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We present a superconductor-semiconductor materials system that is both scalable and monolithically integrated on a silicon substrate. It uses selective-area growth of $\mathrm{Al}$-$\mathrm{In}\mathrm{As}$ hybrid structures on a planar III-V buffer layer, grown directly on a high-resistivity silicon substrate. We characterize the electrical properties of this materials system at millikelvin temperatures and observe a high average field-effect mobility of $\ensuremath{\mu}\ensuremath{\approx}3200\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{2}\mathrm{/Vs}$ for the $\mathrm{In}\mathrm{As}$ channel and a hard induced superconducting gap. Josephson junctions exhibit a high interface transmission, $\mathcal{T}\ensuremath{\approx}0.75$, a gate-voltage-tunable switching current with a product of critical current and normal state resistance, ${I}_{C}{R}_{N}\ensuremath{\approx}83\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{V}$, and signatures of multiple Andreev reflections. These results pave the way for scalable and high-coherence gate-voltage-tunable transmon devices and other superconductor-semiconductor hybrids fabricated directly on silicon.

We present a hybrid semiconductor-based superconducting qubit device that remains coherent at magnetic fields up to 1 T. The qubit transition frequency exhibits periodic oscillations with the magnetic field, consistent with interference effects due to the magnetic flux threading the cross section of the proximitized semiconductor nanowire junction. As the 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.

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 2 pi winding of superconducting phase, and are absent in the zeroth lobe. As junction density was increased by gate voltage, qubit coherence was suppressed then lost in the first lobe. These observations and numerical simulations highlight the role of winding-induced Andreev states in the junction.

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 (2(phi)) Josephson element, reflecting coherent transport of pairs of Cooper pairs. We demonstrate that relaxation of the qubit can be suppressed tenfold by tuning into the protected regime.

We investigate superconducting quantum interference devices consisting of two highly transmissive Josephson junctions coupled by a superconducting loop, all defined in an epitaxial InAs/Al heterostructure. A novel device design allows for independent measurements of the Andreev bound state spectrum within the normal region of a junction and the resulting current-phase relation. We show that knowledge of the Andreev bound state spectrum alone is enough to derive the independently measured phase dependent supercurrent. On the other hand, the opposite relation does not generally hold true as details of the energy spectrum are averaged out in a critical current measurement. Finally, quantitative understanding of field dependent spectrum and supercurrent require taking into account the second junction in the loop and the kinetic inductance of the epitaxial Al film.

A semiconductor transmon with an epitaxial Al shell fully surrounding an InAs nanowire core is investigated in the low ${E}_{J}/{E}_{C}$ regime. Little-Parks oscillations as a function of flux along the hybrid wire axis are destructive, creating lobes of reentrant superconductivity separated by a metallic state at a half quantum of applied flux. In the first lobe, phase winding around the shell can induce topological superconductivity in the core. Coherent qubit operation is observed in both the zeroth and first lobes. Splitting of parity bands by coherent single-electron coupling across the junction is not resolved beyond line broadening, placing a bound on Majorana coupling, ${E}_{M}/hl10\text{ }\text{ }\mathrm{MHz}$, much smaller than the Josephson coupling ${E}_{J}/h\ensuremath{\sim}4.7\text{ }\text{ }\mathrm{GHz}$.

We present conductance-matrix measurements of a three-terminal superconductor-semiconductor hybrid device consisting of two normal leads and one superconducting lead. Using a symmetry decomposition of the conductance, we find that the antisymmetric components of pairs of local and nonlocal conductances match at energies below the superconducting gap, consistent with expectations based on a non-interacting scattering matrix approach. Further, the local charge character of Andreev bound states is extracted from the symmetry-decomposed conductance data and is found to be similar at both ends of the device and tunable with gate voltage. Finally, we measure the conductance matrix as a function of magnetic field and identify correlated splittings in low-energy features, demonstrating how conductance-matrix measurements can complement traditional tunneling-probe measurements in the search for Majorana zero modes., Comment: 6 + 2 pages, 4 + 2 figures

Majorana zero modes are leading candidates for topological quantum computation due to non-local qubit encoding and non-abelian exchange statistics. Spatially separated Majorana modes are expected to allow phase-coherent single-electron transport through a topological superconducting island via a mechanism referred to as teleportation. Here we experimentally investigate such a system by patterning an elongated epitaxial InAs-Al island embedded in an Aharonov-Bohm interferometer. With increasing parallel magnetic field, a discrete sub-gap state in the island is lowered to zero energy yielding persistent 1e-periodic Coulomb blockade conductance peaks (e is the elementary charge). In this condition, conductance through the interferometer is observed to oscillate in a perpendicular magnetic field with a flux period of h/e (h is Planck’s constant), indicating coherent transport of single electrons through the islands, a signature of electron teleportation via Majorana modes., Theories predict teleportation of phase-coherent single electrons through a topological superconducting island. Here, the authors report persistent Coulomb blockade conductance peaks due to coherent transport of single electrons through patterned InAs-Al islands embedded in an Aharonov-Bohm interferometer.

Hybrid superconductor-semiconductor nanowires are predicted to undergo a field-induced phase transition from a trivial to a topological superconductor, marked by the closure and re-opening of the excitation gap, followed by the emergence of Majorana bound states at the nanowire ends. Many local density-of-states measurements have reported signatures of the topological phase, however this interpretation has been challenged by alternative explanations. Here, by measuring nonlocal conductance, we identify the closure of the excitation gap in the bulk of the semiconductor before the emergence of zero-bias peaks. This observation is inconsistent with scenarios where zero-bias peaks occur due to end-states with a trivially gapped bulk, which have been extensively considered in the theoretical and experimental literature. We observe that after the gap closes, nonlocal signals fluctuate strongly and persist irrespective of the presence of local-conductance zero-bias peaks. Thus, our observations are also incompatible with a simple picture of clean topological superconductivity. This work presents a new experimental approach for probing the spatial extent of states in Majorana wires, and reveals the presence of a regime with a continuum of spatially extended states and uncorrelated zero-bias peaks.

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.

Nanowires can serve as flexible substrates for hybrid epitaxial growth on selected facets, allowing for design of heterostructures with complex material combinations and geometries. In this work we report on hybrid epitaxy of semiconductor - ferromagnetic insulator - superconductor (InAs/EuS/Al) nanowire heterostructures. We study the crystal growth and complex epitaxial matching of wurtzite InAs / rock-salt EuS interfaces as well as rock-salt EuS / face-centered cubic Al interfaces. Because of the magnetic anisotropy originating from the nanowire shape, the magnetic structure of the EuS phase are easily tuned into single magnetic domains. This effect efficiently ejects the stray field lines along the nanowires. With tunnel spectroscopy measurements of the density of states, we show the material has a hard induced superconducting gap, and magnetic hysteretic evolution which indicates that the magnetic exchange fields are not negligible. These hybrid nanowires fulfil key material requirements for serving as a platform for spin-based quantum applications, such as scalable topological quantum computing., 15 pages, 5 figures

Gate-tunable semiconductor-superconductor 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 current-phase 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 electron-electron interactions are apparent, indicating the presence of a quantum dot. To take into account electrostatic and geometrical effects, we perform microscopic self-consistent Schrodinger-Poisson 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., Comment: Main: 16 pages, 4 figures. Supplement: 8 pages, 4 figures

End-to-end correlated bound states are investigated in superconductor-semiconductor hybrid nanowires at zero magnetic field. Peaks in subgap conductance are independently identified from each wire end, and a cross-correlation function is computed that counts end-to-end coincidences, averaging over thousands of subgap features. Strong correlations in a short, $300~\mathrm{nm}$ device are reduced by a factor of four in a long, $900~\mathrm{nm}$ device. In addition, subgap conductance distributions are investigated, and correlations between the left and right distributions are identified based on their mutual information., 6+4 pages, 4+4 figures

Quantum dot arrays are a versatile platform for the implementation of spin qubits, as high-bandwidth sensor dots can be integrated with single-, double- and triple-dot qubits yielding fast and high-fidelity qubit readout. However, for undoped silicon devices, reflectometry off sensor ohmics suffers from the finite resistivity of the two-dimensional electron gas (2DEG), and alternative readout methods are limited to measuring qubit capacitance, rather than qubit charge. By coupling a surface-mount resonant circuit to the plunger gate of a high-impedance sensor, we realized a fast charge sensing technique that is compatible with resistive 2DEGs. We demonstrate this by acquiring at high speed charge stability diagrams of double- and triple-dot arrays in Si/SiGe heterostructures as well as pulsed-gate single-shot charge and spin readout with integration times as low as 2.4 $\mu$s., Comment: 10 pages, 5 figures, plus supplementary information with 9 pages and 6 figures

We present a superconducting device showing a clear parity effect in the number of electrons, even when there is, on average, a single nonequilibrium quasiparticle present and the parity of the island switches due to quasiparticles tunneling in and out of the device at rates on the order of 100 Hz. We detect the switching by monitoring in real time the charge state of a superconducting island connected to normal leads by tunnel junctions. The quasiparticles are created by Cooper pairs breaking on the island at a rate of a few kHz. We demonstrate that the pair breaking is caused by the backaction of the single-electron transistor used as a charge detector. With sufficiently low probing currents, our superconducting island is free of quasiparticles 97% of the time., Supplementary material included

One-dimensional (1D) electronic transport and induced superconductivity in semiconductor nanostructures are crucial ingredients to realize topological superconductivity. Our approach for topological superconductivity employs a two-dimensional electron gas (2DEG) formed by an InAs quantum well, cleanly interfaced with an epitaxial superconductor (epi-Al). This epi-Al/InAs quantum well heterostructure is advantageous for fabricating large-scale nanostructures consisting of multiple Majorana zero modes. Here, we demonstrate transport studies of building-blocks using a high-quality epi-Al/InAs 2DEG heterostructure, which could be put together to realize various proposed 1D nanowire-based nanostructures and 2DEG-based networks that could host multiple Majorana zero modes. The studies include (1) gate-defined quasi-1D channels in the InAs 2DEG and (2) quantum point contacts for tunneling spectroscopy, as well as induced superconductivity in (3) a ballistic Al-InAs 2DEG-Al Josephson junction. From 1D transport, systematic evolution of conductance plateaus in half-integer conductance quanta is observed with Landé g-factor of 17, indicating the strong spin-orbit coupling and high quality of the InAs 2DEG. The improved 2DEG quality leads to ballistic Josephson junctions with enhanced characteristic parameters such as I

Majorana bound states at the end of nanowires may be used for quantum computation if they can be coupled sufficiently strongly. Here, the Copenhagen lab show strong and tunable coupling, a step along the road towards devices.Hybrid nanowires with proximity-induced superconductivity in the topological regime host Majorana zero modes at their ends. Networks of such structures can produce topologically protected qubits where the fundamental energy scale is given by the inter-pair coupling E-M between the zero modes belonging to different wire segments. Here we report on the spectroscopic measurement of E-M in an InAs/Al double-island device by tracking the position of the microwave-induced quasiparticle excitations using a radiofrequency charge sensor. At zero magnetic field, photon-assisted tunnelling of Cooper pairs allows us to estimate the Josephson coupling between the islands. In the presence of a magnetic field aligned along the nanowire, we observe the 1e periodic excitation spectrum resulting from a zero-energy subgap state that emerges in a magnetic field. The discrete 1e periodic excitation spectrum is consistent with the coherent hybridization of single-electron states belonging to two opposite-parity branches. The dependence of excitation frequency on detuning indicates a sizable (GHz-scale) and controllable hybridization of zero modes across the junction separating islands, a requirement for applications related to Majorana-based qubits.

We study single-electron 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 radio-frequency 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 zero-field superconducting coherence length of ~ 90 nm.

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 structures 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. 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 co-tunnelling peaks as a function of axial magnetic field and show that the individual dots host weakly hybridized Majorana modes.

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., Comment: main text and methods section

We present measurements of one-dimensional superconductor-semiconductor Coulomb islands, fabricated by gate confinement of a two-dimensional InAs heterostructure with an epitaxial Al layer. When tuned via electrostatic side gates to regimes without sub-gap states, Coulomb blockade reveals Cooper-pair mediated transport. When sub-gap states are present, Coulomb peak positions and heights oscillate in a correlated way with magnetic field and gate voltage, as predicted theoretically, with (anti) crossings in (parallel) transverse magnetic field indicating Rashba-type spin-orbit coupling. Overall results are consistent with a picture of overlapping Majorana zero modes in finite wires.

Josephson junctions defined in strong spin orbit semiconductors are highly interesting for the search for topological systems. However, next to topological edge states that emerge in a sufficient magnetic field, trivial edge states can also occur. We study the trivial edge states with superconducting quantum interference measurements on nontopological InAs Josephson junctions. We observe a SQUID pattern, an indication of superconducting edge transport. Also, a remarkable h/e SQUID signal is observed that, as we find, stems from crossed Andreev states.

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., Comment: Combined text and supplementary information, Nature Nanotechnology (2015)

By operating a one-electron quantum dot (fabricated between a multielectron dot and a one-electron reference dot) as a spectroscopic probe, we study the spin properties of a gate-controlled multielectron GaAs quantum dot at the transition between odd and even occupation number. We observe that the multielectron groundstate transitions from spin-1/2-like to singlet-like to triplet-like as we increase the detuning towards the next higher charge state. The sign reversal in the inferred exchange energy persists at zero magnetic field, and the exchange strength is tunable by gate voltages and in-plane magnetic fields. Complementing spin leakage spectroscopy data, the inspection of coherent multielectron spin exchange oscillations provides further evidence for the sign reversal and, inferentially, for the importance of non-trivial multielectron spin exchange correlations., Comment: 8 pages, including 4 main figures and 2 supplementary figurures

The coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconducting circuits, from setting qubit transition frequencies1 and interqubit coupling strengths2 to the gain of parametric amplifiers3 for quantum-limited readout. The inductance is either set by tailoring the metal oxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices with local current-biased flux lines. JJs based on superconductor–semiconductor hybrids represent a tantalizing all-electric alternative. The gatemon is a recently developed transmon variant that employs locally gated nanowire superconductor–semiconductor JJs for qubit control4,5. Here we go beyond proof-of-concept and demonstrate that semiconducting channels etched from a wafer-scale two-dimensional electron gas (2DEG) are a suitable platform for building a scalable gatemon-based quantum computer. We show that 2DEG gatemons meet the requirements6 by performing voltage-controlled single qubit rotations and two-qubit swap operations. We measure qubit coherence times up to ~2 μs, limited by dielectric loss in the 2DEG substrate. Scalable gate tunable superconducting qubits can be realized using a proximitized InAs two-dimensional electron gas.

The superconductor–insulator transition in two dimensions has been widely investigated as a paradigmatic quantum phase transition. The topic remains controversial because many experiments exhibit a metallic regime with saturating low-temperature resistance, which is at odds with conventional theory. Here, we explore this transition in a highly controllable system, a semiconductor heterostructure with epitaxial aluminium, patterned to form a regular array of superconducting islands connected by a gateable quantum well. Spanning nine orders of magnitude in resistance, the system exhibits regimes of superconducting, metallic and insulating behaviour, along with signatures of flux commensurability and vortex penetration. An in-plane magnetic field eliminates the metallic regime, restoring the direct superconductor–insulator transition; it also improves the scaling behaviour while strongly altering the scaling exponent. The phase transition between a superconductor and insulator is examined in a new type of heterostructure. A metallic regime is found, which disappears in a magnetic field, giving fresh insight to a paradigmatic quantum phase transition.

We present a quantitative characterization of an electrically tunable Josephson junction defined in an InAs nanowire proximitized by an epitax-ially-grown superconducting Al shell. The gate-dependence of the number of conduction channels and of the set of transmission coefficients are extracted from the highly nonlinear current-voltage characteristics. Although the transmissions evolve non-monotonically, the number of independent channels can be tuned, and configurations with a single quasi-ballistic channel achieved., Added reference in New Journal of Physics, corrected a few typos, and updated references

We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological $T$-junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states., Comment: 34 pages, 17 figures; v4: minor changes, final version

We report an experimental study of the scaling of zero-bias conductance peaks compatible with Majorana zero modes as a function of magnetic field, tunnel coupling, and temperature in one-dimensional structures fabricated from an epitaxial semiconductor-superconductor 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 field-dependent gap, and collapses onto a simple scaling function in the dimensionless ratio of temperature and tunnel coupling., Accepted in Physical Review Letters

We investigate patterns of critical current as a function of perpendicular and in-plane magnetic fields in superconductor-semiconductor-superconductor (SNS) junctions based on InAs/InGaAs heterostructures with an epitaxial Al layer. This material system is of interest due to its exceptionally good superconductor-semiconductor coupling, as well as large spin-orbit interaction and g-factor in the semiconductor. Thin epitaxial Al allows the application of large in-plane field without destroying superconductivity. For fields perpendicular to the junction, flux focusing results in aperiodic node spacings in the pattern of critical currents known as Fraunhofer patterns by analogy to the related interference effect in optics. Adding an in-plane field yields two further anomalies in the pattern. First, higher order nodes are systematically strengthened, indicating current flow along the edges of the device, as a result of confinement of Andreev states driven by an induced flux dipole; second, asymmetries in the interference appear that depend on the field direction and magnitude. A model is presented, showing good agreement with experiment, elucidating the roles of flux focusing, Zeeman and spin-orbit coupling, and disorder in producing these effects., Includes Supplementary Material

Spin-orbit interaction is investigated in a dual gated InAs/GaSb quantum well. Using an electric field the quantum well can be tuned between a single carrier regime with exclusively electrons as carriers and a two-carriers regime where electrons and holes coexist. Spin-orbit interaction in both regimes manifests itself as a beating in the Shubnikov-de Haas oscillations. In the single carrier regime the linear Dresselhaus strength is characterized by $\beta =$ 28.5 meV$\AA$ and the Rashba coefficient $\alpha$ is tuned from 75 to 53 meV$\AA$ by changing the electric field. In the two-carriers regime the spin splitting shows a nonmonotonic behavior with gate voltage, which is consistent with our band structure calculations.

Epitaxially connected nanowires allow for the design of electron transport experiments and applications beyond the standard two terminal device geometries. In this Letter, we present growth methods of three distinct types of wurtzite structured InAs nanocrosses via the vapor-liquid-solid mechanism. Two methods use conventional wurtzite nanowire arrays as a 6-fold hexagonal basis for growing single crystal wurtzite nanocrosses. A third method uses the 2-fold cubic symmetry of (100) substrates to form well-defined coherent inclusions of zinc blende in the center of the nanocrosses. We show that all three types of nanocrosses can be transferred undamaged to arbitrary substrates, which allows for structural, compositional, and electrical characterization. We further demonstrate the potential for synthesis of as-grown nanowire networks and for using nanowires as shadow masks for in situ fabricated junctions in radial nanowire heterostructures.

We operate a resonant exchange qubit in a highly symmetric triple-dot configuration using IQ-modulated RF pulses. At the resulting three-dimensional sweet spot the qubit splitting is an order of magnitude less sensitive to all relevant control voltages, compared to the conventional operating point, but we observe no significant improvement in the quality of Rabi oscillations. For weak driving this is consistent with Overhauser field fluctuations modulating the qubit splitting. For strong driving we infer that effective voltage noise modulates the coupling strength between RF drive and the qubit, thereby quickening Rabi decay. Application of CPMG dynamical decoupling sequences consisting of up to n = 32 {\pi} pulses significantly prolongs qubit coherence, leading to marginally longer dephasing times in the symmetric configuration. This is consistent with dynamical decoupling from low frequency noise, but quantitatively cannot be explained by effective gate voltage noise and Overhauser field fluctuations alone. Our results inform recent strategies for the utilization of partial sweet spots in the operation and long-distance coupling of triple-dot qubits., Comment: 6 pages, 5 figures

Semiconductor nanowires with superconducting leads are considered promising for quantum computation. The current–phase relation is systematically explored in gate-tunable InAs Josephson junctions, and is shown to provide a clean handle for characterizing the transport properties of these structures. Gate-tunable semiconductor nanowires with superconducting leads have great potential for quantum computation1,2,3 and as model systems for mesoscopic Josephson junctions4,5. The supercurrent, I, versus the phase, φ, across the junction is called the current–phase 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 few-mode junctions with high transmissions. In a gate-tunable junction, we found that the CPR varied with gate voltage: near the onset of supercurrent, we observed behaviour consistent with resonant tunnelling through a single, highly transmitting mode. The gate dependence is consistent with modelled subband structure that includes an effective tunnelling barrier due to an abrupt change in the Fermi level at the boundary of the gate-tuned region. These measurements of skewed, tunable, few-mode CPRs are promising both for applications that require anharmonic junctions6,7 and for Majorana readout proposals8.

We investigate zero-bias conductance peaks that arise from coalescing subgap Andreev states, consistent with emerging Majorana zero modes, in hybrid semiconductor-superconductor wires defined in a two-dimensional InAs/Al heterostructure using top-down lithography and gating. The measurements indicate a hard superconducting gap, ballistic tunneling contact, and in-plane critical fields up to $3$~T. Top-down lithography allows complex geometries, branched structures, and straightforward scaling to multicomponent devices compared to structures made from assembled nanowires., Comment: Includes Supplementary Material

Relaxation and dephasing of hole spins are measured in a gate-defined Ge/Si nanowire double quantum dot using a fast pulsed-gate method and dispersive readout. An inhomogeneous dephasing time $T_2^* \sim 0.18~\mathrm{\mu s}$ exceeds corresponding measurements in III-V semiconductors by more than an order of magnitude, as expected for predominately nuclear-spin-free materials. Dephasing is observed to be exponential in time, indicating the presence of a broadband noise source, rather than Gaussian, previously seen in systems with nuclear-spin-dominated dephasing., Comment: 15 pages, 4 figures

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 {\mu}s) and sets a bound for a weakly coupled island (> 10 {\mu}s). 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., Comment: includes supplementary material

We demonstrate the transfer of the superconducting properties of NbTi---a large-gap high-critical-field superconductor---into an InAs heterostructure via a thin intermediate layer of epitaxial Al. Two device geometries, a Josephson junction and a gate-defined quantum point contact, are used to characterize interface transparency and the two-step proximity effect. In the Josephson junction, multiple Andreev reflection reveal near-unity transparency, with an induced gap $\Delta^*=0.50~\mathrm{meV}$ and a critical temperature of $7.8~\mathrm{K}$. Tunneling spectroscopy yields a hard induced gap in the InAs adjacent to the superconductor of $\Delta^*=0.43~\mathrm{meV}$ with substructure characteristic of both Al and NbTi.

Due to a strong spin-orbit interaction and a large Land\'e g-factor, InSb plays an important role in research on Majorana fermions. To further explore novel properties of Majorana fermions, hybrid devices based on quantum wells are conceived as an alternative approach to nanowires. In this work, we report a pronounced conductance quantization of quantum point contact devices in InSb/InAlSb quantum wells. Using a rotating magnetic field, we observe a large in-plane (|g1|=26) and out-of-plane (|g1|=52) g-factor anisotropy. Additionally, we investigate crossings of subbands with opposite spins and extract the electron effective mass from magnetic depopulation of one-dimensional subbands., Comment: 25 pages including Supporting Information

The growth and the density dependence of the low temperature mobility of a series of two-dimensional electron systems confined to un-intentionally doped, low extended defect density InAs quantum wells with Al$_{1-x}$Ga$_{x}$Sb barriers are reported. The electron mobility limiting scattering mechanisms were determined by utilizing dual-gated devices to study the dependence of mobility on carrier density and electric field independently. Analysis of the possible scattering mechanisms indicate the mobility was limited primarily by rough interfaces in narrow quantum wells and a combination of alloy disorder and interface roughness in wide wells at high carrier density within the first occupied electronic sub-band. At low carrier density the functional dependence of the mobility on carrier density provided evidence of coulombic scattering from charged defects. A gate-tuned electron mobility exceeding 750,000 cm$^{2}$/Vs was achieved at a sample temperature of 2 K., 23 pages, 7 figures, 1 table

A Corbino ring geometry is utilized to analyze edge and bulk conductance of InAs/GaSb quantum well structures. We show that edge conductance exists in the trivial regime of this theoretically predicted topological system with a temperature-insensitive linear resistivity per unit length in the range of 2 kΩ/μm. A resistor network model of the device is developed to decouple the edge conductance from the bulk conductance, providing a quantitative technique to further investigate the nature of this trivial edge conductance, conclusively identified here as being of n type.

Initialization, manipulation, and measurement of a three-spin qubit are demonstrated using a few-electron triple quantum dot, where all operations can be driven by tuning the nearest-neighbor exchange interaction. Multiplexed reflectometry, applied to two nearby charge sensors, allows for qubit readout. Decoherence is found to be consistent with predictions based on gate voltage noise with a uniform power spectrum. The theory of the exchange-only qubit is developed and it is shown that initialization of only two spins suffices for operation. Requirements for full multi-qubit control using only exchange and electrostatic interactions are outlined., Comment: related work at http://marcuslab.harvard.edu

Measurement of multiple Andreev reflection (MAR) in a Josephson junction made from an InAs heterostructure with epitaxial aluminum is used to quantify the highly transparent semiconductor-superconductor interface, indicating near-unity transmission. The observed temperature dependence of MAR does not follow a conventional BCS form, but instead agrees with a model in which the density of states in the quantum well acquires an effective induced gap, in our case 180 {\mu}eV, close to that of the epitaxial superconductor. Carrier density dependence of MAR is investigated using a depletion gate, revealing the subband structure of the semiconductor quantum well, consistent with magnetotransport experiment of the bare InAs performed on the same wafer., Comment: Includes supplementary material

Transport measurements in inverted InAs/GaSb quantum wells reveal a giant spin-orbit splitting of the energy bands close to the hybridization gap. The splitting results from the interplay of electron-hole mixing and spin-orbit coupling, and can exceed the hybridization gap. We experimentally investigate the band splitting as a function of top gate voltage for both electronlike and holelike states. Unlike conventional, noninverted two-dimensional electron gases, the Fermi energy in InAs/GaSb can cross a single spin-resolved band, resulting in full spin-orbit polarization. In the fully polarized regime we observe exotic transport phenomena such as quantum Hall plateaus evolving in e2/h steps and a nontrivial Berry phase.

Electron spins in gate-defined quantum dots provide a promising platform for quantum computation. In particular, spin-based quantum computing in gallium arsenide takes advantage of the high quality of semiconducting materials, reliability in fabricating arrays of quantum dots, and accurate qubit operations. However, the effective magnetic noise arising from the hyperfine interaction with uncontrolled nuclear spins in the host lattice constitutes a major source of decoherence. Low frequency nuclear noise, responsible for fast (10 ns) inhomogeneous dephasing, can be removed by echo techniques. High frequency nuclear noise, recently studied via echo revivals, occurs in narrow frequency bands related to differences in Larmor precession of the three isotopes $\mathbf{^{69}Ga}$, $\mathbf{^{71}Ga}$, and $\mathbf{^{75}As}$. Here we show that both low and high frequency nuclear noise can be filtered by appropriate dynamical decoupling sequences, resulting in a substantial enhancement of spin qubit coherence times. Using nuclear notch filtering, we demonstrate a spin coherence time ($\mathbf{T_{2}}$) of 0.87 ms, five orders of magnitude longer than typical exchange gate times, and exceeding the longest coherence times reported to date in Si/SiGe gate-defined quantum dots., 10 pages, including main text (5 figures) and supplementary information (2 figures)

The prospect of coupling a two-dimensional (2D) semiconductor heterostructure to a superconductor opens new research and technology opportunities, including fundamental problems in mesoscopic superconductivity, scalable superconducting electronics, and new topological states of matter. For instance, one route toward realizing topological matter is by coupling a 2D electron gas (2DEG) with strong spin-orbit interaction to an s-wave superconductor. Previous efforts along these lines have been hindered by interface disorder and unstable gating. Here, we report measurements on a gateable InGaAs/InAs 2DEG with patterned epitaxial Al, yielding multilayer devices with atomically pristine interfaces between semiconductor and superconductor. Using surface gates to form a quantum point contact (QPC), we find a hard superconducting gap in the tunneling regime, overcoming the soft-gap problem in 2D superconductor-semiconductor hybrid systems. With the QPC in the open regime, we observe a first conductance plateau at 4e^2/h, as expected theoretically for a normal-QPC-superconductor structure. The realization of a hard-gap semiconductor-superconductor system that is amenable to top-down processing provides a means of fabricating scalable multicomponent hybrid systems for applications in low-dissipation electronics and topological quantum information., includes main text, supplementary information and code for simulations. Published version

Controlling decoherence is the biggest challenge in efforts to develop quantum information hardware. Single electron spins in gallium arsenide are a leading candidate among implementations of solid-state quantum bits, but their strong coupling to nuclear spins produces high decoherence rates. Group IV semiconductors, on the other hand, have relatively low nuclear spin densities, making them an attractive platform for spin quantum bits. However, device fabrication remains a challenge, particularly with respect to the control of materials and interfaces. Here, we demonstrate state preparation, pulsed gate control and charge-sensing spin readout of hole spins confined in a Ge-Si core-shell nanowire. With fast gating, we measure T(1) spin relaxation times of up to 0.6 ms in coupled quantum dots at zero magnetic field. Relaxation time increases as the magnetic field is reduced, which is consistent with a spin-orbit mechanism that is usually masked by hyperfine contributions.

Fabrication of graphene devices is often hindered by incompatibility between the silicon technology and the methods of graphene growth. Exfoliation from graphite yields excellent films but is good mainly for research. Graphene grown on metal has a technological potential but requires mechanical transfer. Growth by SiC decomposition requires a temperature budget exceeding the technological limits. These issues could be circumvented by growing graphene directly on insulator, implying Van der Waals growth. During growth, the insulator acts as a support defining the growth plane. In the device, it insulates graphene from the Si substrate. We demonstrate planar growth of graphene on mica surface. This was achieved by molecular beam deposition above 600°C. High resolution Raman scans illustrate the effect of growth parameters and substrate topography on the film perfection. Ab initio calculations suggest a growth model. Data analysis highlights the competition between nucleation at surface steps and flat surface. As a proof of concept, we show the evidence of electric field effect in a transistor with a directly grown channel.

Ballistic semiconductor structures have allowed the realization of optics-like phenomena in electronics, including magnetic focusing and lensing. An extension that appears unique to graphene is to use both n and p carrier types to create electronic analogs of optical devices having both positive and negative indices of refraction. Here, we use gate-controlled density with both p and n carrier types to demonstrate the analog of the fiber-optic guiding in graphene. Two basic effects are investigated: (1) bipolar p-n junction guiding, based on the principle of angle-selective transmission though the graphene p-n interface, and (2) unipolar fiber-optic guiding, using total internal reflection controlled by carrier density. Modulation of guiding efficiency through gating is demonstrated and compared to numerical simulations, which indicates that interface roughness limits guiding performance, with few-nanometer effective roughness extracted. The development of p-n and fiber-optic guiding in graphene may lead to electrically reconfigurable wiring in high-mobility devices., Comment: supplementary materal at http://marcuslab.harvard.edu/papers/OG_SI.pdf