Publications by Peter Krogstrup

  • 2025
    • Spin-split superconductivity in spin-orbit coupled hybrid nanowires with ferromagnetic barriers - Abstract
      • We report transport studies of hybrid Josephson junctions based on semiconducting InAs nanowires with fully overlapping epitaxial ferromagnetic insulator EuS and superconducting Al partial shells. Current-biased measurements reveal a hysteretic superconducting window with a sizable supercurrent near the coercive field of the ferromagnetic insulator, accompanied by multiple Andreev reflections. Tunneling spectroscopy shows a superconducting gap characterized by three peaks, which we attribute to tunneling between exchange-split superconductors. A theoretical model reproduces the observed features and indicates that spin mixing, driven by sizable spin-orbit coupling, is essential to their formation. Our results demonstrate proximity-induced superconductivity through a ferromagnetic insulator and establish a new platform for exploring spin-triplet pairing.
    • 2506.08247v2 [pdf]
      J. Zhao, A. Mazanik, D. Razmadze, Y. Liu, P. Krogstrup, F. S. Bergeret, S. Vaitiekėnas
      [pdf]
  • 2024
    • Supercurrent transport through - Abstract
      • We experimentally investigate supercurrent through Coulomb islands, where island and leads are fabricated from semiconducting nanowires with fully surrounding superconducting shells. Applying flux along the wire yields a series of destructive Little-Parks lobes with reentrant supercurrent. We find Coulomb blockade with 2$e$ peak spacing in the zeroth lobe and 1$e$ average spacing, with regions of significant even-odd modulation, in the first lobe. Evolution of Coulomb-peak amplitude through the first lobe is consistent with a theoretical model of supercurrent carried predominantly by zero-energy states in the leads and the island.
    • D. Razmadze, R. Seoane Souto, E. C. T. O'Farrell, P. Krogstrup, M. Leijnse, C. M. Marcus, S. Vaitiekėnas
      Journal reference: Phys. Rev. B 109, L041302 (2024) [pdf]
      DOI: 10.1103/PhysRevB.109.L041302
  • 2023
    • Supercurrent reversal in ferromagnetic hybrid nanowire Josephson junctions - Abstract
      • We report supercurrent transport measurements in hybrid Josephson junctions comprised of semiconducting InAs nanowires with epitaxial ferromagnetic insulator EuS and superconducting Al coatings. The wires display a hysteretic superconducting window close to the coercivity, away from zero external magnetic field. Using a multi-interferometer setup, we measure the current-phase relation of multiple magnetic junctions and find an abrupt switch between $π$ and 0 phases within the superconducting window. We attribute the 0-$π$ transition to the discrete flipping of the EuS domains and provide a qualitative theory showing that a sizable exchange field can polarize the junction and lead to the supercurrent reversal. Both $0$ and $π$ phases can be realized at zero external field by demagnetizing the wire.
    • D. Razmadze, R. Seoane Souto, L. Galletti, A. Maiani, Y. Liu, P. Krogstrup, C. Schrade, A. Gyenis, C. M. Marcus, S. Vaitiekėnas
      Journal reference: Phys. Rev. B 107, L081301 (2023) [pdf]
      DOI: 10.1103/PhysRevB.107.L081301
    • Parity switching in a full-shell superconductor-semiconductor nanowire qubit - Abstract
      • The rate of charge-parity switching in a full-shell superconductor-semiconductor nanowire qubit is measured by directly monitoring the dispersive shift of a readout resonator. At zero magnetic field, the measured switching time scale $T_P$ is on the order of 100 ms. Two-tone spectroscopy data post-selected on charge-parity is demonstrated. With increasing temperature or magnetic field, TP is at first constant, then exponentially suppressed, consistent with a model that includes both non-equilibrium and thermally activated quasiparticles. As TP is suppressed, qubit lifetime T1 also decreases. The long $T_P\sim 0.1$ s at zero field is promising for future development of qubits based on hybrid nanowires.
    • O. Erlandsson, D. Sabonis, A. Kringhøj, T. W. Larsen, P. Krogstrup, K. D. Petersson, C. M. Marcus
      Journal reference: Phys. Rev. B 108, L121406 (2023) [pdf]
      DOI: 10.1103/PhysRevB.108.L121406
    • Electrostatic control of quasiparticle poisoning in a hybrid semiconductor-superconductor island - Abstract
      • The performance of superconducting devices is often degraded by the uncontrolled appearance and disappearance of quasiparticles, a process known as poisoning. We demonstrate electrostatic control of quasiparticle poisoning in the form of single-charge tunneling across a fixed barrier onto a Coulomb island in an InAs/Al hybrid nanowire. High-bandwidth charge sensing was used to monitor charge occupancy of the island across Coulomb blockade peaks, where tunneling rates were maximal, and Coulomb valleys, where tunneling was absent. Electrostatic gates changed on-peak tunneling rates by two orders of magnitude for a barrier with fixed normal-state resistance, which we attribute to gate dependence of the size and softness of the induced superconducting gap on the island, corroborated by separate density-of-states measurements. Temperature and magnetic field dependence of tunneling rates are also investigated.
    • H. Q. Nguyen, D. Sabonis, D. Razmadze, E. T. Mannila, V. F. Maisi, D. M. T. van Zanten, E. C. T. O'Farrell, P. Krogstrup, F. Kuemmeth, J. P. Pekola, C. M. Marcus
      Journal reference: Phys. Rev. B 108, L041302 (2023) [pdf]
      DOI: 10.1103/PhysRevB.108.L041302
  • 2022
    • Evidence for spin-polarized bound states in semiconductor–superconductor–ferromagnetic-insulator islands - Abstract
      • We report Coulomb blockade transport studies of semiconducting InAs nanowires grown with epitaxial superconducting Al and ferromagnetic insulator EuS on overlapping facets. Comparing experiment to a theoretical model, we associate cotunneling features in even-odd bias spectra with spin-polarized Andreev levels. Results are consistent with zero-field spin splitting exceeding the induced superconducting gap. Energies of subgap states are tunable on either side of zero via electrostatic gates.
    • S. Vaitiekėnas, R. Seoane Souto, Y. Liu, P. Krogstrup, K. Flensberg, M. Leijnse, C. M. Marcus
      Journal reference: Phys. Rev. B 105, L041304 (2022) [pdf]
      DOI: 10.1103/PhysRevB.105.L041304
  • 2021
    • Magnetic-Field-Compatible Superconducting Transmon Qubit - Abstract
      • We present a hybrid semiconductor-based 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 low-energy 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
    • Andreev Modes from Phase Winding in a Full-Shell Nanowire-Based 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 Little-Parks effect, numerous coherent transitions are observed in the first reentrant lobe, where the shell carries 2π 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 winding-induced 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
    • Zero-bias 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 zero-bias 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 non-overlapping 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
      Journal reference: Nat. Phys. 17, 43 (2021) [pdf]
      DOI: 10.1038/s41567-020-1017-3
  • 2020
    • Two-impurity Yu-Shiba-Rusinov states in coupled quantum dots - Abstract
      • Using double quantum dots as the weak link of a Josephson junction, we realize the superconducting analog of the celebrated two-impurity Kondo model. The device shows a cusped current-voltage characteristic, which can be modelled by an overdamped circuit relating the observed cusp current to the Josephson critical current. The gate dependence of the cusp current and of the subgap spectra are used as complementary ground-state indicators to demonstrate gate-tuned changes of the ground state from an inter-dot singlet to independently screened Yu-Shiba-Rusinov (YSR) singlets. In contrast to the two-impurity Kondo effect in normal-state systems, the crossover between these two singlets is heralded by quantum phase boundaries to nearby doublet YSR phases in which only a single spin is screened.
    • J. C. Estrada Saldaña, A. Vekris, R. Žitko, G. Steffensen, P. Krogstrup, J. Paaske, K. Grove-Rasmussen, J. Nygård
      Journal reference: Physical Review B 102, 195143 (2020) [pdf]
      DOI: 10.1103/PhysRevB.102.195143
    • Parity-Protected Superconductor-Semiconductor 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 parity-protected qubit based on voltage-controlled semiconductor nanowire Josephson junctions, taking advantage of the higher harmonic content in the energy-phase relation of few-channel junctions. A symmetric interferometer formed by two such junctions, gate-tuned into balance and frustrated by a half-quantum of applied flux, yields a cos(2φ) 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
    • Quantum Dot Parity Effects in Trivial and Topological Josephson Junctions - Abstract
      • An odd-occupied quantum dot in a Josephson junction can flip transmission phase, creating a π-junction. When the junction couples topological superconductors, no phase flip is expected. We investigate this and related effects in a full-shell hybrid interferometer, using gate voltage to control dot-junction parity and axial magnetic flux to control the transition from trivial to topological superconductivity. Enhanced zero-bias conductance and critical current for odd parity in the topological phase reflects hybridization of the confined spin with zero-energy 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
    • 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 mean-field theory across multiple reentrant transitions. Near the crossover between destructive and nondestructive regimes, an anomalous metal phase is observed with temperature-independent resistance, controlled over two orders of magnitude by a millitesla-scale 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
    • Suppressed Charge Dispersion via Resonant Tunneling in a Single-Channel Transmon - Abstract
      • We demonstrate strong suppression of charge dispersion in a semiconductor-based 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 single-channel 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 semiconductor-superconductor 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 field-effect 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 normal-state resistance. Gradually opening the FET to the monitoring circuit allows the influence of weak-to-strong 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 gate-controlled 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
    • Flux-induced topological superconductivity in full-shell 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 Little-Parks 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 zero-energy state for flux around Φ_0 = h/2e, corresponding to 2π phase winding. Coulomb peak spacing in full-shell 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
  • 2019
    • Voltage-controlled superconducting quantum bus - Abstract
      • We demonstrate the ability of an epitaxial semiconductor-superconductor nanowire to serve as a field-effect 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 qubit-qubit coupling between the on and off states without detrimental effect on qubit coherence. High-bandwidth 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
  • 2018
    • 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 electron-hole and left-right 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 two-impurity Anderson model.
    • J. C. Estrada Saldaña, A. Vekris, G. Steffensen, R. Žitko, P. Krogstrup, J. Paaske, K. Grove-Rasmussen, J. Nygård
      Journal reference: Phys. Rev. Lett. 121, 257701 (2018) [pdf]
      DOI: 10.1103/PhysRevLett.121.257701
    • 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 superconductor-semiconductor 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 well-developed Majorana mode.
    • M. T. Deng, S. Vaitiekénas, E. Prada, P. San-Jose, 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 g-factor 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 step-like 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 g-factor of the proximitizing superconductor. Additionally, we observe the closing and reopening of a gap in the subgap spectrum coincident with the appearance of a zero-bias 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
    • Anharmonicity of a superconducting qubit with a few-mode Josephson junction - Abstract
      • Coherent operation of gate-voltage-controlled hybrid transmon qubits (gatemons) based on semiconductor nanowires was recently demonstrated. Here we experimentally investigate the anharmonicity in epitaxial InAs-Al 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
  • 2017
    • 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 normal-metal 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 μs) and sets a bound for a weakly coupled island (> 10 μs). Fluctuations in the gate-voltage 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
    • Normal, superconducting and topological regimes of hybrid double quantum dots - Abstract
      • Epitaxial semiconductor-superconductor 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 double-quantum-dot devices made from InAs nanowires with a patterned epitaxial Al two-facet shell that proximitizes two gate-defined segments along the nanowire. We follow the evolution of mesoscopic superconductivity and charging energy in this system as a function of magnetic field and voltage-tuned barriers. Inter-dot 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
  • 2016
    • Majorana bound state in a coupled quantum-dot hybrid-nanowire 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 end-dot 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, 1557-1562 (2016) [pdf]
      DOI: 10.1126/science.aaf3961
    • InAs Nanowire with Epitaxial Aluminum as a Single-Electron Transistor with Fixed Tunnel Barriers - Abstract
      • We report on fabrication of single-electron 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 single-electron 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
    • 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 fault-tolerant quantum computers [1]. They are expected to exhibit non-Abelian 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 mode-splitting potentially explained by hybridization of Majoranas. Here, we use Coulomb-blockade spectroscopy in an InAs nanowire segment with epitaxial aluminum, which forms a proximity-induced superconducting Coulomb island (a Majorana island) that is isolated from normal-metal leads by tunnel barriers, to measure the splitting of near-zero-energy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometers, sub-gap 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 zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes. Our results help explain the trivial-to-topological transition in finite systems and to quantify the scaling of topological protection with end-mode 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
    • Gatemon Benchmarking and Two-Qubit 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 flux-controlled transmons. Here, we present experiments with a two-qubit gatemon circuit. We characterize qubit coherence and stability and use randomized benchmarking to demonstrate single-qubit gate errors below 0.7% for all gates, including voltage-controlled $Z$ rotations. We show coherent capacitive coupling between two gatemons and coherent swap operations. Finally, we perform a two-qubit controlled-phase 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
    • Two-dimensional epitaxial superconductor-semiconductor 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 spin-orbit coupling (SOC). For example, theory [1-4] indicates that the interface between a one-dimensional (1D) semiconductor (Sm) with strong SOC and a superconductor (S) hosts Majorana modes with nontrivial topological properties [5-8]. Recently, epitaxial growth of Al on InAs nanowires was shown to yield a high quality S-Sm 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 two-dimensional (2D) InAs/InGaAs heterostructure with epitaxial Al, yielding a planar S-Sm system with structural and transport characteristics as good as the epitaxial wires. The realization of 2D epitaxial S-Sm systems represent a significant advance over wires, allowing extended networks via top-down processing. Among numerous potential applications, this new material system can serve as a platform for complex networks of topological superconductors with gate-controlled Majorana zero modes [1-4]. We demonstrate gateable Josephson junctions and a highly transparent 2D S-Sm 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
  • 2015
    • Raman spectroscopy and electrical properties of InAs nanowires with local oxidation enabled by substrate micro-trenches and laser irradiation - Abstract
      • The thermal gradient along indium-arsenide 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 micro-Raman 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) [pdf]
      DOI: 10.1063/1.4937442
    • Semiconductor-Nanowire-Based Superconducting Qubit - Abstract
      • We introduce a hybrid qubit based on a semiconductor nanowire with an epitaxially grown superconductor layer. Josephson energy of the transmon-like device ("gatemon") is controlled by an electrostatic gate that depletes carriers in a semiconducting weak link region. Strong coupling to an on-chip microwave cavity and coherent qubit control via gate voltage pulses is demonstrated, yielding reasonably long relaxation times (0.8 μs) and dephasing times (1 μs), exceeding gate operation times by two orders of magnitude, in these first-generation 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 states---a situation that nullifies topological protection. Here, we report a hard superconducting gap induced by proximity effect in a semiconductor, using epitaxial Al-InAs superconductor-semiconductor nanowires. The hard gap, along with favorable material properties and gate-tunability, 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 Majorana-based topological quantum computers. Quasiparticle dynamics have been studied in detail in metallic superconductors but remain relatively unexplored in semiconductor-superconductor 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 gate-confined semiconductor nanowire with an epitaxially grown superconductor layer, yielding an isolated, proximitized nanowire segment. We identify Andreev-like 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 semiconductor-metal core-shell 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 gate-controlled 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 soft-gap 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
  • 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 barrier-free electrical contact, and the properties in the superconducting state are investigated at low temperature. Half-covering aluminum contacts are realized without the need of lithography and we demonstrate how to controllably insert high-band gap layers in the interface region. These developments are relevant to hybrid superconductor-nanowire 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]