Center for Quantum Devices > Research > Publications > Peter Krogstrup
Publications by Peter Krogstrup
 2019

Revealing chargetunneling processes between a quantum dot and a
superconducting island through gate sensing 
Abstract
 We report the detection and identification of chargetunneling processes between a quantum dot and a superconducting island through radiofrequency gate sensing. We are able to resolve spindependent quasiparticle tunneling as well as twoparticle tunneling involving Cooperpairs. The sensor allows us to characterize the superconductor excitation spectrum, enabling us to access subgap states without transport. Our results provide crucial guidance for future dispersive parity measurements of Majorana modes, which can be realized by detecting the paritydependent tunneling between dots and islands.
Jasper van Veen, Damaz de Jong, Lin Han, Christian Prosko, Peter Krogstrup, John D. Watson, Leo P. Kouwenhoven, Wolfgang Pfaff 1903.09066v1 [pdf]

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

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

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

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

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

Broadband microwave spectroscopy of semiconductor nanowirebased
Cooperpair transistors 
Abstract
 The Cooperpair transistor (CPT), a small superconducting island enclosed between two Josephson weak links, is the atomic building block of various superconducting quantum circuits. Utilizing gatetunable semiconductor channels as weak links, the energy scale associated with the Josephson tunneling can be changed with respect to the charging energy of the island, tuning the extent of its charge fluctuations. Here we directly demonstrate this control by mapping the energy level structure of a CPT made of an indium arsenide (InAs) nanowire (NW) with a superconducting aluminum (Al) shell. We extract the device parameters based on the exhaustive modeling of the quantum dynamics of the phasebiased nanowire CPT and directly measure the evenodd parity occupation ratio as a function of the device temperature, relevant for superconducting and prospective topological qubits.
Alex Proutski, Dominique Laroche, Bas van 't Hooft, Peter Krogstrup, Jesper Nygård, Leo P. Kouwenhoven, Attila Geresdi 1901.10992v1 [pdf]

Revealing chargetunneling processes between a quantum dot and a
superconducting island through gate sensing 
Abstract
 2018

TwoImpurity YuShibaRusinov States in Coupled Quantum Dots 
Abstract
 Using Coulomb blockaded double quantum dots, we realize the superconducting analog of the celebrated twoimpurity Kondo model. Focusing on gate regions with a single spin1/2 on each dot, we demonstrate gatetuned changes of the ground state from an interdot singlet to independently screened YuShibaRusinov singlets. In contrast to the zerotemperature twoimpurity Kondo model, the crossover between these two singlets is heralded by quantum phase boundaries to nearby doublet phases, in which only a single spin is screened. We identify all four ground states via transport measurements.
J. C. Estrada Saldaña, A. Vekris, R. Žitko, G. Steffensen, P. Krogstrup, J. Paaske, K. GroveRasmussen, J. Nygård 1812.09303v1 [pdf]

Rapid detection of coherent tunneling in an InAs nanowire quantum dot
through dispersive gate sensing 
Abstract
 Dispersive sensing is a powerful technique that enables scalable and highfidelity readout of solidstate quantum bits. In particular, gatebased dispersive sensing has been proposed as the readout mechanism for future topological qubits, which can be measured by single electrons tunneling through zeroenergy modes. The development of such a readout requires resolving the coherent charge tunneling amplitude from a quantum dot in a Majoranazeromode host system faithfully on short time scales. Here, we demonstrate rapid singleshot detection of a coherent singleelectron tunneling amplitude between InAs nanowire quantum dots. We have realized a sensitive dispersive detection circuit by connecting a subGHz, lumped element microwave resonator to a highlever arm gate on one of dots. The resulting large dotresonator coupling leads to an observed dispersive shift that is of the order of the resonator linewidth at charge degeneracy. This shift enables us to differentiate between Coulomb blockade and resonance, corresponding to the scenarios expected for qubit state readout, with a signal to noise ratio exceeding 2 for an integration time of 1 microsecond. Our result paves the way for single shot measurements of fermion parity on microsecond timescales in topological qubits.
Damaz de Jong, Jasper van Veen, Luca Binci, Amrita Singh, Peter Krogstrup, Leo P. Kouwenhoven, Wolfgang Pfaff, John D. Watson Journal reference: Phys. Rev. Applied 11, 044061 (2019) [ 1812.08609v1 ] DOI: 10.1103/PhysRevApplied.11.044061

SpinOrbit Splitting of Andreev States Revealed by Microwave Spectroscopy 
Abstract
 We have performed microwave spectroscopy of Andreev states in superconducting weak links tailored in an InAsAl (corefull shell) epitaxiallygrown nanowire. The spectra present distinctive features, with bundles of four lines crossing when the superconducting phase difference across the weak link is 0 or $\pi.$ We interpret these as arising from zerofield spinsplit Andreev states. A simple analytical model, which takes into account the Rashba spinorbit interaction in a nanowire containing several transverse subbands, explains these features and their evolution with magnetic field. Our results show that the spin degree of freedom is addressable in Josephson junctions, and constitute a first step towards its manipulation.
L. Tosi, C. Metzger, M. F. Goffman, C. Urbina, H. Pothier, Sunghun Park, A. Levy Yeyati, J. Nygård, P. Krogstrup Journal reference: Phys. Rev. X 9, 011010 (2019) [ 1810.02591v2 ] DOI: 10.1103/PhysRevX.9.011010

Supercurrent in a Double Quantum Dot 
Abstract
 We demonstrate the Josephson effect in a serial double quantum dot defined in a nanowire with epitaxial superconducting leads. The supercurrent stability diagram adopts a honeycomb pattern with electronhole and leftright reflection symmetry. We observe sharp discontinuities in the magnitude of the critical current, $I_c$, as a function of dot occupation, related to doublet to singlet ground state transitions. Detuning of the energy levels offers a tuning knob for $I_c$, which attains a maximum at zero detuning. The consistency between experiment and theory indicates that our device is a faithful realization of the twoimpurity Anderson model.
J. C. Estrada Saldaña, A. Vekris, G. Steffensen, R. Žitko, P. Krogstrup, J. Paaske, K. GroveRasmussen, J. Nygård Journal reference: Phys. Rev. Lett. 121, 257701 (2018) [ 1808.05837v2 ] DOI: 10.1103/PhysRevLett.121.257701

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

pGaAs Nanowire Metal–Semiconductor FieldEffect Transistors with NearThermal Limit Gating 
Abstract
 Difficulties in obtaining highperformance ptype transistors and gate insulator chargetrapping effects present two major challenges for IIIV complementary metaloxide semiconductor (CMOS) electronics. We report a pGaAs nanowire metalsemiconductor fieldeffect transistor (MESFET) that eliminates the need for a gate insulator by exploiting the Schottky barrier at the metalGaAs interface. Our device beats the bestperforming pGaSb nanowire metaloxidesemiconductor field effect transistor (MOSFET), giving a typical subthreshold swing of 62 mV/dec, within 4% of the thermal limit, onoff ratio $\sim 10^{5}$, onresistance ~700 k$\Omega$, contact resistance ~30 k$\Omega$, peak transconductance 1.2 $\mu$S/$\mu$m and highfidelity ac operation at frequencies up to 10 kHz. The device consists of a GaAs nanowire with an undoped core and heavily Bedoped shell. We carefully etch back the nanowire at the gate locations to obtain Schottkybarrier insulated gates whilst leaving the doped shell intact at the contacts to obtain low contact resistance. Our device opens a path to allGaAs nanowire MESFET complementary circuits with simplified fabrication and improved performance.
A. R. Ullah, F. Meyer, J. G. Gluschke, S. Naureen, P. Caroff, P. Krogstrup, J. Nygard, A. P. Micolich Journal reference: Nano Letters 18, 56735680 (2018) [ 1809.10479v1 ] DOI: 10.1021/acs.nanolett.8b02249

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

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

Hybridization at SuperconductorSemiconductor Interfaces 
Abstract
 Hybrid superconductorsemiconductor devices are currently one of the most promising platforms for realizing Majorana zero modes. Their topological properties are controlled by the band alignment of the two materials, as well as the electrostatic environment, which are currently not well understood. Here, we pursue to fill in this gap and address the role of band bending and superconductorsemiconductor hybridization in such devices by analyzing a gated single AlInAs interface using a selfconsistent SchrodingerPoisson approach. Our numerical analysis shows that the band bending leads to an interface quantum well, which localizes the charge in the system near the superconductorsemiconductor interface. We investigate the hybrid band structure and analyze its response to varying the gate voltage and thickness of the Al layer. This is done by studying the hybridization degrees of the individual subbands, which determine the induced pairing and effective $g$factors. The numerical results are backed by approximate analytical expressions which further clarify key aspects of the band structure. We find that one can obtain states with strong superconductorsemiconductor hybridization at the Fermi energy, but this requires a fine balance of parameters, with the most important constraint being on the width of the Al layer. In fact, in the regime of interest, we find an almost periodic dependence of the hybridization degree on the Al width, with a period roughly equal to the thickness of an Al monolayer. This implies that disorder and shape irregularities, present in realistic devices, may play an important role for averaging out this sensitivity and, thus, may be necessary for stabilizing the topological phase.
August E. G. Mikkelsen, Panagiotis Kotetes, Peter Krogstrup, Karsten Flensberg Journal reference: Phys. Rev. X 8, 031040 (2018) [ 1801.03439v3 ] DOI: 10.1103/PhysRevX.8.031040

Magneticfielddependent quasiparticle dynamics of nanowire singleCooperpair transistors 
Abstract
 Parity control of superconducting islands hosting Majorana zero modes (MZMs) is required to operate topological qubits made from proximitized semiconductor nanowires. We, therefore, study parity effects in hybrid InAsAl singleCooperpair transistors (SCPTs) as a first step. In particular, we investigate the gatecharge supercurrent modulation and observe a consistent 2$e$periodic pattern indicating a general lack of lowenergy subgap states in these nanowires at zero magnetic field. In a parallel magnetic field, an evenodd pattern develops with a gatecharge spacing that oscillates as a function of field demonstrating that the modulation pattern is sensitive to the presence of a single subgap state. In addition, we find that the parity lifetime of the SCPT decreases exponentially with magnetic field as the subgap state approaches zero energy. Our work highlights the important role that intentional quasiparticle traps and superconducting gap engineering would play in topological qubits that require quenching of the island charge dispersion.
Jasper van Veen, Alex Proutski, Torsten Karzig, Dmitry I. Pikulin, Roman M. Lutchyn, Jesper Nygård, Peter Krogstrup, Attila Geresdi, Leo P. Kouwenhoven, John D. Watson Journal reference: Phys. Rev. B 98, 174502 (2018) [ 1805.10266v1 ] DOI: 10.1103/PhysRevB.98.174502

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

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

Nearthermal limit gating in heavily doped IIIV semiconductor nanowires using polymer electrolytes 
Abstract
 Doping is a common route to reducing nanowire transistor onresistance but has limits. High doping level gives significant loss in gate performance and ultimately complete gate failure. We show that electrolyte gating remains effective even when the Be doping in our GaAs nanowires is so high that traditional metaloxide gates fail. In this regime we obtain a combination of subthreshold swing and contact resistance that surpasses the best existing ptype nanowire MOSFETs. Our subthreshold swing of 75 mV/dec is within 25% of the roomtemperature thermal limit and comparable with nInP and nGaAs nanowire MOSFETs. Our results open a new path to extending the performance and application of nanowire transistors, and motivate further work on improved solid electrolytes for nanoscale device applications.
A. R. Ullah, D. J. Carrad, P. Krogstrup, J. Nygård, A. P. Micolich Journal reference: Phys. Rev. Materials 2, 025601 (2018) [ 1710.06950v2 ] DOI: 10.1103/PhysRevMaterials.2.025601

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

TwoImpurity YuShibaRusinov States in Coupled Quantum Dots 
Abstract
 2017

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

Observation of the 4πperiodic Josephson effect in indium arsenide nanowires 
Abstract
 Quantum computation by nonAbelian Majorana zero modes (MZMs) offers an approach to achieve fault tolerance by encoding quantum information in the nonlocal charge parity states of semiconductor nanowire networks in the topological superconductor regime. Thus far, experimental studies of MZMs chiefly relied on single electron tunneling measurements which leads to decoherence of the quantum information stored in the MZM. As a next step towards topological quantum computation, charge parity conserving experiments based on the Josephson effect are required, which can also help exclude suggested nontopological origins of the zero bias conductance anomaly. Here we report the direct measurement of the Josephson radiation frequency in InAs nanowires with epitaxial aluminium shells. For the first time, we observe the $4\pi$periodic Josephson effect above a magnetic field of $\approx 200\,$mT, consistent with the estimated and measured topological phase transition of similar devices.
Dominique Laroche, Daniël Bouman, David J. van Woerkom, Alex Proutski, Chaitanya Murthy, Dmitry I. Pikulin, Chetan Nayak, Ruben J. J. van Gulik, Jesper Nygård, Peter Krogstrup, Leo P. Kouwenhoven, Attila Geresdi Journal reference: Nature Communications 10, 245 (2019) [ 1712.08459v1 ] DOI: 10.1038/s41467018081612

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

Evolution of Nanowire Transmon Qubits and Their Coherence in a Magnetic Field 
Abstract
 We present an experimental study of nanowire transmons at zero and applied inplane magnetic field. With Josephson nonlinearities provided by the nanowires, our qubits operate at higher magnetic fields than standard transmons. Nanowire transmons exhibit coherence up to 70 mT, where the induced superconducting gap in the nanowire closes. We demonstrate that onchip charge noise coupling to the Josephson energy plays a dominant role in the qubit dephasing. This takes the form of stronglycoupled twolevel systems switching on 100 ms timescales and a more weakly coupled background producing $1/f$ noise. Several observations, including the field dependence of qubit energy relaxation and dephasing, are not fully understood, inviting further experimental investigation and theory. Using nanowires with a thinner superconducting shell will enable operation of these circuits up to 0.5 T, a regime relevant for topological quantum computation.
F. Luthi, T. Stavenga, O. W. Enzing, A. Bruno, C. Dickel, N. K. Langford, M. A. Rol, T. S. Jespersen, J. Nygard, P. Krogstrup, L. DiCarlo Journal reference: Phys. Rev. Lett. 120, 100502 (2018) [ 1711.07961v1 ] DOI: 10.1103/PhysRevLett.120.100502

Direct Microwave Measurement of AndreevBoundState Dynamics in a SemiconductorNanowire Josephson Junction 
Abstract
 The modern understanding of the Josephson effect in mesosopic devices derives from the physics of Andreev bound states, fermionic modes that are localized in a superconducting weak link. Recently, Josephson junctions constructed using semiconducting nanowires have led to the realization of superconducting qubits with gatetunable Josephson energies. We have used a microwave circuit QED architecture to detect Andreev bound states in such a gatetunable junction based on an aluminumproximitized InAs nanowire. We demonstrate coherent manipulation of these bound states, and track the boundstate fermion parity in real time. Individual parityswitching events due to nonequilibrium quasiparticles are observed with a characteristic timescale $T_\mathrm{parity} = 160\pm 10~\mathrm{\mu s}$. The $T_\mathrm{parity}$ of a topological nanowire junction sets a lower bound on the bandwidth required for control of Majorana bound states.
M. Hays, G. de Lange, K. Serniak, D. J. van Woerkom, D. Bouman, P. Krogstrup, J. Nygård, A. Geresdi, M. H. Devoret Journal reference: Phys. Rev. Lett. 121, 047001 (2018) [ 1711.01645v1 ] DOI: 10.1103/PhysRevLett.121.047001

Microwave spectroscopy of spinful Andreev bound states in ballistic semiconductor Josephson junctions 
Abstract
 The superconducting proximity effect in semiconductor nanowires has recently enabled the study of new superconducting architectures, such as gatetunable superconducting qubits and multiterminal Josephson junctions. As opposed to their metallic counterparts, the electron density in semiconductor nanosystems is tunable by external electrostatic gates providing a highly scalable and insitu variation of the device properties. In addition, semiconductors with large $g$factor and spinorbit coupling have been shown to give rise to exotic phenomena in superconductivity, such as $\varphi_0$ Josephson junctions and the emergence of Majorana bound states. Here, we report microwave spectroscopy measurements that directly reveal the presence of Andreev bound states (ABS) in ballistic semiconductor channels. We show that the measured ABS spectra are the result of transport channels with gatetunable, high transmission probabilities up to $0.9$, which is required for gatetunable Andreev qubits and beneficial for braiding schemes of Majorana states. For the first time, we detect excitations of a spinsplit pair of ABS and observe symmetrybroken ABS, a direct consequence of the spinorbit coupling in the semiconductor.
David J. van Woerkom, Alex Proutski, Bernard van Heck, Daniël Bouman, Jukka I. Väyrynen, Leonid I. Glazman, Peter Krogstrup, Jesper Nygård, Leo P. Kouwenhoven, Attila Geresdi Journal reference: Nature Physics 13, 876 (2017) [ 1609.00333v2 ] DOI: 10.1038/nphys4150

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

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

Epitaxy of advanced nanowire quantum devices 
Abstract
 Semiconductor nanowires provide an ideal platform for various lowdimensional quantum devices. In particular, topological phases of matter hosting nonAbelian quasiparticles can emerge when a semiconductor nanowire with strong spinorbit coupling is brought in contact with a superconductor. To fully exploit the potential of nonAbelian anyons for topological quantum computing, they need to be exchanged in a wellcontrolled braiding operation. Essential hardware for braiding is a network of singlecrystalline nanowires coupled to superconducting islands. Here, we demonstrate a technique for generic bottomup synthesis of complex quantum devices with a special focus on nanowire networks having a predefined number of superconducting islands. Structural analysis confirms the high crystalline quality of the nanowire junctions, as well as an epitaxial superconductorsemiconductor interface. Quantum transport measurements of nanowire "hashtags" reveal AharonovBohm and weakantilocalization effects, indicating a phase coherent system with strong spinorbit coupling. In addition, a proximityinduced hard superconducting gap is demonstrated in these hybrid superconductorsemiconductor nanowires, highlighting the successful materials development necessary for a first braiding experiment. Our approach opens new avenues for the realization of epitaxial 3dimensional quantum device architectures.
Sasa Gazibegovic, Diana Car, Hao Zhang, Stijn C. Balk, John A. Logan, Michiel W. A. de Moor, Maja C. Cassidy, Rudi Schmits, Di Xu, Guanzhong Wang, Peter Krogstrup, Roy L. M. Op het Veld, Jie Shen, Daniël Bouman, Borzoyeh Shojaei, Daniel Pennachio, Joon Sue Lee, Petrus J. van Veldhoven, Sebastian Koelling, Marcel A. Verheijen, Leo P. Kouwenhoven, Chris J. Palmstrøm, Erik P. A. M. Bakkers Journal reference: Nature 548, 434438 (2017) [ 1705.01480v2 ] DOI: 10.1038/nature23468

Hybrid Nanowire IontoElectron Transducers for Integrated Bioelectronic Circuitry 
Abstract
 A key task in the emerging field of bioelectronics is the transduction between ionic/protonic and electronic signals at high fidelity. This is a considerable challenge since the two carrier types exhibit intrinsically different physics and are best supported by very different materials types  electronic signals in inorganic semiconductors and ionic/protonic signals in organic or bioorganic polymers, gels or electrolytes. Here we demonstrate a new class of organicinorganic transducing interface featuring semiconducting nanowires electrostatically gated using a solid protontransporting hygroscopic polymer. This model platform allows us to study the basic transducing mechanisms as well as deliver high fidelity signal conversion by tapping into and drawing together the best candidates from traditionally disparate realms of electronic materials research. By combining complementary n and ptype transducers we demonstrate functional logic with significant potential for scaling towards highdensity integrated bioelectronic circuitry.
D. J. Carrad, A. B. Mostert, A. R. Ullah, A. M. Burke, H. J. Joyce, H. H. Tan, C. Jagadish, P. Krogstrup, J. Nygård, P. Meredith, A. P. Micolich Journal reference: Nano Letters 17, 827833 (2017) [ 1705.00611v1 ] DOI: 10.1021/acs.nanolett.6b04075

Towards lowdimensional hole systems in Bedoped GaAs nanowires 
Abstract
 GaAs was central to the development of quantum devices but is rarely used for nanowirebased quantum devices with InAs, InSb and SiGe instead taking the leading role. ptype GaAs nanowires offer a path to studying stronglyconfined 0D and 1D hole systems with strong spinorbit effects, motivating our development of nanowire transistors featuring Bedoped ptype GaAs nanowires, AuBe alloy contacts and patterned local gate electrodes towards making nanowirebased quantum hole devices. We report on nanowire transistors with traditional substrate backgates and EBLdefined metal/oxide topgates produced using GaAs nanowires with three different Bedoping densities and various AuBe contact processing recipes. We show that contact annealing only brings small improvements for the moderatelydoped devices under conditions of lower anneal temperature and short anneal time. We only obtain good transistor performance for moderate doping, with conduction freezing out at low temperature for lowlydoped nanowires and inability to reach a clear offstate under gating for the highlydoped nanowires. Our best devices give onstate conductivity 95 nS, offstate conductivity 2 pS, onoff ratio ~$10^{4}$, and subthreshold slope 50 mV/dec at T = 4 K. Lastly, we made a device featuring a moderatelydoped nanowire with annealed contacts and multiple topgates. Topgate sweeps show a plateau in the subthreshold region that is reproducible in separate cooldowns and indicative of possible conductance quantization highlighting the potential for future quantum device studies in this material system.
A. R. Ullah, J. G. Gluschke, P. Krogstrup, C. B. Sørensen, J. Nygård, A. P. Micolich Journal reference: Nanotechnology 28, 134005 (2017) [ 1704.03957v1 ] DOI: 10.1088/13616528/aa6067

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

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

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

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

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

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

Topological Phases in InAs$_{1x}$Sb$_x$: From Novel Topological
Semimetal to Majorana Wire 
Abstract
 Superconductor proximitized onedimensional semiconductor nanowires with strong spinorbit interaction (SOI) are at this time the most promising candidates for the realization of topological quantum information processing. In current experiments the SOI originates predominantly from extrinsic fields, induced by finite size effects and applied gate voltages. The dependence of the topological transition in these devices on microscopic details makes scaling to a large number of devices difficult unless a material with dominant intrinsic bulk SOI is used. Here we show that wires made of certain ordered alloys InAs$_{1x}$Sb$_x$ have spinsplittings up to 20 times larger than those reached in pristine InSb wires. In particular, we show this for a stable ordered CuPtstructure at $x = 0.5$, which has an inverted band ordering and realizes a novel type of a topological semimetal with triple degeneracy points in the bulk spectrum that produce topological surface Fermi arcs. Experimentally achievable strains can drive this compound either into a topological insulator phase, or restore the normal band ordering making the CuPtordered InAs$_{0.5}$Sb$_{0.5}$ a semiconductor with a large intrinsic linear in $k$ bulk spin splitting.
Georg W. Winkler, QuanSheng Wu, Matthias Troyer, Peter Krogstrup, Alexey A. Soluyanov Journal reference: Phys. Rev. Lett. 117, 076403 (2016) [ 1602.07001v3 ] DOI: 10.1103/PhysRevLett.117.076403

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

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

Raman spectroscopy and electrical properties of InAs nanowires with local oxidation enabled by substrate microtrenches and laser irradiation 
Abstract
 The thermal gradient along indiumarsenide nanowires was engineered by a combination of fabricated micro trenches in the supporting substrate and focused laser irradiation. This allowed local control of thermally activated oxidation reactions of the nanowire on the scale of the diffraction limit. The locality of the oxidation was detected by microRaman mapping, and the results were found consistent with numerical simulations of the temperature profile. Applying the technique to nanowires in electrical devices the locally oxidized nanowires remained conducting with a lower conductance as expected for an effectively thinner conducting core.
R. Tanta, M. H. Madsen, Z. Liao, P. Krogstrup, T. Vosch, J. Nygard, T. S. Jespersen Journal reference: Appl. Phys. Lett. 107, 243101 (2015) [ 1601.06583v1 ] DOI: 10.1063/1.4937442

Transport Signatures of Quasiparticle Poisoning in a Majorana Island 
Abstract
 2015

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

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

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

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

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

Gatemon Benchmarking and TwoQubit Operations 
Abstract
 2014

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

Epitaxy of semiconductor–superconductor nanowires 
Abstract
 2013

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

Direct observation of interface and nanoscale compositional modulation in ternary IIIAs heterostructure nanowires 
Abstract
 Straight, axial InAs nanowire with multiple segments of GaInAs were grown. High resolution Xray energydispersive spectroscopy (EDS) mapping reveal the distribution of group III atoms at the axial interfaces and at the sidewalls. Significant Ga enrichment, accompanied by a structural change is observed at the GaInAs/InAs interfaces and a higher Ga concentration for the early grown GaInAs segments. The elemental map and EDS line profile infer Ga enrichment at the facet junctions between the sidewalls. The relative chemical potentials of ternary alloys and the thermodynamic driving force for liquid to solid transition explains the growth mechanisms behind the enrichment.
Sriram Venkatesan, Morten H. Madsen, Herbert Schmid, Peter Krogstrup, Erik Johnson, Christina Scheu Journal reference: Appl. Phys. Lett. 103, 063106 (2013) [pdf] DOI: 10.1063/1.4818338

Advances in the theory of III–V nanowire growth dynamics 
Abstract
 Nanowire (NW) crystal growth via the vapour_liquid_solid mechanism is a complex dynamic process involving interactions between many atoms of various thermodynamic states. With increasing speed over the last few decades many works have reported on various aspects of the growth mechanisms, both experimentally and theoretically. We will here propose a general continuum formalism for growth kinetics based on thermodynamic parameters and transition state kinetics. We use the formalism together with key elements of recent research to present a more overall treatment of III_V NW growth, which can serve as a basis to model and understand the dynamical mechanisms in terms of the basic control parameters, temperature and pressures/beam fluxes. Selfcatalysed GaAs NW growth on Si substrates by molecular beam epitaxy is used as a model system.
Peter Krogstrup, Henrik I. Jørgensen, Erik Johnson, Morten Hannibal Madsen, Claus B. Sørensen, Anna Fontcuberta i Morral, Martin Aagesen, Jesper Nygård, Frank Glas Journal reference: J. Phys. D: Appl. Phys. 46 (2013) 313001 [pdf] DOI: 10.1088/00223727/46/31/313001

Singlenanowire solar cells beyond the Shockley–Queisser limit 
Abstract
 Light management is of great importance to photovoltaic cells, as it determines the fraction of incident light entering the device. An optimal pnjunction combined with an optimal light absorption can lead to a solar cell efficiency above the ShockleyQueisser limit. Here, we show how this is possible by studying photocurrent generation for a single coreshell pin junction GaAs nanowire solar cell grown on a silicon substrate. At one sun illumination a short circuit current of 180 mA/cm^2 is obtained, which is more than one order of magnitude higher than what would be predicted from LambertBeer law. The enhanced light absorption is shown to be due to a light concentrating property of the standing nanowire as shown by photocurrent maps of the device. The results imply new limits for the maximum efficiency obtainable with IIIV based nanowire solar cells under one sun illumination.
Peter Krogstrup, Henrik Ingerslev Jørgensen, Martin Heiss, Olivier Demichel, Jeppe V. Holm, Martin Aagesen, Jesper Nygard, Anna Fontcuberta i Morral Journal reference: Nature Photonics 7, 306310 (2013) [pdf] DOI: 10.1038/nphoton.2013.32

Epitaxial aluminum contacts to InAs nanowires 
Abstract
 2012

Doping incorporation paths in catalystfree Bedoped GaAs nanowires 
Abstract
 The incorporation paths of Be in GaAs nanowires grown by the Gaassisted method in molecular beam epitaxy has been investigated by electrical measurements of nanowires with different doping profiles. We find that Be atoms incorporate preferentially via the nanowire side facets, while the incorporation path through the Ga droplet is negligible. We also demonstrate that Be can diffuse into the volume of the nanowire giving an alternative incorporation path. This work is an important step towards controlled doping of nanowires and will serve as a help for designing future devices based on nanowires.
Alberto Casadei, Peter Krogstrup, Martin Heiss, Jason A. Röhr, Carlo Colombo, Thibaud Ruelle, Shivendra Upadhyay, Claus B. Sørensen, Jesper Nygård, Anna Fontcuberta i Morral Journal reference: Appl. Phys. Lett. 102, 013117 (2013) [pdf] DOI: 10.1063/1.4772020

Doping incorporation paths in catalystfree Bedoped GaAs nanowires 
Abstract
 2010

Absolute dimensions of eclipsing binaries. XXVIII. BK Pegasi and other
Ftype binaries: Prospects for calibration of convective core overshoot 
Abstract
 We present a detailed study of the Ftype detached eclipsing binary BK Peg, based on new photometric and spectroscopic observations. The two components, which have evolved to the upper half of the mainsequence band, are quite different with masses and radii of (1.414 +/ 0.007 Msun, 1.988 +/ 0.008 Rsun) and (1.257 +/ 0.005 Msun, 1.474 +/ 0.017 Rsun), respectively. The 5.49 day period orbit of BK Peg is slightly eccentric (e = 0.053). The measured rotational velocities are 16.6 +/ 0.2 (primary) and 13.4 +/ 0.2 (secondary) km/s. For the secondary component this corresponds to (pseudo)synchronous rotation, whereas the primary component seems to rotate at a slightly lower rate. We derive an iron abundance of [Fe/H] =0.12 +/ 0.07 and similar abundances for Si, Ca, Sc, Ti, Cr and Ni. YonseiYale and VictoriaRegina evolutionary models for the observed metal abundance reproduce BK Peg at ages of 2.75 and 2.50 Gyr, respectively, but tend to predict a lower age for the more massive primary component than for the secondary. We find the same age trend for three other upper mainsequence systems in a sample of well studied eclipsing binaries with components in the 1.151.70 Msun range, where convective core overshoot is gradually ramped up in the models. We also find that the YonseiYale models systematically predict higher ages than the VictoriaRegina models. The sample includes BW Aqr, and as a supplement we have determined a [Fe/H] abundance of 0.07 +/ 0.11 for this late Ftype binary. We propose to use BK Peg, BW Aqr, and other wellstudied 1.151.70 Msun eclipsing binaries to finetune convective core overshoot, diffusion, and possibly other ingredients of modern theoretical evolutionary models.
J. V. Clausen, S. Frandsen, H. Bruntt, E. H. Olsen, B. E. Helt, K. Gregersen, D. Juncher, P. Krogstrup DOI: 10.1051/00046361/201014266 1004.1903v1 [pdf]

Absolute dimensions of eclipsing binaries. XXVIII. BK Pegasi and other
Ftype binaries: Prospects for calibration of convective core overshoot 
Abstract