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.

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.

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.

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.

Spin-orbit qubit in a semiconductor nanowire.

Motion of electrons can influence their spins through a fundamental effect called spin-orbit interaction. This interaction provides a way to control spins electrically and thus lies at the foundation of spintronics. Even at the level of single electrons, the spin-orbit interaction has proven promising for coherent spin rotations. Here we implement a spin-orbit quantum bit (qubit) in an indium arsenide nanowire, where the spin-orbit interaction is so strong that spin and motion can no longer be separated. In this regime, we realize fast qubit rotations and universal single-qubit control using only electric fields; the qubits are hosted in single-electron quantum dots that are individually addressable. We enhance coherence by dynamically decoupling the qubits from the environment. Nanowires offer various advantages for quantum computing: they can serve as one-dimensional templates for scalable qubit registers, and it is possible to vary the material even during wire growth. Such flexibility can be used to design wires with suppressed decoherence and to push semiconductor qubit fidelities towards error correction levels. Furthermore, electrical dots can be integrated with optical dots in p-n junction nanowires. The coherence times achieved here are sufficient for the conversion of an electronic qubit into a photon, which can serve as a flying qubit for long-distance quantum communication.

Ballistic spin resonance.

The phenomenon of spin resonance has had far-reaching influence since its discovery 70 years ago. Electron spin resonance driven by high-frequency magnetic fields has enhanced our understanding of quantum mechanics, and finds application in fields as diverse as medicine and quantum information. Spin resonance can also be induced by high-frequency electric fields in materials with a spin-orbit interaction; the oscillation of the electrons creates a momentum-dependent effective magnetic field acting on the electron spin. Here we report electron spin resonance due to a spin-orbit interaction that does not require external driving fields. The effect, which we term ballistic spin resonance, is driven by the free motion of electrons that bounce at frequencies of tens of gigahertz in micrometre-scale channels of a two-dimensional electron gas. This is a frequency range that is experimentally challenging to access in spin resonance, and especially difficult on a chip. The resonance is manifest in electrical measurements of pure spin currents-we see a strong suppression of spin relaxation length when the oscillating spin-orbit field is in resonance with spin precession in a static magnetic field. These findings illustrate how the spin-orbit interaction can be harnessed for spin manipulation in a spintronic circuit, and point the way to gate-tunable coherent spin rotations in ballistic nanostructures without external alternating current fields.

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.

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.

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.

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.

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.