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.

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. ± Majorana (dot) states are defined in the text. 2469-9950/2018/98(8)/085125(10) 085125-1 ©2018 American Physical Society M.-T. DENG et al. PHYSICAL REVIEW B 98, 085125 (2018)

We present a novel route to realizing topological superconductivity using magnetic flux applied to a full superconducting shell surrounding a semiconducting nanowire core. 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 around one applied flux quantum, Φ0 = h/2e, corresponding to 2π phase winding. Theoretical analysis indicates that in the presence of radial spin-orbit coupling in the semiconductor, the winding of the superconducting phase can induce a transition to a topological phase supporting Majorana zero modes. Realistic modeling shows a topological phase persisting over a wide range of parameters, and reproduces experimental tunneling conductance data. Further measurements of Coulomb blockade peak spacing around one flux quantum in full-shell nanowire islands shows exponentially decreasing deviation from 1e periodicity with device length, consistent with Majorana modes at the ends of the nanowire. arXiv:2003.13177v1 [cond-mat.mes-hall]

III-V semiconductor nanowires have shown great potential in various quantum transport experiments. However, realizing a scalable high-quality nanowire-based 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 GaAs-based 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 spin-orbit 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.Material science plays a key role in quantum computing research. Long quantum state lifetimes -the fundamental prerequisite for realizing quantum computers -rely on the ability to produce materials with high purity and structural quality. Together with the requirements of scalability and reproducibility, these properties are what mainly defines the challenges of material science in quantum computing today. Proposals for topological quantum computing, 1-3 which are based on hybrid semiconductor-superconductor nanowire (NW) networks, are being pursued by numerous research groups and have ignited intense research efforts on hybrid epitaxy. 4-8 NW scalability is tightly related to the semiconductor growth approach. Top-down lithography has been used to define NWs in two-dimensional layers 5,9 and a variety of methods have been pursued for alignment and positioning of bottom-up vapor-liquid-solid (VLS) grown NWs, such as dielectrophoresis techniques, 10 nanoscale combing 11 and magnetic aligning of NWs. 12 Despite of these developments, large-scale synthesis of bottom-up grown high-mobility NW networks that are compatible with epitaxial interwire connections and semiconductor/superconductor epitaxy has still not been realized. To realize the epitaxial connections, a lot of effort has been put into the growth of branched NWs via the VLS method. 8,13-15 A scalable approach has been developed in Ref. [16,17] using template assisted growth of inplane NW networks. 18 Nonetheless, this approach is not yet compatible with superconductor epitaxy. An alternative scalable approach is to use lithographically defined openings in a mask on a crystalline substrate. This method is referred to as selective area growth (SAG) and until recently has mainly been used in conjunction with metal organic chemical vapour deposition 19,20 , metal organic vapour phase epitaxy 21,22 , chemical beam epitaxy and metal organic molecular beam epitaxy (chemical beam epitaxy). [23][24][25][26] In contrast to molecular beam epitaxy (MBE), the dissociation kinetics of the chemical precursors in these methods enhance the growth selectivity on masked substrates by expanding the growth parameter window, ...

We introduce selective area grown hybrid InAs/Al nanowires based on molecular beam epitaxy, allowing arbitrary semiconductor-superconductor networks containing loops and branches. Transport reveals a hard induced gap and unpoisoned 2e-periodic Coulomb blockade, with temperature dependent 1e features in agreement with theory. Coulomb peak spacing in parallel magnetic field displays overshoot, indicating an oscillating discrete near-zero subgap state consistent with device length. Finally, we investigate a loop network, finding strong spin-orbit coupling and a coherence length of several microns. These results demonstrate the potential of this platform for scalable topological networks among other applications.Majorana zero modes (MZMs) at the ends of onedimensional topological superconductors are expected to exhibit non-Abelian braiding statistics [1, 2], providing naturally fault-tolerant qubits [3, 4]. Proposed realizations of braiding [5, 6], interference-based topological qubits [7-9] and topological quantum computing architectures [10] require scalable nanowire networks. While relatively simple branched or looped wires can be realized by specialized growth methods [11,12] or by etchand gate-confined two-dimensional hybrid heterostructures [13][14][15][16], selective area growth [17] enables deterministic patterning of arbitrarily complex structures. This allows complex continuous patterns of superconductorsemiconductor hybrids and topological networks.Following initial theoretical proposals [18,19], a number of experiments have reported signatures of Majorana zero modes (MZMs) in hybrid semiconductorsuperconductor nanowires [11], including zero-bias conductance peaks [15,16,[20][21][22][23][24][25][26] and Coulomb blockade peak spacing oscillations [27,28]. To date, experiments have used individual vapor-liquid-solid (VLS) nanowires [20][21][22][23][24][25] or gate-confined two-dimensional heterostructures [15,16]. Within these approaches, constructing complex topological devices and networks containing branches and loops [5-10] is a challenge. Recently, branched and looped VLS growth has been developed toward this goal [12,29].In this Letter, we investigate a novel approach to the growth of semiconductor-superconductor hybrids that allows deterministic on-chip patterning of topological superconducting networks based on SAG. We characterize key physical properties required for building Majorana networks, including a hard superconducting gap, induced in the semiconductor, phase-coherence length of several microns, strong spin-orbit coupling, and Coulomb block-ade peak motion compatible with interacting Majoranas. Overall, these properties show great promise for SAGbased topological networks.Selective area growth was realized on a semi-insulating (001) InP substrate. PECVD grown SiO x was patterned using electron beam lithography and wet etching. InAs wires with triangular cross-sections were grown by molecular beam epitaxy (MBE). The Al was grown in-situ by MBE using angled deposition covering one of the facet...

We use the effective g factor of Andreev subgap states in an axial magnetic field to investigate how the superconducting density of states is distributed between the semiconductor core and the superconducting shell in hybrid nanowires. We find a steplike reduction of the Andreev g factor and an 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 a g factor exceeding that of the parent superconductor.

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Gate-tunable semiconductor nanowires with superconducting leads have great potential for quantum computation 1-3 and as model systems for mesoscopic Josephson junctions 4,5 . 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 e ective 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 junctions 6,7 and for Majorana readout proposals 8 .In superconductor-normal-superconductor (SNS) Josephson junctions, the critical current is predicted to be quantized as refs 4,5), where N is the number of occupied subbands and ∆ 0 is the superconducting gap, as long as N is sufficiently small and the junctions are short, ballistic and adiabatically smooth. This quantization shows the number of Andreev bound states or modes, each coming from a single occupied subband, that carry the supercurrent. Single-mode junctions are desirable for the observation of Majoranas. Quantized supercurrent has been difficult to realize experimentally, and it is difficult from transport measurements alone to determine which conditions for quantization are unmet. In transport measurements of proximitized InAs and InSb nanowires, critical currents are far below the expected quantized values for perfectly transmitting modes, and fluctuate with gate voltage 9-13 . Nanowire Josephson junction qubits also display similar fluctuations in the measured resonant frequency 6,7 . Here, we make direct, non-contact measurements (Fig. 1a) of Al/InAs nanowire/Al junctions (Fig. 1b,c) using an inductively coupled 14 scanning superconducting quantum interference device 15,16 (SQUID) to measure the CPR (Methods). The contact between Al and InAs nanowires is epitaxial 17 , greatly reducing the presence of in-gap states 2 . In the low-temperature, few-mode limit, the shape of the CPR and its dependence on gate voltage, junction length and temperature yield unique insights into the number and transmission of Andreev bound states.The vast majority of CPRs we measured were forward-skewed; their first maximum after zero was forward of a sine wave (Fig. 1d). Fourier transforms of the CPRs revealed that they were well described by a Fourier series with up to seven harmonics (for example, Fig. 1e). In...