Publications by Charles M. Marcus
 2022

Nonlocal signatures of hybridization between quantum dot and Andreev
bound states 
Abstract
 We investigate local and nonlocal signatures of hybridization between a quantum dot state and an extended Andreev bound state (ABS) in a gatedefined InAs nanowire with multiple side probes. When a quantum dot in one of the side probes was hybridized with an ABS in the nanowire, a characteristic spectroscopic pattern was observed both locally, i.e., in the probe with the quantum dot, and nonlocally, in the tunnel conductance of a remote probe. Nonlocal signatures of hybridization reveal the extended nature of the ABS.
 2201.03687v1 [pdf]
Andreas Pöschl, Alisa Danilenko, Deividas Sabonis, Kaur Kristjuhan, Tyler Lindemann, Candice Thomas, Michael J. Manfra, Charles M. Marcus [pdf]

Signatures of a topological phase transition in a planar Josephson
junction 
Abstract
 A growing body of work suggests that planar Josephson junctions fabricated using superconducting hybrid materials provide a highly controllable route toward onedimensional topological superconductivity. Among the experimental controls are inplane magnetic field, phase difference across the junction, and carrier density set by electrostatic gate voltages. Here, we investigate planar Josephson junctions with an improved design based on an epitaxial InAs/Al heterostructure, embedded in a superconducting loop, probed with integrated quantum point contacts (QPCs) at both ends of the junction. For particular ranges of inplane field and gate voltages, a closing and reopening of the superconducting gap is observed, along with a zerobias conductance peak (ZBCP) that appears upon reopening of the gap. Consistency with a simple theoretical model supports the interpretation of a topological phase transition. While gap closings and reopenings generally occurred together at the two ends of the junction, the height, shape, and even presence of ZBCPs typically differed between the ends, presumably due to disorder and variation of couplings to local probes.
 2201.03453v1 [pdf]
A. Banerjee, O. Lesser, M. A. Rahman, H. R. Wang, M. R. Li, A. Kringhøj, A. M. Whiticar, A. C. C. Drachmann, C. Thomas, T. Wang, M. J. Manfra, E. Berg, Y. Oreg, Ady Stern, C. M. Marcus [pdf]

Nonlocal signatures of hybridization between quantum dot and Andreev
bound states 
Abstract
 2021

Comparing tunneling spectroscopy and charge sensing of Andreev bound
states in a semiconductorsuperconductor hybrid nanowire structure 
Abstract
 Transport studies of Andreev bound states (ABSs) are complicated by the interplay of charging effects and superconductivity. Here, we compare transport approaches to ABS spectroscopy in a semiconductorsuperconductor island to a chargesensing approach based on an integrated radiofrequency singleelectron transistor. Consistency of the methods demonstrates that fast, noninvasive charge sensing allows accurate quantitative measurement of ABSs while eluding some complexities of transport.
 2105.08871v1 [pdf]
Deividas Sabonis, David van Zanten, Judith Suter, Torsten Karzig, Dmitry I. Pikulin, Jukka I. Väyrynen, Eoin O'Farrell, Davydas Razmadze, Peter Krogstrup, Charles M. Marcus [pdf]

Spinpolarized bound states in
semiconductorsuperconductorferromagnetic insulator islands 
Abstract
 We report Coulomb blockade transport studies of InAs nanowires grown with epitaxial superconducting Al and ferromagnetic insulator EuS on overlapping facets. By comparing experimental results to a theoretical model, we associate cotunneling features in evenodd bias spectra with spinpolarized Andreev levels, indicating that spin splitting exceeding the induced superconducting gap at zero applied magnetic field. Energies of the polarized subgap states can be tuned on either side of zero by electrostatic gates.
 2104.01463v1 [pdf]
S. Vaitiekėnas, R. Seoane Souto, Y. Liu, P. Krogstrup, K. Flensberg, M. Leijnse, C. M. Marcus [pdf]

Zeemandriven parity transitions in an Andreev quantum dot 
Abstract
 The Andreev spectrum of a quantum dot embedded in a hybrid semiconductorsuperconductor interferometer can be modulated by electrostatic gating, magnetic flux through the interferometer, and Zeeman splitting from inplane magnetic field. We demonstrate parity transitions in the embedded quantum dot system, and show that the Zeemandriven transition is accompanied by a 0{\pi} transition in the superconducting phase across the dot. We further demonstrate that flux through the interferometer modulates both dot parity and 0{\pi} transitions.
A. M. Whiticar, A. Fornieri, A. Banerjee, A. C. C. Drachmann, S. Gronin, G. C. Gardner, T. Lindemann, M. J. Manfra, C. M. Marcus Journal reference: Phys. Rev. B 103, 245308 (2021) [pdf] DOI: 10.1103/PhysRevB.103.245308

MagneticFieldCompatible Superconducting Transmon Qubit 
Abstract
 We present a hybrid semiconductorbased superconducting qubit device which remains coherent at magnetic fields up to 1 T. The qubit transition frequency exhibits periodic oscillations with magnetic field, consistent with interference effects due to the magnetic flux threading the cross section of the proximitized semiconductor nanowire junction. As induced superconductivity revives, additional coherent modes emerge at high magnetic fields, which we attribute to the interaction of the qubit and lowenergy Andreev states.
A. Kringhøj, T. W. Larsen, O. Erlandsson, W. Uilhoorn, J. G. Kroll, M. Hesselberg, R. P. G. McNeil, P. Krogstrup, L. Casparis, C. M. Marcus, K. D. Petersson Journal reference: Phys. Rev. Applied 15, 054001 (2021) [pdf] DOI: 10.1103/PhysRevApplied.15.054001

Anodic oxidation of epitaxial superconductorsemiconductor hybrids 
Abstract
 We demonstrate a new fabrication process for hybrid semiconductorsuperconductor heterostructures based on anodic oxidation (AO), allowing controlled thinning of epitaxial Al films. Structural and transport studies of oxidized epitaxial Al films grown on insulating GaAs substrates reveal spatial nonuniformity and enhanced critical temperature and magnetic fields. Oxidation of epitaxial Al on hybrid InAs heterostructures with a conducting quantum well show similarly enhanced superconducting properties transferred to the twodimensional electron gas (2DEG) by proximity effect, with critical perpendicular magnetic fields up to 3.5 T. An insulating AlOx film, that passivates the heterostructure from exposure to air, is obtained by complete oxidation of the Al. It simultaneously removes the need to strip Al which damages the underlying semiconductor. AO passivation yielded 2DEG mobilities two times higher than similar devices with Al removed by wet etching. An AOpassivated Hall bar showed quantum Hall features emerging at a transverse field of 2.5 T, below the critical transverse field of thinned films, eventually allowing transparent coupling of quantum Hall effect and superconductivity. AO thinning and passivation are compatible with standard lithographic techniques, giving lateral resolution below <50 nm. We demonstrate local patterning of AO by realizing a semiconductorbased Josephson junction operating up to 0.3 T perpendicular.
Asbjørn C. C. Drachmann, Rosa E. Diaz, Candice Thomas, Henri J. Suominen, Alexander M. Whiticar, Antonio Fornieri, Sergei Gronin, Tiantian Wang, Geoffrey C. Gardner, Alex R. Hamilton, Fabrizio Nichele, Michael J. Manfra, Charles M. Marcus Journal reference: Phys. Rev. Materials 5, 013805 (2021) [pdf] DOI: 10.1103/PhysRevMaterials.5.013805

Andreev Modes from Phase Winding in a FullShell NanowireBased Transmon 
Abstract
 We investigate transmon qubits made from semiconductor nanowires with a fully surrounding superconducting shell. In the regime of reentrant superconductivity associated with the destructive LittleParks effect, numerous coherent transitions are observed in the first reentrant lobe, where the shell carries 2{\pi} winding of superconducting phase, and are absent in the zeroth lobe. As junction density was increased by gate voltage, qubit coherence was suppressed then lost in the first lobe. These observations and numerical simulations highlight the role of windinginduced Andreev states in the junction.
A. Kringhøj, G. W. Winkler, T. W. Larsen, D. Sabonis, O. Erlandsson, P. Krogstrup, B. van Heck, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. Lett. 126, 047701 (2021) [pdf] DOI: 10.1103/PhysRevLett.126.047701

Closing of the induced gap in a hybrid superconductorsemiconductor nanowire 
Abstract
 Hybrid superconductorsemiconductor nanowires are predicted to undergo a fieldinduced phase transition from a trivial to a topological superconductor, marked by the closure and reopening of the excitation gap, followed by the emergence of Majorana bound states at the nanowire ends. Many local densityofstates measurements have reported signatures of the topological phase, however this interpretation has been challenged by alternative explanations. Here, by measuring nonlocal conductance, we identify the closure of the excitation gap in the bulk of the semiconductor before the emergence of zerobias peaks. This observation is inconsistent with scenarios where zerobias peaks occur due to endstates with a trivially gapped bulk, which have been extensively considered in the theoretical and experimental literature. We observe that after the gap closes, nonlocal signals fluctuate strongly and persist irrespective of the presence of localconductance zerobias peaks. Thus, our observations are also incompatible with a simple picture of clean topological superconductivity. This work presents a new experimental approach for probing the spatial extent of states in Majorana wires, and reveals the presence of a regime with a continuum of spatially extended states and uncorrelated zerobias peaks.
D. Puglia, E. A. Martinez, G. C. Ménard, A. Pöschl, S. Gronin, G. C. Gardner, R. Kallaher, M. J. Manfra, C. M. Marcus, A. P. Higginbotham, L. Casparis Journal reference: Phys. Rev. B 103, 235201 (2021) [pdf] DOI: 10.1103/PhysRevB.103.235201

Comparing tunneling spectroscopy and charge sensing of Andreev bound
states in a semiconductorsuperconductor hybrid nanowire structure 
Abstract
 2020

ParityProtected SuperconductorSemiconductor Qubit 
Abstract
 Coherence of superconducting qubits can be improved by implementing designs that protect the parity of Cooper pairs on superconducting islands. Here, we introduce a parityprotected qubit based on voltagecontrolled semiconductor nanowire Josephson junctions, taking advantage of the higher harmonic content in the energyphase relation of fewchannel junctions. A symmetric interferometer formed by two such junctions, gatetuned into balance and frustrated by a halfquantum of applied flux, yields a cos(2{\phi}) Josephson element, reflecting coherent transport of pairs of Cooper pairs. We demonstrate that relaxation of the qubit can be suppressed tenfold by tuning into the protected regime.
T. W. Larsen, M. E. Gershenson, L. Casparis, A. Kringhøj, N. J. Pearson, R. P. G. McNeil, F. Kuemmeth, P. Krogstrup, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. Lett. 125, 056801 (2020) [pdf] DOI: 10.1103/PhysRevLett.125.056801

Coherent transport through a Majorana island in an Aharonov–Bohm interferometer 
Abstract
 Majorana zero modes are leading candidates for topological quantum computation due to nonlocal qubit encoding and nonabelian exchange statistics. Spatially separated Majorana modes are expected to allow phasecoherent singleelectron transport through a topological superconducting island via a mechanism referred to as teleportation. Here we experimentally investigate such a system by patterning an elongated epitaxial InAsAl island embedded in an AharonovBohm interferometer. With increasing parallel magnetic field, a discrete subgap state in the island is lowered to zero energy yielding persistent 1eperiodic Coulomb blockade conductance peaks (e is the elementary charge). In this condition, conductance through the interferometer is observed to oscillate in a perpendicular magnetic field with a flux period of h/e (h is Planck's constant), indicating coherent transport of single electrons through the islands, a signature of electron teleportation via Majorana modes, 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 Journal reference: Nat. Comm. 11, 3212 (2020) [pdf] DOI: 10.1038/s4146702016988x

Quantum Dot Parity Effects in Trivial and Topological Josephson Junctions 
Abstract
 An oddoccupied quantum dot in a Josephson junction can flip transmission phase, creating a {\pi}junction. When the junction couples topological superconductors, no phase flip is expected. We investigate this and related effects in a fullshell hybrid interferometer, using gate voltage to control dotjunction parity and axial magnetic flux to control the transition from trivial to topological superconductivity. Enhanced zerobias conductance and critical current for odd parity in the topological phase reflects hybridization of the confined spin with zeroenergy modes in the leads.
D. Razmadze, E. C. T. O'Farrell, P. Krogstrup, C. M. Marcus Journal reference: Phys. Rev. Lett. 125, 116803 (2020) [pdf] DOI: 10.1103/PhysRevLett.125.116803

Destructive LittleParks Effect in a FullShell NanowireBased Transmon 
Abstract
 A semiconductor transmon with an epitaxial Al shell fully surrounding an InAs nanowire core is investigated in the low $E_J/E_C$ regime. LittleParks oscillations as a function of flux along the hybrid wire axis are destructive, creating lobes of reentrant superconductivity separated by a metallic state at a halfquantum of applied flux. In the first lobe, phase winding around the shell can induce topological superconductivity in the core. Coherent qubit operation is observed in both the zeroth and first lobes. Splitting of parity bands by coherent singleelectron coupling across the junction is not resolved beyond line broadening, placing a bound on Majorana coupling, $E_M/h$ < 10 MHz, much smaller than the Josephson coupling $E_J/h$ ~ 4.7 GHz.
Deividas Sabonis, Oscar Erlandsson, Anders Kringhøj, Bernard van Heck, Thorvald W. Larsen, Ivana Petkovic, Peter Krogstrup, Karl D. Petersson, Charles M. Marcus Journal reference: Phys. Rev. Lett. 125, 156804 (2020) [pdf] DOI: 10.1103/PhysRevLett.125.156804

Zerobias peaks at zero magnetic field in ferromagnetic hybrid nanowires 
Abstract
 We report transport measurements and tunneling spectroscopy in hybrid nanowires with epitaxial layers of superconducting Al and the ferromagnetic insulator EuS, grown on semiconducting InAs nanowires. In devices where the Al and EuS covered facets overlap, we infer a remanent effective Zeeman field of order 1 T, and observe stable zerobias conductance peaks in tunneling spectroscopy into the end of the nanowire, consistent with topological superconductivity at zero applied field. Hysteretic features in critical current and tunneling spectra as a function of applied magnetic field support this picture. Nanowires with nonoverlapping Al and EuS covered facets do not show comparable features. Topological superconductivity in zero applied field allows new device geometries and types of control.
S. Vaitiekėnas, Y. Liu, P. Krogstrup, C. M. Marcus [pdf] DOI: 10.1038/s4156702010173 2004.02226v1 [pdf]

Anomalous metallic phase in tunable destructive superconductors 
Abstract
 Multiply connected superconductors smaller than the coherence length show destructive superconductivity, characterized by reentrant quantum phase transitions driven by magnetic flux. We investigate the dependence of destructive superconductivity on flux, transverse magnetic field, temperature, and current in InAs nanowires with a surrounding epitaxial Al shell, finding excellent agreement with meanfield theory across multiple reentrant transitions. Near the crossover between destructive and nondestructive regimes, an anomalous metal phase is observed with temperatureindependent resistance, controlled over two orders of magnitude by a milliteslascale transverse magnetic field.
S. Vaitiekėnas, P. Krogstrup, C. M. Marcus Journal reference: Phys. Rev. B 101, 060507 (2020) [pdf] DOI: 10.1103/PhysRevB.101.060507

Relating Andreev Bound States and Supercurrents in Hybrid Josephson Junctions 
Abstract
 We investigate superconducting quantum interference devices consisting of two highly transmissive Josephson junctions coupled by a superconducting loop, all defined in an epitaxial InAs/Al heterostructure. A novel device design allows for independent measurements of the Andreev bound state spectrum within the normal region of a junction and the resulting currentphase relation. We show that knowledge of the Andreev bound state spectrum alone is enough to derive the independently measured phase dependent supercurrent. On the other hand, the opposite relation does not generally hold true as details of the energy spectrum are averaged out in a critical current measurement. Finally, quantitative understanding of field dependent spectrum and supercurrent require taking into account the second junction in the loop and the kinetic inductance of the epitaxial Al film.
F. Nichele, E. Portolés, A. Fornieri, A. M. Whiticar, A. C. C. Drachmann, T. Wang, G. C. Gardner, C. Thomas, A. T. Hatke, M. J. Manfra, C. M. Marcus Journal reference: Phys. Rev. Lett. 124, 226801 (2020) [pdf] DOI: 10.1103/PhysRevLett.124.226801

Suppressed Charge Dispersion via Resonant Tunneling in a SingleChannel Transmon 
Abstract
 We demonstrate strong suppression of charge dispersion in a semiconductorbased transmon qubit across Josephson resonances associated with a quantum dot in the junction. On resonance, dispersion is drastically reduced compared to conventional transmons with corresponding Josephson and charging energies. We develop a model of qubit dispersion for a singlechannel resonance, which is in quantitative agreement with experimental data.
A. Kringhøj, B. van Heck, T. W. Larsen, O. Erlandsson, D. Sabonis, P. Krogstrup, L. Casparis, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. Lett. 124, 246803 (2020) [pdf] DOI: 10.1103/PhysRevLett.124.246803

Controlled dc Monitoring of a Superconducting Qubit 
Abstract
 Creating a transmon qubit using semiconductorsuperconductor hybrid materials not only provides electrostatic control of the qubit frequency, it also allows parts of the circuit to be electrically connected and disconnected in situ by operating a semiconductor region of the device as a fieldeffect transistor (FET). Here, we exploit this feature to compare in the same device characteristics of the qubit, such as frequency and relaxation time, with related transport properties such as critical supercurrent and normalstate resistance. Gradually opening the FET to the monitoring circuit allows the influence of weaktostrong DC monitoring of a live qubit to be measured. A model of this influence yields excellent agreement with experiment, demonstrating a relaxation rate mediated by a gatecontrolled environmental coupling.
A. Kringhøj, T. W. Larsen, B. van Heck, D. Sabonis, O. Erlandsson, I. Petkovic, D. I. Pikulin, P. Krogstrup, K. D. Petersson, C. M. Marcus Journal reference: Phys. Rev. Lett. 124, 056801 (2020) [pdf] DOI: 10.1103/PhysRevLett.124.056801

ConductanceMatrix Symmetries of a ThreeTerminal Hybrid Device 
Abstract
 We present conductancematrix measurements of a threeterminal superconductorsemiconductor hybrid device consisting of two normal leads and one superconducting lead. Using a symmetry decomposition of the conductance, we find that the antisymmetric components of pairs of local and nonlocal conductances match at energies below the superconducting gap, consistent with expectations based on a noninteracting scattering matrix approach. Further, the local charge character of Andreev bound states is extracted from the symmetrydecomposed conductance data and is found to be similar at both ends of the device and tunable with gate voltage. Finally, we measure the conductance matrix as a function of magnetic field and identify correlated splittings in lowenergy features, demonstrating how conductancematrix measurements can complement traditional tunnelingprobe measurements in the search for Majorana zero modes.
G. C. Ménard, G. L. R. Anselmetti, E. A. Martinez, D. Puglia, F. K. Malinowski, J. S. Lee, S. Choi, M. Pendharkar, C. J. Palmstrøm, K. Flensberg, C. M. Marcus, L. Casparis, A. P. Higginbotham Journal reference: Phys. Rev. Lett. 124, 036802 (2020) [pdf] DOI: 10.1103/PhysRevLett.124.036802

Photonassisted tunnelling 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.
David M. T. van Zanten, Deividas Sabonis, Judith Suter, Jukka I. Väyrynen, Torsten Karzig, Dmitry I. Pikulin, Eoin C. T. O'Farrell, Davydas Razmadze, Karl D. Petersson, Peter Krogstrup, Charles M. Marcus Journal reference: Nature Physics (2020) [pdf] DOI: 10.1038/s4156702008580

Fluxinduced topological superconductivity 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 Journal reference: Science 367, eaav3392 (2020) [pdf] DOI: 10.1126/science.aav3392

ParityProtected SuperconductorSemiconductor Qubit 
Abstract
 2019

Fast Charge Sensing of Si/SiGe Quantum Dots via a HighFrequency Accumulation Gate 
Abstract
 Quantum dot arrays are a versatile platform for the implementation of spin qubits, as highbandwidth sensor dots can be integrated with single, double and tripledot qubits yielding fast and highfidelity qubit readout. However, for undoped silicon devices, reflectometry off sensor ohmics suffers from the finite resistivity of the twodimensional electron gas (2DEG), and alternative readout methods are limited to measuring qubit capacitance, rather than qubit charge. By coupling a surfacemount resonant circuit to the plunger gate of a highimpedance sensor, we realized a fast charge sensing technique that is compatible with resistive 2DEGs. We demonstrate this by acquiring at high speed charge stability diagrams of double and tripledot arrays in Si/SiGe heterostructures as well as pulsedgate singleshot charge and spin readout with integration times as low as 2.4 $\mu$s.
Christian Volk, Anasua Chatterjee, Fabio Ansaloni, Charles M. Marcus, Ferdinand Kuemmeth Journal reference: Nano Letters 19, 56285633 (2019) [pdf] DOI: 10.1021/acs.nanolett.9b02149

Semiconductor–Ferromagnetic Insulator–Superconductor Nanowires: Stray Field and Exchange Field 
Abstract
 Nanowires can serve as flexible substrates for hybrid epitaxial growth on selected facets, allowing for design of heterostructures with complex material combinations and geometries. In this work we report on hybrid epitaxy of semiconductor  ferromagnetic insulator  superconductor (InAs/EuS/Al) nanowire heterostructures. We study the crystal growth and complex epitaxial matching of wurtzite InAs / rocksalt EuS interfaces as well as rocksalt EuS / facecentered cubic Al interfaces. Because of the magnetic anisotropy originating from the nanowire shape, the magnetic structure of the EuS phase are easily tuned into single magnetic domains. This effect efficiently ejects the stray field lines along the nanowires. With tunnel spectroscopy measurements of the density of states, we show the material has a hard induced superconducting gap, and magnetic hysteretic evolution which indicates that the magnetic exchange fields are not negligible. These hybrid nanowires fulfil key material requirements for serving as a platform for spinbased quantum applications, such as scalable topological quantum computing.
Yu Liu, Saulius Vaitiekenas, Sara MartiSanchez, Christian Koch, Sean Hart, Zheng Cui, Thomas Kanne, Sabbir A. Khan, Rawa Tanta, Shivendra Upadhyay, Martin Espineira Cachaza, Charles M. Marcus, Jordi Arbiol, Kathryn A. Moler, Peter Krogstrup [pdf] DOI: 10.1021/acs.nanolett.9b04187 1910.03364v1 [pdf]

Endtoend correlated subgap states in hybrid nanowires 
Abstract
 Endtoend correlated bound states are investigated in superconductorsemiconductor hybrid nanowires at zero magnetic field. Peaks in subgap conductance are independently identified from each wire end, and a crosscorrelation function is computed that counts endtoend coincidences, averaging over thousands of subgap features. Strong correlations in a short, $300~\mathrm{nm}$ device are reduced by a factor of four in a long, $900~\mathrm{nm}$ device. In addition, subgap conductance distributions are investigated, and correlations between the left and right distributions are identified based on their mutual information.
G. L. R. Anselmetti, E. A. Martinez, G. C. Ménard, D. Puglia, F. K. Malinowski, J. S. Lee, S. Choi, M. Pendharkar, C. J. Palmstrøm, C. M. Marcus, L. Casparis, A. P. Higginbotham Journal reference: Phys. Rev. B 100, 205412 (2019) [pdf] DOI: 10.1103/PhysRevB.100.205412

Dispersive sensing in hybrid InAs/Al nanowires 
Abstract
 Dispersive charge sensing is realized in hybrid semiconductorsuperconductor nanowires in gatedefined single and doubleisland device geometries. Signaltonoise ratios (SNRs) were measured both in the frequency and time domain. Frequencydomain measurements were carried out as a function of frequency and power and yield a charge sensitivity of $1 \times 10^{3} e/\sqrt{\rm Hz}$ for an 11 MHz measurement bandwidth. Timedomain measurements yield SNR > 1 for 20 $\mu$s integration time. At zero magnetic field, photonassisted tunneling was detected dispersively in a doubleisland geometry, indicating coherent hybridization of the two superconducting islands. At an axial magnetic field of 0.6 T, subgap states are detected dispersively, demonstrating the suitability of the method for sensing in the topological regime.
Deividas Sabonis, Eoin C. T. O'Farrell, Davydas Razmadze, David M. T. van Zanten, Judith Suter, Peter Krogstrup, Charles M. Marcus Journal reference: Appl. Phys. Lett. 115, 102601 (2019) [pdf] DOI: 10.1063/1.5116377

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.
 1902.07570v1 [pdf]
J. T. Mlack, K. S. Wickramasinghe, T. D. Mishima, M. B. Santos, C. M. Marcus [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 Journal reference: Phys. Rev. B 100, 165307 (2019) [pdf] DOI: 10.1103/PhysRevB.100.165307

RadioFrequency Methods for MajoranaBased Quantum Devices: Fast Charge Sensing and PhaseDiagram 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.
Davydas Razmadze, Deividas Sabonis, Filip K. Malinowski, Gerbold C. Menard, Sebastian Pauka, Hung Nguyen, David M. T. van Zanten, Eoin C. T. O'Farrell, Judith Suter, Peter Krogstrup, Ferdinand Kuemmeth, Charles M. Marcus Journal reference: Phys. Rev. Applied 11, 064011 (2019) [pdf] DOI: 10.1103/PhysRevApplied.11.064011

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) [pdf] 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) [pdf] DOI: 10.1038/s4146701909194x

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) [pdf] DOI: 10.1103/PhysRevB.99.085434

Fast Charge Sensing of Si/SiGe Quantum Dots via a HighFrequency Accumulation Gate 
Abstract
 2018

Nonlocality of Majorana modes in hybrid nanowires 
Abstract
 Spatial separation of Majorana zero modes distinguishes trivial from topological midgap states and is key to topological protection in quantum computing applications. Although signatures of Majorana zero modes in tunneling spectroscopy have been reported in numerous studies, a quantitative measure of the degree of separation, or nonlocality, of the emergent zero modes has not been reported. Here, we present results of an experimental study of nonlocality of emergent zero modes in superconductorsemiconductor hybrid nanowire devices. The approach takes advantage of recent theory showing that nonlocality can be measured from splitting due to hybridization of the zero mode in resonance with a quantum dot state at one end of the nanowire. From these splittings as well as anticrossing of the dot states, measured for even and odd occupied quantum dot states, we extract both the degree of nonlocality of the emergent zero mode, as well as the spin canting angles of the nonlocal zero mode. Depending on the device measured, we obtain either a moderate degree of nonlocality, suggesting a partially separated Andreev subgap state, or a highly nonlocal state consistent with a welldeveloped Majorana mode.
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) [pdf] DOI: 10.1103/PhysRevB.98.085125

Effective

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

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) [pdf] 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) [pdf] DOI: 10.1103/PhysRevMaterials.2.093401

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) [pdf] DOI: 10.1103/PhysRevMaterials.2.044202

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) [pdf] DOI: 10.1038/s415650180207y

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) [pdf] DOI: 10.1103/PhysRevX.8.011045

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) [pdf] DOI: 10.1103/PhysRevB.97.060508

Nonlocality of Majorana modes in hybrid nanowires 
Abstract
 2017

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) [pdf] DOI: 10.1103/PhysRevLett.119.176805

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) [pdf] 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) [pdf] 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) [pdf] DOI: 10.1103/PhysRevLett.119.227701

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) [pdf] DOI: 10.1103/PhysRevLett.118.177702

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) [pdf] DOI: 10.1103/PhysRevB.96.045443

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) [pdf] 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) [pdf] DOI: 10.1038/nphys4224

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) [pdf] 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) [pdf] DOI: 10.1021/acs.nanolett.6b04964

Giant SpinOrbit Splitting in Inverted

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) [pdf] 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) [pdf] DOI: 10.1103/PhysRevB.95.035307

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) [pdf] DOI: 10.1103/PhysRevApplied.7.034029

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) [pdf] DOI: 10.1038/nnano.2016.227

ZeroEnergy Modes from Coalescing Andreev States in a TwoDimensional SemiconductorSuperconductor Hybrid Platform 
Abstract
 2016

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) [pdf] DOI: 10.1126/science.aaf3961

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) [pdf] 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) [pdf] DOI: 10.1103/PhysRevApplied.6.054017

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) [pdf] DOI: 10.1088/13672630/18/8/083005

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) [pdf] 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

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) [pdf] 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

Majorana bound state in a coupled quantumdot hybridnanowire system 
Abstract
 2015

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

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

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

SemiconductorNanowireBased Superconducting Qubit 
Abstract
 2014

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

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

Hole Spin Coherence in a Ge/Si Heterostructure Nanowire 
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.
 1309.4569v1 [pdf]
N. L. B. Ziino, P. Krogstrup, M. H. Madsen, E. Johnson, J. B. Wagner, C. M. Marcus, J. Nygård, T. S. Jespersen [pdf]

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 Long

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

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

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

Epitaxial aluminum contacts to InAs nanowires 
Abstract
 2012


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


Abstract