Erratum: Ubiquitous Non-Majorana Zero-Bias Conductance Peaks in Nanowire Devices [Phys. Rev. Lett. 123, 107703 (2019)]

This corrects the article DOI: 10.1103/PhysRevLett.123.107703.

Role of a capping layer on the crystalline structure of Sn thin films grown at cryogenic temperatures on InSb substrates

Metal deposition with cryogenic cooling is a common technique in the condensed matter community for producing ultra-thin epitaxial superconducting layers on semiconductors. However, a significant challenge arises when these films return to room temperature, as they tend to undergo dewetting. This issue can be mitigated by capping the films with an amorphous layer. In this study, we investigate the influence of differentin situfabricated caps on the structural characteristics of Sn thin films deposited at 80 K on InSb substrates. Regardless of the type of capping, we consistently observe that the films remain smooth upon returning to room temperature and exhibit epitaxy on InSb in the cubic Sn (α-Sn) phase. Notably, we identify a correlation between alumina capping using an electron beam evaporator and an increased presence of tetragonal Sn (β-Sn) grains. This suggests that heating from the alumina source may induce a partial phase transition in the Sn layer. The existence of theβ-Sn phase induces superconducting behavior of the films by percolation effect. This study highlights the potential for tailoring the structural properties of cryogenic Sn thin films throughin situcapping. This development opens avenues for precise control in the production of superconducting Sn films, facilitating their integration into quantum computing platforms.

Sn/InAs Josephson Junctions on Selective Area Grown Nanowires with in Situ Shadowed Superconductor Evaporation

Superconductor-semiconductor nanowire hybrid structures are useful in fabricating devices for quantum information processing. While selective area growth (SAG) offers the flexibility to grow semiconductor nanowires in arbitrary geometries, in situ evaporation of superconductors ensures pristine superconductor-semiconductor interfaces, resulting in strong induced superconductivity in the semiconducting nanowire. In this work, we used high-aspect-ratio SiOx dielectric walls to in situ evaporate islands of superconductor tin on in-plane InAs SAG nanowires. Our technique enables customization in the designs of such hybrid nanostructures, while simultaneously performing the nanowire and superconductor growth without breaking vacuum. Using this technique, we grew super(S)-normal(N)-super(S), NS, and SNSNS junctions. We performed cryogenic electron transport measurements revealing the presence of gate and field tunable supercurrents. We further measured the superconducting gap and critical fields in the hybrid nanostructures and the crossover from 2e to 1e periodicity in the SNSNS junctions as a proof of the usability of these hybrid nanostructures.

First-Principles Assessment of CdTe as a Tunnel Barrier at the α-Sn/InSb Interface

Majorana zero modes, with prospective applications in topological quantum computing, are expected to arise in superconductor/semiconductor interfaces, such as β-Sn and InSb. However, proximity to the superconductor may also adversely affect the semiconductor's local properties. A tunnel barrier inserted at the interface could resolve this issue. We assess the wide band gap semiconductor, CdTe, as a candidate material to mediate the coupling at the lattice-matched interface between α-Sn and InSb. To this end, we use density functional theory (DFT) with Hubbard U corrections, whose values are machine-learned via Bayesian optimization (BO) [ npj Computational Materials 2020, 6, 180]. The results of DFT+U(BO) are validated against angle resolved photoemission spectroscopy (ARPES) experiments for α-Sn and CdTe. For CdTe, the z-unfolding method [ Advanced Quantum Technologies 2022, 5, 2100033] is used to resolve the contributions of different k_z values to the ARPES. We then study the band offsets and the penetration depth of metal-induced gap states (MIGS) in bilayer interfaces of InSb/α-Sn, InSb/CdTe, and CdTe/α-Sn, as well as in trilayer interfaces of InSb/CdTe/α-Sn with increasing thickness of CdTe. We find that 16 atomic layers (3.5 nm) of CdTe can serve as a tunnel barrier, effectively shielding the InSb from MIGS from the α-Sn. This may guide the choice of dimensions of the CdTe barrier to mediate the coupling in semiconductor-superconductor devices in future Majorana zero modes experiments.

Kinetic Model and Experiment for Self-Ignition of Triethylaluminum and Triethylborane Droplets in Air

Triethylaluminum Al(C₂H₅)₃, TEA, and triethylborane, B(C₂H₅)₃, TEB, are transparent, colorless, pyrophoric liquids with boiling points of approximately 190 °C and 95 °C, respectively. Upon contact with ambient air, TEA, TEB, as well as their mixtures and solutions, in hydrocarbon solvents, ignite. They can also violently react with water. TEA and TEB can be used as hypergolic rocket propellants and incendiary compositions. In this manuscript, a novel scheme of the heterogeneous interaction of gaseous oxygen with liquid TEA/TEB microdroplets accompanied by the release of light hydrocarbon radicals into the gas phase is used for calculating the self-ignition of a spatially homogeneous mixture of fuel microdroplets in ambient air at normal pressure and temperature (NPT) conditions. In the primary initiation step, TEA and TEB react with oxygen, producing an ethyl radical, which can initiate an autoxidation chain. The ignition delay is shown to decrease with the decrease in the droplet size. Preliminary experiments on the self-ignition of pulsed and continuous TEA-TEB sprays in ambient air at NPT conditions are used for estimating the Arrhenius parameters of the rate-limiting reaction. Experiments confirm that the self-ignition delay of TEA-TEB sprays decreases with the injection pressure and provide the data for estimating the activation energy of the rate-limiting reaction, which appears to be close to 2 kcal/mol.

Interaction of Shock Waves with Water Saturated by Nonreacting or Reacting Gas Bubbles

A compressible medium represented by pure water saturated by small nonreactive or reactive gas bubbles can be used for generating a propulsive force in large-, medium-, and small-scale thrusters referred to as a pulsed detonation hydroramjet (PDH), which is a novel device for underwater propulsion. The PDH thrust is produced due to the acceleration of bubbly water (BW) in a water guide by periodic shock waves (SWs) and product gas jets generated by pulsed detonations of a fuel-oxidizer mixture. Theoretically, the PDH thrust is proportional to the operation frequency, which depends on both the SW velocity in BW and pulsed detonation frequency. The studies reported in this manuscript were aimed at exploring two possible directions of the improvement of thruster performances, namely, (1) the replacement of chemically nonreacting gas bubbles by chemically reactive ones, and (2) the increase in the pulsed detonation frequency from tens of hertz to some kilohertz. To better understand the SW-to-BW momentum transfer, the interaction of a single SW and a high-frequency (≈7 kHz) sequence of three SWs with chemically inert or active BW containing bubbles of air or stoichiometric acetylene-oxygen mixture was studied experimentally. Single SWs and SW packages were generated by burning or detonating a gaseous stoichiometric acetylene-oxygen or propane-oxygen mixture and transmitting the arising SWs to BW. The initial volume fraction of gas in BW was varied from 2% to 16% with gas bubbles 1.5-4 mm in diameter. The propagation velocity of SWs in BW ranged from 40 to 580 m/s. In experiments with single SWs in chemically active BW, a detonation-like mode of reaction front propagation ("bubbly quasidetonation") was realized. This mode consisted of a SW followed by the front of bubble explosions and was characterized by a considerably higher propagation velocity as compared to the chemically inert BW. The latter could allow increasing the PDH operation frequency and thrust. Experiments with high-frequency SW packages showed that on the one hand, the individual SWs quickly merged, feeding each other and increasing the BW velocity, but on the other hand, the initial gas content for each successive SW decreased and, accordingly, the SW-to-BW momentum transfer worsened. Estimates showed that for a small-scale water guide 0.5 m long, the optimal pulsed detonation frequency was about 50-60 Hz.

Electronic Structure and Epitaxy of CdTe Shells on InSb Nanowires

Indium antimonide (InSb) nanowires are used as building blocks for quantum devices because of their unique properties, that is, strong spin-orbit interaction and large Landé g-factor. Integrating InSb nanowires with other materials could potentially unfold novel devices with distinctive functionality. A prominent example is the combination of InSb nanowires with superconductors for the emerging topological particles research. Here, the combination of the II-VI cadmium telluride (CdTe) with the III-V InSb in the form of core-shell (InSb-CdTe) nanowires is investigated and potential applications based on the electronic structure of the InSb-CdTe interface and the epitaxy of CdTe on the InSb nanowires are explored. The electronic structure of the InSb-CdTe interface using density functional theory is determined and a type-I band alignment is extracted with a small conduction band offset ( ⩽0.3 eV). These results indicate the potential application of these shells for surface passivation or as tunnel barriers in combination with superconductors. In terms of structural quality, it is demonstrated that the lattice-matched CdTe can be grown epitaxially on the InSb nanowires without interfacial strain or defects. These shells do not introduce disorder to the InSb nanowires as indicated by the comparable field-effect mobility measured for both uncapped and CdTe-capped nanowires.

Signatures of Andreev Blockade in a Double Quantum Dot Coupled to a Superconductor

We investigate an electron transport blockade regime in which a spin triplet localized in the path of current is forbidden from entering a spin-singlet superconductor. To stabilize the triplet, a double quantum dot is created electrostatically near a superconducting Al lead in an InAs nanowire. The quantum dot closest to the normal lead exhibits Coulomb diamonds, and the dot closest to the superconducting lead exhibits Andreev bound states and an induced gap. The experimental observations compare favorably to a theoretical model of Andreev blockade, named so because the triplet double dot configuration suppresses Andreev reflections. Observed leakage currents can be accounted for by finite temperature. We observe the predicted quadruple level degeneracy points of high current and a periodic conductance pattern controlled by the occupation of the normal dot. Even-odd transport asymmetry is lifted with increased temperature and magnetic field. This blockade phenomenon can be used to study spin structure of superconductors. It may also find utility in quantum computing devices that use Andreev or Majorana states.

Parity-preserving and magnetic field-resilient superconductivity in InSb nanowires with Sn shells

Improving materials used to make qubits is crucial to further progress in quantum information processing. Of particular interest are semiconductor-superconductor heterostructures that are expected to form the basis of topological quantum computing. We grew semiconductor indium antimonide nanowires that were coated with shells of tin of uniform thickness. No interdiffusion was observed at the interface between Sn and InSb. Tunnel junctions were prepared by in situ shadowing. Despite the lack of lattice matching between Sn and InSb, a 15-nanometer-thick shell of tin was found to induce a hard superconducting gap, with superconductivity persisting in magnetic field up to 4 teslas. A small island of Sn-InSb exhibits the two-electron charging effect. These findings suggest a less restrictive approach to fabricating superconducting and topological quantum circuits.

Hysteretic magnetoresistance in nanowire devices due to stray fields induced by micromagnets

We study hysteretic magnetoresistance in InSb nanowires due to stray magnetic fields from CoFe micromagnets. Devices without any ferromagnetic components show that the magnetoresistance of InSb nanowires commonly exhibits either a local maximum or local minimum at zero magnetic field. Switching of microstrip magnetizations then results in positive or negative hysteretic dependence as conductance maxima or minima shift with respect to the global external field. Stray fields are found to be in the range of tens of millitesla, comparable to the scale over which the nanowire magnetoresistance develops. We observe that the stray field signal is similar to that obtained in devices with ferromagnetic contacts (spin valves). We perform micromagnetic simulations which are in reasonable agreement with the experiment. The use of locally varying magnetic fields may bring new ideas for Majorana circuits in which nanowire networks require control over field orientation at the nanoscale.

Ubiquitous Non-Majorana Zero-Bias Conductance Peaks in Nanowire Devices

We perform tunneling measurements on indium antimonide nanowire-superconductor hybrid devices fabricated for the studies of Majorana bound states. At finite magnetic field, resonances that strongly resemble Majorana bound states, including zero-bias pinning, become common to the point of ubiquity. Since Majorana bound states are predicted in only a limited parameter range in nanowire devices, we seek an alternative explanation for the observed zero-bias peaks. With the help of a self-consistent Poission-Schrödinger multiband model developed in parallel, we identify several families of trivial subgap states that overlap and interact, giving rise to a crowded spectrum near zero energy and zero-bias conductance peaks in experiments. These findings advance the search for Majorana bound states through improved understanding of broader phenomena found in superconductor-semiconductor systems.

Second-Harmonic Current-Phase Relation in Josephson Junctions with Ferromagnetic Barriers

We report the observation of a current-phase relation dominated by the second Josephson harmonic in superconductor-ferromagnet-superconductor junctions. The exotic current-phase relation is realized in the vicinity of a temperature-controlled 0-to-π junction transition, at which the first Josephson harmonic vanishes. Direct current-phase relation measurements, as well as Josephson interferometry, nonvanishing supercurrent and half-integer Shapiro steps at the 0-π transition self-consistently point to an intrinsic second harmonic term, making it possible to rule out common alternative origins of half-periodic behavior. While surprising for diffusive multimode junctions, the large second harmonic is in agreement with theory predictions for thin ferromagnetic interlayers.

Mirage Andreev Spectra Generated by Mesoscopic Leads in Nanowire Quantum Dots

We study transport mediated by Andreev bound states formed in InSb nanowire quantum dots. Two kinds of superconducting source and drain contacts are used: epitaxial Al/InSb devices exhibit a doubling of tunneling resonances, while, in NbTiN/InSb devices, Andreev spectra of the dot appear to be replicated multiple times at increasing source-drain bias voltages. In both devices, a mirage of a crowded spectrum is created. To describe the observations a model is developed that combines the effects of a soft induced gap and of additional Andreev bound states both in the quantum dot and in the finite regions of the nanowire adjacent to the quantum dot. Understanding of Andreev spectroscopy is important for the correct interpretation of Majorana experiments done on the same structures.

Supercurrent Interference in Few-Mode Nanowire Josephson Junctions

Junctions created by coupling two superconductors via a semiconductor nanowire in the presence of high magnetic fields are the basis for the potential detection, fusion, and braiding of Majorana bound states. We study NbTiN/InSb nanowire/NbTiN Josephson junctions and find that the dependence of the critical current on the magnetic field exhibits gate-tunable nodes. This is in contrast with a well-known Fraunhofer effect, under which critical current nodes form a regular pattern with a period fixed by the junction area. Based on a realistic numerical model we conclude that the Zeeman effect induced by the magnetic field and the spin-orbit interaction in the nanowire are insufficient to explain the observed evolution of the Josephson effect. We find the interference between the few occupied one-dimensional modes in the nanowire to be the dominant mechanism responsible for the critical current behavior. We also report a strong suppression of critical currents at finite magnetic fields that should be taken into account when designing circuits based on Majorana bound states.

Quasiballistic quantum transport through Ge/Si core/shell nanowires

We study signatures of ballistic quantum transport of holes through Ge/Si core/shell nanowires at low temperatures. We observe Fabry-Pérot interference patterns as well as conductance plateaus at integer multiples of 2e ²/h at zero magnetic field. Magnetic field evolution of these plateaus reveals relatively large effective Landé g-factors. Ballistic effects are observed in nanowires with silicon shell thickness of 1-3 nm, but not in bare germanium wires. These findings inform the future development of spin and topological quantum devices which rely on ballistic sub-band-resolved transport.

Andreev molecules in semiconductor nanowire double quantum dots

Chains of quantum dots coupled to superconductors are promising for the realization of the Kitaev model of a topological superconductor. While individual superconducting quantum dots have been explored, control of longer chains requires understanding of interdot coupling. Here, double quantum dots are defined by gate voltages in indium antimonide nanowires. High transparency superconducting niobium titanium nitride contacts are made to each of the dots in order to induce superconductivity, as well as probe electron transport. Andreev bound states induced on each of dots hybridize to define Andreev molecular states. The evolution of these states is studied as a function of charge parity on the dots, and in magnetic field. The experiments are found in agreement with a numerical model.

Quantum dots in a nanowire are one possible approach to creating a solid-state quantum simulator. Here, the authors demonstrate the coupling of electronic states in a double quantum dot to form Andreev molecule states; a potential building block for longer chains suitable for quantum simulation.

Experimental phase diagram of zero-bias conductance peaks in superconductor/semiconductor nanowire devices

Topological superconductivity is an exotic state of matter characterized by spinless p-wave Cooper pairing of electrons and by Majorana zero modes at the edges. The first signature of topological superconductivity is a robust zero-bias peak in tunneling conductance. We perform tunneling experiments on semiconductor nanowires (InSb) coupled to superconductors (NbTiN) and establish the zero-bias peak phase in the space of gate voltage and external magnetic field. Our findings are consistent with calculations for a finite-length topological nanowire and provide means for Majorana manipulation as required for braiding and topological quantum bits.

New perspectives for Rashba spin-orbit coupling

In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain the peculiarities of electron spin resonance in two-dimensional semiconductors. Over the past 30 years, Rashba spin-orbit coupling has inspired a vast number of predictions, discoveries and innovative concepts far beyond semiconductors. The past decade has been particularly creative, with the realizations of manipulating spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and the discovery of new topological classes of materials. This progress has reinvigorated the interest of physicists and materials scientists in the development of inversion asymmetric structures, ranging from layered graphene-like materials to cold atoms. This Review discusses relevant recent and ongoing realizations of Rashba physics in condensed matter.

Formation and electronic properties of InSb nanocrosses

Signatures of Majorana fermions have recently been reported from measurements on hybrid superconductor-semiconductor nanowire devices. Majorana fermions are predicted to obey special quantum statistics, known as non-Abelian statistics. To probe this requires an exchange operation, in which two Majorana fermions are moved around one another, which requires at least a simple network of nanowires. Here, we report on the synthesis and electrical characterization of crosses of InSb nanowires. The InSb wires grow horizontally on flexible vertical stems, allowing nearby wires to meet and merge. In this way, near-planar single-crystalline nanocrosses are created, which can be measured by four electrical contacts. Our transport measurements show that the favourable properties of the InSb nanowire devices-high carrier mobility and the ability to induce superconductivity--are preserved in the cross devices. Our nanocrosses thus represent a promising system for the exchange of Majorana fermions.

Electrical control of single hole spins in nanowire quantum dots

The development of viable quantum computation devices will require the ability to preserve the coherence of quantum bits (qubits). Single electron spins in semiconductor quantum dots are a versatile platform for quantum information processing, but controlling decoherence remains a considerable challenge. Hole spins in III-V semiconductors have unique properties, such as a strong spin-orbit interaction and weak coupling to nuclear spins, and therefore, have the potential for enhanced spin control and longer coherence times. A weaker hyperfine interaction has previously been reported in self-assembled quantum dots using quantum optics techniques, but the development of hole-spin-based electronic devices in conventional III-V heterostructures has been limited by fabrication challenges. Here, we show that gate-tunable hole quantum dots can be formed in InSb nanowires and used to demonstrate Pauli spin blockade and electrical control of single hole spins. The devices are fully tunable between hole and electron quantum dots, which allows the hyperfine interaction strengths, g-factors and spin blockade anisotropies to be compared directly in the two regimes.

Quantized conductance in an InSb nanowire

Ballistic one-dimensional transport in semiconductor nanowires plays a central role in creating topological and helical states. The hallmark of such one-dimensional transport is conductance quantization. Here we show conductance quantization in InSb nanowires at nonzero magnetic fields. Conductance plateaus are studied as a function of source-drain bias and magnetic field, enabling extraction of the Landé g factor and the subband spacing.

Fast spin-orbit qubit in an indium antimonide nanowire

Because of the strong spin-orbit interaction in indium antimonide, orbital motion and spin are no longer separated. This enables fast manipulation of qubit states by means of microwave electric fields. We report Rabi oscillation frequencies exceeding 100 MHz for spin-orbit qubits in InSb nanowires. Individual qubits can be selectively addressed due to intrinsic differences in their g factors. Based on Ramsey fringe measurements, we extract a coherence time T(2)(*)=8±1 ns at a driving frequency of 18.65 GHz. Applying a Hahn echo sequence extends this coherence time to 34 ns.

Suppression of Zeeman gradients by nuclear polarization in double quantum dots

We use electric dipole spin resonance to measure dynamic nuclear polarization in InAs nanowire quantum dots. The resonance shifts in frequency when the system transitions between metastable high and low current states, indicating the presence of nuclear polarization. We propose that the low and the high current states correspond to different total Zeeman energy gradients between the two quantum dots. In the low current state, dynamic nuclear polarization efficiently compensates the Zeeman gradient due to the g-factor mismatch, resulting in a suppressed total Zeeman gradient. We present a theoretical model of electron-nuclear feedback that demonstrates a fixed point in nuclear polarization for nearly equal Zeeman splittings in the two dots and predicts a narrowed hyperfine gradient distribution.

Spectroscopy of spin-orbit quantum bits in indium antimonide nanowires

A double quantum dot in the few-electron regime is achieved using local gating in an InSb nanowire. The spectrum of two-electron eigenstates is investigated using electric dipole spin resonance. Singlet-triplet level repulsion caused by spin-orbit interaction is observed. The size and the anisotropy of singlet-triplet repulsion are used to determine the magnitude and the orientation of the spin-orbit effective field in an InSb nanowire double dot. The obtained results are confirmed using spin blockade leakage current anisotropy and transport spectroscopy of individual quantum dots.

Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices

Majorana fermions are particles identical to their own antiparticles. They have been theoretically predicted to exist in topological superconductors. Here, we report electrical measurements on indium antimonide nanowires contacted with one normal (gold) and one superconducting (niobium titanium nitride) electrode. Gate voltages vary electron density and define a tunnel barrier between normal and superconducting contacts. In the presence of magnetic fields on the order of 100 millitesla, we observe bound, midgap states at zero bias voltage. These bound states remain fixed to zero bias, even when magnetic fields and gate voltages are changed over considerable ranges. Our observations support the hypothesis of Majorana fermions in nanowires coupled to superconductors.

From InSb nanowires to nanocubes: looking for the sweet spot

High aspect ratios are highly desired to fully exploit the one-dimensional properties of indium antimonide nanowires. Here we systematically investigate the growth mechanisms and find parameters leading to long and thin nanowires. Variation of the V/III ratio and the nanowire density are found to have the same influence on the "local" growth conditions and can control the InSb shape from thin nanowires to nanocubes. We propose that the V/III ratio controls the droplet composition and the radial growth rate and these parameters determine the nanowire shape. A sweet spot is found for nanowire interdistances around 500 nm leading to aspect ratios up to 35. High electron mobilities up to 3.5 × 10(4) cm(2) V(-1) s(-1) enable the realization of complex spintronic and topological devices.

Electrical generation of pure spin currents in a two-dimensional electron gas

Pure spin currents are generated and detected in micron-wide channels of a GaAs two-dimensional electron gas, using quantum point contacts in an in-plane magnetic field as injectors and detectors. The enhanced sensitivity to spin transport offered by a nonlocal measurement geometry enables accurate spin current measurements in this widely studied physical system. The polarization of the contacts is used to extract the quantum point contact g factor and provides a test for spontaneous polarization at 0.7 structure. The spin relaxation length in the channel is 30-50 microm over the magnetic field range 3-10 T, much longer than has been reported in GaAs two-dimensional electron gases but shorter than that expected from Dyakonov-Perel relaxation.