Quantum fluctuations of Coulomb blockade are investigated as a function of the coupling to reservoirs in semiconductor quantum dots. We use fluctuations in the distance between peaks $\Delta N$ apart to characterize both the amplitude and correlation of peak motion. For strong coupling, peak motion is greatly enhanced at low temperature, but does not show an increase in peaktopeak correlation. These effects can lead to anomalous temperature dependence in the Coulomb valleys, similar to behavior ascribed to Kondo physics.
S. M. Maurer, S. R. Patel, C. M. Marcus, C. I. Duruoz, J. S. Harris, Jr Journal reference: Phys. Rev. Lett. 83, 1403 (1999) [ condmat/9810283v2 ] DOI: 10.1103/PhysRevLett.83.1403

An Adiabatic Quantum Electron Pump 
Abstract
 A quantum pumping mechanism which produces dc current or voltage in response to a cyclic deformation of the confining potential in an open quantum dot is reported. The voltage produced at zero current bias is sinusoidal in the phase difference between the two ac voltages deforming the potential and shows random fluctuations in amplitude and direction with small changes in external parameters such as magnetic field. The amplitude of the pumping response increases linearly with the frequency of the deformation. Dependencies of pumping on the strength of the deformations, temperature, and breaking of timereversal symmetry are also investigated.
M. Switkes, C. M. Marcus, K. Campman, A. C. Gossard Journal reference: Science 283, 1905 (1999) [ condmat/9904238v1 ] DOI: 10.1126/science.283.5409.1905

Controlled Fabrication of Metallic Electrodes with Atomic Separation 
Abstract
 We report a new technique for fabricating metallic electrodes on insulating substrates with separations on the 1 nm scale. The fabrication technique, which combines lithographic and electrochemical methods, provides atomic resolution without requiring sophisticated instrumentation. The process is simple, controllable, reversible, and robust, allowing rapid fabrication of electrode pairs with high yield. We expect the method to prove useful in interfacing molecularscale structures to macroscopic probes and electronic devices .
A. F. Morpurgo, D. B. Robinson, C. M. Marcus DOI: 10.1063/1.123765 condmat/9811265v2 [pdf]

LowTemperature Saturation of the Dephasing Time and Effects of Microwave Radiation on Open Quantum Dots 
Abstract
 1998

Changing the Electronic Spectrum of a Quantum Dot by Adding Electrons 
Abstract
 The temperature dependence of Coulomb blockade peak height correlation is used to investigate how adding electrons to a quantum dot alters or "scrambles" its electronic spectrum. Deviations from finitetemperature random matrix theory with an unchanging spectrum indicate spectral scrambling after a small number of electrons are added. Enhanced peaktopeak correlations at low temperature are observed. Peak height statistics show similar behavior in several dot configurations despite significant differences in correlations.
S. R. Patel, D. R. Stewart, C. M. Marcus, M. Gokcedag, Y. Alhassid, A. D. Stone, C. I. Duruoz, J. S. Harris Jr DOI: 10.1103/PhysRevLett.81.5900 condmat/9808166v3 [pdf]

Feedback Control of a Quantum Dot 
Abstract
 Mesoscopic structures are generally operated in an openloop configuration, whereas most practical electronics including quantum interference devices such as SQUIDs are operated closedloop, taking advantage of feedback. This paper presents some basic considerations on the use of feedback in mesoscopic samples with universal statistical properties. The controllability of mesoscopic fluctuations is shown to be connected to problems in continuum percolation, leading to the requirement of two control parameters to achieve robust control.
C. M. Marcus condmat/9807380v1 [pdf]

Mesoscopic Coulomb Blockade in Onechannel Quantum Dots 
Abstract
 Signatures of "mesoscopic Coulomb blockade" are reported for quantum dots with one fully transmitting pointcontact lead, T1 = 1, T2 << 1. Unlike Coulomb blockade (CB) in weaktunneling devices (T1, T2 << 1), onechannel CB is a mesoscopic effect requiring quantum coherence. Several distinctive features of mesoscopic CB are observed, including a reduction in CB upon breaking timereversal symmetry with a magnetic field, relatively large fluctuations of peak position as a function of magnetic field, and strong temperature dependence on the scale of the quantum level spacing.
S. M. Cronenwett, S. M. Maurer, S. R. Patel, C. M. Marcus, C. I. Duruoz, J. S. Harris DOI: 10.1103/PhysRevLett.81.5904 condmat/9807311v1 [pdf]

Statistics of Coulomb Blockade Peak Spacings 
Abstract
 Distributions of Coulomb blockade peak spacing are reported for large ensembles of both unbroken (magnetic field B = 0) and broken (B <> 0) time reversal symmetry in GaAs quantum dots. Both distributions are symmetric and roughly gaussian with a width ~ 26% of the average spacing, with broad, nongaussian tails. The distribution is systematically wider at B = 0 by a factor of ~ 1.2 + 0.1. No evenodd spacing correlations or bimodal structure in the spacing distribution is found, suggesting an absence of spindegeneracy. There is no observed correlation between peak spacing and peak height.
S. R. Patel, S. M. Cronenwett, D. R. Stewart, A. G. Huibers, C. M. Marcus, C. I. Duruoz, J. S. Harris, K. Campman, A. C. Gossard DOI: 10.1103/PhysRevLett.80.4522 condmat/9708090v2 [pdf]

Classical Advection of Guiding Centers in a Random Magnetic Field 
Abstract
 We investigate theoretically and experimentally classical advective transport in a 2D electron gas in a random magnetic field. For uniform external perpendicular magnetic fields large compared to the random field we observe a strong enhancement of conductance compared to the ordinary Drude value. This can be understood as resulting from advection of cyclotron guiding centers. For low disorder this enhancement shows nontrivial scaling as a function of scattering time, with consistency between theory and experiment.
L. Zielinski, K. Chaltikian, K. Birnbaum, C. M. Marcus, K. Campman, A. C. Gossard DOI: 10.1209/epl/i1998005547 condmat/9704058v2 [pdf]

Distributions of the Conductance and its Parametric Derivatives in
Quantum Dots 
Abstract
 Full distributions of conductance through quantum dots with singlemode leads are reported for both broken and unbroken timereversal symmetry. Distributions are nongaussian and agree well with random matrix theory calculations that account for a finite dephasing time, $\tau_\phi$, once broadening due to finite temperature $T$ is also included. Full distributions of the derivatives of conductance with respect to gate voltage $P(dg/dV_g)$ are also investigated.
A. G. Huibers, S. R. Patel, C. M. Marcus, P. W. Brouwer, C. I. Duruoz, J. S. Harris, Jr DOI: 10.1103/PhysRevLett.81.1917 condmat/9801174v1 [pdf]

Changing the Electronic Spectrum of a Quantum Dot by Adding Electrons 
Abstract
 1997

Correlations between Ground and Excited State Spectra of a Quantum Dot 
Abstract
 We have studied the ground and excited state spectra of a semiconductor quantum dot for successive numbers of electron occupancy using linear and nonlinear magnetoconductance measurements. We present the first observation of direct correlation between the mth excited state of the N electron system and the ground state of the N+m electron system for m up to 4. Results are consistent with a nonspindegenerate single particle picture of the filling of levels. Electronelectron interaction effects are also observed as a perturbation to this model. Magnetoconductance fluctuations of ground states are shown as anticrossings where wavefunction characteristics are exchanged between adjacent levels.
D. R. Stewart, D. Sprinzak, C. M. Marcus, C. I. Duruoz, J. S. Harris Jr DOI: 10.1126/science.278.5344.1784 condmat/9709126v2 [pdf]

High bias transport and magnetometer design in open quantum dots 
Abstract
 We report transport measurements as a function of bias in open semiconductor quantum dots. These measurements are well described by an effective electron temperature derived from Joule heating at the point contacts and cooling by WiedemannFranz outdiffusion of thermal electrons. Using this model, we propose and analyze a quantum dot based sensor which measures absolute magnetic field at micron scales with a noise floor of $\sim 50 \mu\phi_{0} / \sqrt{Hz}$ at 300 mK.
M. Switkes, A. G. Huibers, C. M. Marcus, K. Campman, A. C. Gossard Journal reference: Appl. Phys. Lett. 72, p. 471 (1998) [ condmat/9708224v1 ] DOI: 10.1063/1.120789

Dephasing in Open Quantum Dots 
Abstract
 Shapeaveraged magnetoconductance (weak localization) is used for the first time to obtain the electron phase coherence time $\tau_{\phi}$ in open ballistic GaAs quantum dots. Values for $\tau_{\phi}$ in the range of temperature T from 0.335 to 4 K are found to be independent of dot area, and are not consistent with the $\tau_{\phi} \propto T^{2}$ behavior expected for isolated dots. Surprisingly, $\tau_{\phi}(T)$ agrees quantitatively with the predicted dephasing time for disordered twodimensional electron systems.
A. G. Huibers, M. Switkes, C. M. Marcus, K. Campman, A. C. Gossard DOI: 10.1016/S09214526(98)00129X condmat/9708170v1 [pdf]

Mesoscopic Fluctuations of Elastic Cotunneling in Coulomb Blockaded Quantum Dots 
Abstract
 We report measurements of mesoscopic fluctuations of elastic cotunneling in Coulomb blockaded quantum dots. Unlike resonant tunneling on Coulomb peaks, cotunneling in the valleys is sensitive to charging effects. We observe a larger magnetic field scale for the cotunneling (valley) fluctuations compared to the peaks, as well as an absence of "weak localization" (reduced conductance at B = 0) in valleys. Cotunneling fluctuations remain correlated over several valleys while peak conductance correlations decreases quickly.
S. M. Cronenwett, S. R. Patel, C. M. Marcus, K. Campman, A. C. Gossard Journal reference: S.M. Cronenwett et al., PRL 79, 2312 (1997) [ condmat/9707274v1 ] DOI: 10.1103/PhysRevLett.79.2312

Quantum Chaos in Open versus Closed Quantum Dots: Signatures of
Interacting Particles 
Abstract
 This paper reviews recent studies of mesoscopic fluctuations in transport through ballistic quantum dots, emphasizing differences between conduction through open dots and tunneling through nearly isolated dots. Both the open dots and the tunnelcontacted dots show random, repeatable conductance fluctuations with universal statistical properties that are accurately characterized by a variety of theoretical models including random matrix theory, semiclassical methods and nonlinear sigma model calculations. We apply these results in open dots to extract the dephasing rate of electrons within the dot. In the tunneling regime, electron interaction dominates transport since the tunneling of a single electron onto a small dot may be sufficiently energetically costly (due to the small capacitance) that conduction is suppressed altogether. How interactions combine with quantum interference are best seen in this regime.
C. M. Marcus, S. R. Patel, A. G. Huibers, S. M. Cronenwett, M. Switkes, I. H. Chan, R. M. Clarke, J. A. Folk, S. F. Godijn, K. Campman, A. C. Gossard DOI: 10.1016/S09600779(97)000192 condmat/9703038v2 [pdf]

Correlations between Ground and Excited State Spectra of a Quantum Dot 
Abstract