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Semiconducting nanowire Josephson junctions represent an attractive platform to investigate the anomalous Josephson effect and detect topological superconductivity by studying Josephson supercurrent. However, an external magnetic field generally suppresses the supercurrent through hybrid nanowire junctions and significantly limits the field range in which the supercurrent phenomena can be studied. In this work, we investigate the impact of the length of InSb-Al nanowire Josephson junctions on the supercurrent resilience against magnetic fields. We find that the critical parallel field of the supercurrent can be considerably enhanced by reducing the junction length. Particularly, in 30 nm-long junctions supercurrent can persist up to 1.3 T parallel field - approaching the critical field of the superconducting film. Furthermore, we embed such short junctions into a superconducting loop and obtain the supercurrent interference at a parallel field of 1 T. Our findings are highly relevant for multiple experiments on hybrid nanowires requiring a magnetic field-resilient supercurrent., 17 pages, 5 figures in main text. 22 pages, 10 figures in supporting information

The realization of hybrid superconductor–semiconductor quantum devices, in particular a topological qubit, calls for advanced techniques to readily and reproducibly engineer induced superconductivity in semiconductor nanowires. Here, we introduce an on-chip fabrication paradigm based on shadow walls that offers substantial advances in device quality and reproducibility. It allows for the implementation of hybrid quantum devices and ultimately topological qubits while eliminating fabrication steps such as lithography and etching. This is critical to preserve the integrity and homogeneity of the fragile hybrid interfaces. The approach simplifies the reproducible fabrication of devices with a hard induced superconducting gap and ballistic normal-/superconductor junctions. Large gate-tunable supercurrents and high-order multiple Andreev reflections manifest the exceptional coherence of the resulting nanowire Josephson junctions. Our approach enables the realization of 3-terminal devices, where zero-bias conductance peaks emerge in a magnetic field concurrently at both boundaries of the one-dimensional hybrids., Advanced fabrication techniques enable a wide range of quantum devices, such as the realization of a topological qubit. Here, the authors introduce an on-chip fabrication technique based on shadow walls to implement topological qubits in an InSb nanowire without fabrication steps such as lithography and etching.

We systematically study three-terminal InSb-Al nanowire devices by using radio-frequency reflectometry. Tunneling spectroscopy measurements on both ends of the hybrid nanowires are performed while systematically varying the chemical potential, magnetic field and junction transparencies. Identifying the lowest-energy state allows for the construction of lowest- and zero-energy state diagrams, which show how the states evolve as a function of the aforementioned parameters. Importantly, comparing the diagrams taken for each end of the hybrids enables the identification of states which do not coexist simultaneously, ruling out a significant amount of the parameter space as candidates for a topological phase. Furthermore, altering junction transparencies filters out zero-energy states sensitive to a local gate potential. Such a measurement strategy significantly reduces the time necessary to identify a potential topological phase and minimizes the risk of falsely recognizing trivial bound states as Majorana zero modes., Main text: 12 pages, 9 figures. SupplementaryMaterials: 12 pages, 14 figures

In superconducting quantum circuits, aluminum is one of the most widely used materials. It is currently also the superconductor of choice for the development of topological qubits. However, aluminum-based devices suffer from poor magnetic field compatibility. Herein, this limitation is resolved by showing that adatoms of heavy elements (e.g., platinum) increase the critical field of thin aluminum films by more than a factor of two. Using tunnel junctions, it is shown that the increased field resilience originates from spin-orbit scattering introduced by Pt. This property is exploited in the context of the superconducting proximity effect in semiconductor–superconductor hybrids, where it is shown that InSb nanowires strongly coupled to Al/Pt films can maintain superconductivity up to 7 T. The two-electron charging effect is shown to be robust against the presence of heavy adatoms. Additionally, non-local spectroscopy is used in a three-terminal geometry to probe the bulk of hybrid devices, showing that it remains free of sub-gap states. Finally, it is demonstrated that proximitized semiconductor states maintain their ability to Zeeman-split in an applied magnetic field. Combined with the chemical stability and well-known fabrication routes of aluminum, Al/Pt emerges as the natural successor to Al-based systems and is a compelling alternative to other superconductors, whenever high-field resilience is required.

We develop a protocol to determine the presence and extent of a topological phase with Majorana zero modes in a hybrid superconductor-semiconductor device. The protocol is based on conductance measurements in a three-terminal device with two normal leads and one superconducting lead. A radio-frequency technique acts as a proxy for the measurement of local conductance, allowing a rapid, systematic scan of the large experimental phase space of the device. Majorana zero modes cause zero bias conductance peaks at each end of the wire, so we identify promising regions of the phase space by filtering for this condition. To validate the presence of a topological phase, a subsequent measurement of the non-local conductance in these regions is used to detect a topological transition via the closing and reopening of the bulk energy gap. We define data analysis routines that allow for an automated and unbiased execution of the protocol. Our protocol is designed to screen out false positives, especially trivial Andreev bound states that mimic Majorana zero modes in local conductance. We apply the protocol to several examples of simulated data illustrating the detection of topological phases and the screening of false positives., Comment: 28 pages, 18 figures, 1 table

Semiconducting–superconducting hybrids are vital components for the realization of high-performance nanoscale devices. In particular, semiconducting–superconducting nanowires attract widespread interest owing to the possible presence of non-abelian Majorana zero modes, which are quasiparticles that hold promise for topological quantum computing. However, systematic search for Majoranas signatures is challenging because it requires reproducible hybrid devices and reliable fabrication methods. This work introduces a fabrication concept based on shadow walls that enables the in situ, selective, and consecutive depositions of superconductors and normal metals to form normal-superconducting junctions. Crucially, this method allows to realize devices in a single shot, eliminating fabrication steps after the synthesis of the fragile semiconductor/superconductor interface. At the atomic level, all investigated devices reveal a sharp and defect-free semiconducting–superconducting interface and, correspondingly, a hard induced superconducting gap resilient up to 2 T is measured electrically. While the cleanliness of the technique enables systematic studies of topological superconductivity in nanowires, it also allows for the synthesis of advanced nano-devices based on a wide range of material combinations and geometries while maintaining an exceptionally high interface quality.

We measure the charge periodicity of Coulomb blockade conductance oscillations of a hybrid InSb-Al island as a function of gate voltage and parallel magnetic field. The periodicity changes from $2e$ to $1e$ at a gate-dependent value of the magnetic field, $B^*$, decreasing from a high to a low limit upon increasing the gate voltage. In the gate voltage region between the two limits, which our numerical simulations indicate to be the most promising for locating Majorana zero modes, we observe correlated oscillations of peak spacings and heights. For positive gate voltages, the $2e$-$1e$ transition with low $B^*$ is due to the presence of non-topological states whose energy quickly disperses below the charging energy due to the orbital effect of the magnetic field. Our measurements demonstrate the importance of a careful exploration of the entire available phase space of a proximitized nanowire as a prerequisite to define future topological qubits., 5 pages, 4 figures plus supplementary. v2: improved manuscript. v3: published version. Raw data and source code available at https://doi.org/10.4121/13333451.v4

We characterize InSb quantum dots induced by bottom finger gates within a nanowire that is grown via the vapor-liquid-solid process. The gates are separated from the nanowire by an exfoliated 35\,nm thin hexagonal BN flake. We probe the Coulomb diamonds of the gate induced quantum dot exhibiting charging energies of $\sim 2.5\,\mathrm{meV}$ and orbital excitation energies up to $0.3\,\mathrm{meV}$. The gate hysteresis for sweeps covering 5 Coulomb diamonds reveals an energy hysteresis of only $60\mathrm{\mu eV}$ between upwards and downwards sweeps. Charge noise is studied via long-term measurements at the slope of a Coulomb peak revealing potential fluctuations of $\sim 1\,\mu \mathrm{eV}/\mathrm{\sqrt{Hz}}$ at 1\,Hz. This makes h-BN the dielectric with the currently lowest gate hysteresis and lowest low-frequency potential fluctuations reported for low-gap III-V nanowires. The extracted values are similar to state-of-the art quantum dots within Si/SiGe and Si/SiO${_2}$ systems.

High aspect-ratio InSb nanowires (NWs) of high chemical purity are sought for implementing advanced quantum devices. The growth of InSb NWs is challenging, generally requiring a stem of a foreign material for nucleation. Such a stem tends to limit the length of InSb NWs and its material becomes incorporated in the InSb segment. Here, we report on the growth of chemically pure InSb NWs tens of microns long. Using a selective-area mask in combination with gold as a catalyst allows complete omission of the stem, thus demonstrating that InSb NWs can grow directly from the substrate. The introduction of the selective-area mask gives rise to novel growth kinetics, demonstrating high growth rates and complete suppression of layer deposition on the mask for Sb-rich conditions. The crystal quality and chemical purity of these NWs is reflected in the significant enhancement of low-temperature electron mobility, yielding an average of 4.4 × 104 cm2/(V s), compared to previously studied InSb NWs grown on stems.

The contribution of bulk inversion asymmetry to the total spin-orbit coupling is commonly neglected for group III-V nanowires grown in the generic [111] direction. We have solved the complete Hamiltonian of the circular nanowire accounting for bulk inversion asymmetry via exact numerical diagonalization. Three different symmetry classes of angular momentum states exist, which reflects the threefold rotation symmetry of the crystal lattice about the [111] axis. A particular group of angular momentum states contains degenerate modes which are strongly coupled via the Dresselhaus Hamiltonian, which results in a significant energy splitting with increasing momentum. Hence, under certain conditions Dresselhaus spin-orbit coupling is relevant for [111] InAs and [111] InSb nanowires. We demonstrate momentum-dependent energy splittings and the impact of Dresselhaus spin-orbit coupling on the dispersion relation. In view of possible spintronics applications relying on bulk inversion asymmetry we calculate the spin expectation values and the spin texture as a function of the Fermi energy. Finally, we investigate the effect of an axial magnetic field on the energy spectrum and on the corresponding spin polarization., 11 Pages, 7 figures

Selective-area growth is a promising technique for enabling of the fabrication of the scalable III–V nanowire networks required to test proposals for Majorana-based quantum computing devices. However, the contours of the growth parameter window resulting in selective growth remain undefined. Herein, we present a set of experimental techniques that unambiguously establish the parameter space window resulting in selective III–V nanowire networks growth by molecular beam epitaxy. Selectivity maps are constructed for both GaAs and InAs compounds based on in situ characterization of growth kinetics on GaAs(001) substrates, where the difference in group III adatom desorption rates between the III–V surface and the amorphous mask area is identified as the primary mechanism governing selectivity. The broad applicability of this method is demonstrated by the successful realization of high-quality InAs and GaAs nanowire networks on GaAs, InP, and InAs substrates of both (001) and (111)B orientations as well as homoepitaxial InSb nanowire networks. Finally, phase coherence in Aharonov–Bohm ring experiments validates the potential of these crystals for nanoelectronics and quantum transport applications. This work should enable faster and better nanoscale crystal engineering over a range of compound semiconductors for improved device performance., The project was supported by Microsoft Station Q (Delft). S. Martí-Sanchez acknowledges funding from “Programa Internacional de Becas “la Caixa″-Severo Ochoa”. ICN2 members acknowledge funding from Generalitat de Catalunya 2017 SGR 327. ICN2 acknowledges support from the Severo Ochoa Programme (MINECO, grant no. SEV-2013-0295) and is funded by the CERCA Programme/Generalitat de Catalunya. Part of the present work has been performed in the framework of Universitat Autonoma de Barcelona Materials Science PhD program.

One-dimensional ballistic transport is demonstrated for a high-mobility InAs nanowire device. Unlike conventional quantum point contacts (QPCs) created in a two-dimensional electron gas, the nanowire QPCs represent one-dimensional constrictions formed inside a quasi-one-dimensional conductor. For each QPC, the local subband occupation can be controlled individually between zero and up to six degenerate modes. At large out-of-plane magnetic fields Landau quantization and Zeeman splitting emerge and comprehensive voltage bias spectroscopy is performed. Confinement-induced quenching of the orbital motion gives rise to significantly modified subband-dependent Landé g factors. A pronounced g factor enhancement related to Coulomb exchange interaction is reported. Many-body effects of that kind also manifest in the observation of the 0.7·2e(2)/h conductance anomaly, commonly found in planar devices.

We demonstrate the growth and structural characteristics of InAs nanowire junctions evidencing a transformation of the crystalline structure. The junctions are obtained without the use of catalyst particles. Morphological investigations of the junctions reveal three structures having an L-, T-, and X-shape. The formation mechanisms of these structures have been identified. The NW junctions reveal large sections of zinc blende crystal structure free of extended defects, despite the high stacking fault density obtained in individual InAs nanowires. This segment of zinc blende crystal structure in the junction is associated with a crystal phase transformation involving sets of Shockley partial dislocations; the transformation takes place solely in the crystal phase. A model is developed to demonstrate that only the zinc blende phase with the same orientation as the substrate can result in monocrystalline junctions. The suitability of the junctions to be used in nanoelectronic devices is confirmed by room-temperature electrical experiments.

The number of electrons in small metallic or semiconducting islands is quantised. When tunnelling is enabled via opaque barriers this number can change by an integer. In superconductors the addition is in units of two electron charges (2e), reflecting that the Cooper pair condensate must have an even parity. This ground state (GS) is foundational for all superconducting qubit devices. Here, we study a hybrid superconducting–semiconducting island and find three typical GS evolutions in a parallel magnetic field: a robust 2e-periodic even-parity GS, a transition to a 2e-periodic odd-parity GS, and a transition from a 2e- to a 1e-periodic GS. The 2e-periodic odd-parity GS persistent in gate-voltage occurs when a spin-resolved subgap state crosses zero energy. For our 1e-periodic GSs we explicitly show the origin being a single zero-energy state gapped from the continuum, i.e., compatible with an Andreev bound states stabilized at zero energy or the presence of Majorana zero modes., Understanding the ground state (GS) phase transitions in the quantum tunneling regime of a superconducting system is important for future qubit devices. Here, Shen, Heedt and Borsoi et al. report distinct types of fermion parity GS transitions as a function of magnetic field and gate voltages in a Coulomb-blockaded InSb–Al island.

We have modeled InAs nanowires using finite element methods considering the actual device geometry, the semiconducting nature of the channel and surface states, providing a comprehensive picture of charge distribution and gate action. The effective electrostatic gate width and screening effects are taken into account. A pivotal aspect is that the gate coupling to the nanowire is compromised by the concurrent coupling of the gate electrode to the surface/interface states, which provide the vast majority of carriers for undoped nanowires. In conjunction with field-effect transistor (FET) measurements using two gates with distinctly dissimilar couplings, the study reveals the density of surface states that gives rise to a shallow quantum well at the surface. Both gates yield identical results for the electron concentration and mobility only at the actual surface state density. Our method remedies the flaws of conventional FET analysis and provides a straightforward alternative to intricate Hall effect measurements on nanowires.

We study the effects of spin-orbit coupling on the magnetoconductivity in diffusive cylindrical semiconductor nanowires. Following up on our former study on tubular semiconductor nanowires, we focus in this paper on nanowire systems where no surface accumulation layer is formed but instead the electron wave function extends over the entire cross section. We take into account the Dresselhaus spin-orbit coupling resulting from a zinc-blende lattice and the Rashba spin-orbit coupling, which is controlled by a lateral gate electrode. The spin relaxation rate due to Dresselhaus spin-orbit coupling is found to depend neither on the spin density component nor on the wire growth direction and is unaffected by the radial boundary. In contrast, the Rashba spin relaxation rate is strongly reduced for a wire radius that is smaller than the spin precession length. The derived model is fitted to the data of magnetoconductance measurements of a heavily doped back-gated InAs nanowire and transport parameters are extracted. At last, we compare our results to previous theoretical and experimental studies and discuss the occurring discrepancies., 11 pages, 5 figures, to be published in Phys. Rev. B

Spin-momentum locking in a semiconductor device with strong spin-orbit coupling (SOC) is a fundamental goal of nanoscale spintronics and an important prerequisite for the formation of Majorana bound states. Such a helical state is predicted in one-dimensional (1D) nanowires subject to strong Rashba SOC and spin-mixing, its hallmark being a characteristic reentrant behaviour in the conductance. Here, we report the first direct experimental observations of the reentrant conductance feature, which reveals the formation of a helical liquid, in the lowest 1D subband of an InAs nanowire. Surprisingly, the feature is very prominent also in the absence of magnetic fields. This behaviour suggests that exchange interaction exhibits substantial impact on transport in our device. We attribute the opening of the pseudogap to spin-flipping two-particle backscattering. The all-electric origin of the ideal helical transport bears momentous implications for topological quantum computing., submitted to Nature Physics in September 2016

High-quality CdS nanowires with uniform Sn doping were synthesized using a Sn-catalyzed chemical vapor deposition method. X-ray diffraction and transmission electron microscopy demonstrate the single crystalline wurtzite structure of the CdS/Sn nanowires. Both donor and acceptor levels, which originate from the amphoteric nature of Sn in II-VI semiconductors, are identified using low-temperature microphotoluminescence. This self-compensation effect was cross examined by gate modulation and temperature-dependent electrical transport measurement. They show an overall n-type behavior with relatively low carrier concentration and low carrier mobilities. Moreover, two different donor levels due to intrinsic and extrinsic doping could be distinguished. They agree well with both the electrical and optical data.

The basic ingredients for spintronics using semiconductor nanowires are discussed. For spin manipulation spin-orbit coupling is employed. In this respect the effect of the Rashba and Dresselhaus contributions are investigated. The strength of spin-orbit coupling is extracted by measuring the weak anti-localization effect and comparing the experimental results to a theoretical model. On nanowires covered with a set of narrow gate fingers, quantized conductance is observed. By analyzing the transconductance the Zeeman spin splitting is determined at various magnetic fields. It is found that the gyromagnetic factor is lowered due to the reduced effect of spin-orbit coupling. Confinement-induced quenching of the orbital motion results in a modified subband-dependent Lande g-factor. For strong confinement a pronounced g-factor enhancement related to Coulomb exchange interaction is reported. Indications for the formation of a helical gap are found, which is relevant for the realization of Majorana states.

We compute analytically the weak (anti)localization correction to the Drude conductivity for electrons in tubular semiconductor systems of zinc blende type. We include linear Rashba and Dresselhaus spin-orbit coupling (SOC) and compare wires of standard growth directions $\langle100\rangle$, $\langle111\rangle$, and $\langle110\rangle$. The motion on the quasi-two-dimensional surface is considered diffusive in both directions: transversal as well as along the cylinder axis. It is shown that Dresselhaus and Rashba SOC similarly affect the spin relaxation rates. For the $\langle110\rangle$ growth direction, the long-lived spin states are of helical nature. We detect a crossover from weak localization to weak anti-localization depending on spin-orbit coupling strength as well as dephasing and scattering rate. The theory is fitted to experimental data of an undoped $\langle111\rangle$ InAs nanowire device which exhibits a top-gate-controlled crossover from positive to negative magnetoconductivity. Thereby, we extract transport parameters where we quantify the distinct types of SOC individually., 17 pages, 9 figures

The transport in InAs nanowires is investigated at low temperatures. On wires with different n-type doping information on Rashba and Dresselhaus spin-orbit coupling is gained from weak antilocalization measurements. By using a short local gate quantum point contacts are formed, which show quantized conductance. From bias-depended measurements the g-factor is extracted for different subbands.

We report on a prototype device geometry where a number of quantum point contacts are connected in series in a single quasi-ballistic InAs nanowire. At finite magnetic field the backscattering length is increased up to the micron-scale and the quantum point contacts are connected adiabatically. Hence, several input gates can control the outcome of a ballistic logic operation. The absence of backscattering is explained in terms of selective population of spatially separated edge channels. Evidence is provided by regular Aharonov–Bohm-type conductance oscillations in transverse magnetic fields, in agreement with magnetoconductance calculations. The observation of the Shubnikov–de Haas effect at large magnetic fields corroborates the existence of spatially separated edge channels and provides a new means for nanowire characterization.

We investigate magnetoresistance in spin valves involving CoPd-contacted carbon nanotubes. Both temperature and bias voltage dependence clearly indicate tunneling magnetoresistance as the origin. We show that this effect is significantly affected by the tunnel barrier strength, which appears to be one reason for the variation between devices previously detected in similar structures. Modeling the data by means of the scattering matrix approach, we find a non-trivial dependence of the magnetoresistance on the barrier strength. Furthermore, analysis of the spin precession observed in a nonlocal Hanle measurement yields a spin lifetime of $\tau_s = 1.1\,$ns, a value comparable with those found in silicon- or graphene-based spin valve devices., Comment: 10 pages, 5 figures, 1 table

We investigated the growth, crystal structure, elemental composition and electrical transport characteristics of ZnO nanowires, a promising candidate for optoelectronic applications in the UV-range. Nominally-undoped and Ga-doped ZnO nanowires were grown by metal-organic chemical vapor deposition. Photoluminescence measurements confirmed the incorporation of Ga via donor-bound exciton emission. With atom-probe tomography we estimated an upper limit of the Ga impurity concentration (). We studied the electrical transport characteristics of these nanowires with a W-nanoprobe technique inside a scanning electron microscope and with lithographically-defined contacts allowing back-gated measurements. An increase in apparent resistivity by two orders of magnitude with decreasing radius was measured with both techniques with a much larger distribution width for the nanoprobe method. A drop in the effective carrier concentration and mobility was found with decreasing radius which can be attributed to carrier depletion and enhanced scattering due to surface states. Little evidence of a change in resistivity was observed with Ga doping, which indicates that the concentration of native or background dopants is higher than the Ga doping concentration.

Due to their strong spin-orbit coupling III-V semiconductor nanowires are excellent candidates for electrical spin manipulation. Therefore, a major goal is to tailor spin-orbit coupling in these devices. Direct electrical spin injection into quasi one-dimensional nanowires is demonstrated. Furthermore, the weak antilocalization effect was investigated in InAs nanowires. The quantum corrections to the conductivity are interpreted by developing a quasi-one-dimensional diffusive model. It turns out that by means of doping and electric gating the spin-lifetimes can be tuned significantly. By creating few-electron quantum dots inside these devices the impact of the confinement on the spin relaxation properties is investigated.

With the direct measurement of the quantum oscillatory magnetization M of a two-dimensional electron system (2DES) in an InGaAs/InP asymmetric quantum well we discover a frequency anomaly of the de Haas–van Alphen effect which is not consistent with existing theories on spin-orbit interaction (SOI). Strikingly, the oscillatory magnetoresistance of the same heterostructure, that is, the Shubnikov–de Haas effect conventionally used to explore SOI, does not show the frequency anomaly. This explains why our finding has not been reported for almost three decades. The understanding of the ground state energy of a 2DES is evidenced to be incomplete when SOI is present.

We report on the magnetization of ensembles of etched quantum dots with a lateral diameter of 460 nm, which we prepared from InGaAs/InP heterostructures. The quantum dots exhibit 1/B-periodic de-Haas-van-Alphen-type oscillations in the magnetization M(B) for external magnetic fields B 2 T, measured by torque magnetometry at 0.3 K. We compare the experimental data to model calculations assuming different confinement potentials and including ensemble broadening effects. The comparison shows that a hard wall potential with an edge depletion width of 100 nm explains the magnetic behavior. Beating patterns induced by Rashba spin-orbit interaction (SOI) as measured in unpatterned and nanopatterned InGaAs/InP heterostructures are not observed for the quantum dots. From our model we predict that signatures of SOI in the magnetization could be observed in larger dots in tilted magnetic fields.

We report on the conditions necessary for the electrical injection of spin-polarized electrons into indium nitride nanowires synthesized from the bottom up by molecular beam epitaxy. The presented results mark the first unequivocal evidence of spin injection into III-V semiconductor nanowires. Utilizing a newly developed preparation scheme, we are able to surmount shadowing effects during the metal deposition. Thus, we avoid strong local anisotropies that arise if the ferromagnetic leads are wrapping around the nanowire. Using a combination of various complementary techniques, inter alia the local Hall effect, we carried out a comprehensive investigation of the coercive fields and switching behaviors of the cobalt micromagnetic spin probes. This enables the identification of a range of aspect ratios in which the mechanism of magnetization reversal is single domain switching. Lateral nanowire spin valves were prepared. The spin relaxation length is demonstrated to be about 200 nm, which provides an incentive to pursue the route toward nanowire spin logic devices.