Search

Topological superconductors (SCs) hold great promise for fault-tolerant quantum hardware, however, their experimental realization is very challenging. Recently, superconducting artificial molecules (Andreev molecules) have opened new avenues to engineer topological superconducting materials. In this work, we demonstrate a heteroatomic Andreev molecule, where two normal artificial atoms realized by quantum dots (QDs) are coupled by a superconducting island (SCI). We show that the two normal atoms strongly hybridize and form a 3-electron-based molecular state. Our density matrix renormalization group (DMRG) calculations explain quantitatively the robust binding of electrons. The tunability of the structure allows us to drive a quantum phase transition from an antiferromagnetic Andreev molecular state to a heteroatomic Andreev molecule with ferromagnetically coupled QDs using simple electrical gating.

The observation of the gate-controlled supercurrent (GCS) effect in superconducting nanostructures increased the hopes for realizing a superconducting equivalent of semiconductor field-effect transistors. However, recent works attribute this effect to various leakage-based scenarios, giving rise to a debate on its origin. A proper understanding of the microscopic process underlying the GCS effect and the relevant time scales would be beneficial to evaluate the possible applications. In this work, we observed gate-induced two-level fluctuations between the superconducting state and normal state in Al/InAs nanowires (NWs). Noise correlation measurements show a strong correlation with leakage current fluctuations. The time-domain measurements show that these fluctuations have Poissonian statistics. Our detailed analysis of the leakage current measurements reveals that it is consistent with the stress-induced leakage current (SILC), in which inelastic tunneling with phonon generation is the predominant transport mechanism. Our findings shed light on the microscopic origin of the GCS effect and give deeper insight into the switching dynamics of the superconducting NW under the influence of the strong gate voltage.

Understanding heating and cooling mechanisms in mesoscopic superconductor-semiconductor hybrid devices is crucial for their application in quantum technologies. Owing to the poor thermal conductivity of typical devices, heating effects can drive superconducting-to-normal phase transitions even at low applied bias, observed as sharp conductance dips through the loss of Andreev excess currents. Tracking such dips across magnetic field, cryostat temperature, and applied microwave power, which constitutes Joule spectroscopy, allows to uncover the underlying cooling bottlenecks in different parts of a device. By applying this technique, we analyze heat dissipation in devices based on full-shell InAs-Al nanowires and reveal that superconducting islands are strongly susceptible to heating as their cooling is limited by the rather inefficient electron-phonon coupling, as opposed to grounded superconductors that primarily cool by quasiparticle diffusion. Our measurements indicate that powers as low as 50-150 pW are able to fully suprpress the superconductivity of an island. Finally, we show that applied microwaves lead to similar heating effects as DC signals, and explore the interplay of the microwave frequency and the effective electron-phonon relaxation time., Comment: 9 pages, 4 figures

An epitaxial semiconductor-superconductor nanowire is a superconducting system with a complex level structure originating from hybridization: in addition to a dense set of higher-energy states derived predominantly from the metallic superconducting shell above the bulk gap $\Delta$, there is a smaller number of lower-energy proximitized states from the semiconducting core that define the induced gap $\Delta^*$. Nanostructures built from such nanowires can furthermore incorporate quantum dots in order to obtain localized spins for storing and manipulating quantum information. We discuss the magnetic field dependence in three devices with different combinations of embedded quantum dots and superconducting islands. For strong fields, they show pinning of excitation energies to a uniform spacing, even if for weak fields they have non-universal properties with different behaviors for even and odd number of confined electrons. We propose a quantum impurity model for hybrid devices that incorporates all relevant physical effects. We show that the model accounts for the key observations and permits unambiguous interpretation in terms of many-particle states. In particular, we study the replicas of the Yu-Shiba-Rusinov states in the hybrid gap, their collapse and oscillation around zero bias with increasing field, and the strong smoothing effect of the spin-orbit coupling (SOC) on these oscillations. We propose that the SOC-induced mixing of many-body states is a generic mechanism and that magnetic pinning is likely to be a ubiquitous feature in hybrid nanowires., Comment: 15 pages, 7 figures

Implementing superconductors capable of proximity-inducing a large energy-gap in semiconductors in the presence of strong magnetic fields is a major goal towards applications of semiconductor/superconductor hybrid materials in future quantum information technologies. Here, we study the performance of devices consisting of InAs nanowires in electrical contact to molybdenum-rhenium (MoRe) superconducting alloys. The MoRe thin films exhibit transition temperatures ~10 K and critical fields exceeding 6 T. Normal/superconductor devices enabled tunnel spectroscopy of the corresponding induced superconductivity, which was maintained up to ~10 K, and MoRe based Josephson devices exhibit supercurrents and multiple Andreev reflections. We determine an induced superconducting gap lower than expected from the transition temperature, and observe gap softening at finite magnetic field. These may be common features for hybrids based on large gap, type-II superconductors. The results encourage further development of MoRe-based hybrids.

Understanding the microscopic origin of the gate-controlled supercurrent (GCS) in superconducting nanobridges is crucial for engineering superconducting switches suitable for a variety of electronic applications. The origin of GCS is controversial, and various mechanisms have been proposed to explain it. In this work, we have investigated the GCS in a Ta layer deposited on the surface of InAs nanowires. Comparison between switching current distributions at opposite gate polarities and between the gate dependence of two opposite side gates with different nanowire$-$gate spacings shows that the GCS is determined by the power dissipated by the gate leakage. We also found a substantial difference between the influence of the gate and elevated bath temperature on the magnetic field dependence of the supercurrent. Detailed analysis of the switching dynamics at high gate voltages shows that the device is driven into the multiple phase slips regime by high-energy fluctuations arising from the leakage current.

Hybrid superconductor-semiconductor devices offer highly tunable platforms, potentially suitable for quantum technology applications, that have been intensively studied in the past decade. Here we establish that measurements of the superconductor-to-normal transition originating from Joule heating provide a powerful spectroscopical tool to characterize such hybrid devices. Concretely, we apply this technique to junctions in full-shell Al-InAs nanowires in the Little-Parks regime and obtain detailed information of each lead independently and in a single measurement, including differences in the superconducting coherence lengths of the leads, inhomogeneous covering of the epitaxial shell, and the inverse superconducting proximity effect; all-in-all constituting a unique fingerprint of each device and highlighting the large variability present in these systems. Besides the practical uses, our work also underscores the importance of heating in hybrid devices, an effect that is often overlooked.

Hybrid nanostructures consisting of two parallel InAs nanowires connected by an epitaxially grown superconductor (SC) shell recently became available. Due to the defect-free SC-semiconductor interface and the two quasi-one-dimensional channels being close by, these novel platforms can be utilized to spatially separate entangled pairs of electrons by using quantum dots (QD) in the so-called Cooper pair splitting (CPS) process. The minimized distance between the QDs overcomes the limitations of single-wire-based geometries and can boost the splitting efficiency. Here we investigate CPS in such a device, for the first time, where strong inter-dot Coulomb repulsion is also present and studied thoroughly. We analyze theoretically the slight reduction of the CPS efficiency imposed by the Coulomb interaction and compare it to the experiments. Despite the competition between crossed Andreev reflection (CAR) and inter-wire capacitance, a significant CPS signal is observed indicating the dominance of the superconducting coupling. Our results demonstrate that the application of parallel InAs nanowires with epitaxial SC is a promising route for the realization of parafermionic states relying on enhanced CAR between the wires.

We characterize in-situ grown parallel nanowires bridged by a superconducting island. The magnetic-field and temperature dependence of Coulomb blockade peaks measured across different pairs of nanowire ends are consistent with a sub-gap state extended over the hybrid parallel-nanowire island. Being gate-tunable, accessible by multiple terminals and free of quasiparticle poisoning, these nanowires show promise for the implementation of several proposals that rely on parallel nanowire platforms., Comment: 9 pages, 5 figures

Condensed matter is composed of a small set of identical units, yet it shows an immense range of behaviour. Recently, an array of cold atoms was used to generate long-range quantum entanglement, a property of topological matter. Another approach to strong non-local correlations employs the macroscopic coherence of superconductors. Impurity spins in superconductors are thought to be unamenable to the formation of long-range spin entanglement because each spin tends to be screened by binding to a quasiparticle from the superconductor to form a local singlet. Here we demonstrate that it is possible to attach a second quasiparticle to the spin, overscreening it into a doublet state carrying ferromagnetic correlations between two quasiparticles over a micrometer distance. To demonstrate this effect, which is strongest for equal binding, we symmetrically couple the spin of a quantum dot to two ultrasmall superconducting islands. The overscreened state requires sufficiently large Coulomb repulsion and exchange binding to become well defined. We predict that this state will carry long-range correlations for an alternating chain of quantum dots and superconducting islands, opening a new route to controllable large-scale entanglement in the solid state., Comment: 4 figures, 7 extended data figures

We report in-situ synthesis of crystalline indium islands on InAs nanowires grown by molecular beam epitaxy. Structural analysis by transmission electron microscopy showed that In crystals grew in a tetragonal body-centred crystal structure within two families of orientations relative to wurtzite InAs. The crystalline islands had lengths < 500 nm and low-energy surfaces, suggesting that growth was driven mainly by surface energy minimization. Electrical transport through In/InAs devices exhibited Cooper pair charging, evidencing charge parity preservation and a pristine In/InAs interface, with an induced superconducting gap ~ 0.45 meV. Cooper pair charging persisted to temperatures > 1.2 K and magnetic fields ~ 0.7 T, demonstrating that In/InAs hybrids belong to an expanding class of semiconductor/superconductor hybrids operating over a wider parameter space than state-of-the-art Al-based hybrids. Engineering crystal morphology while isolating single islands using shadow epitaxy provides an interesting alternative to previous semiconductor/superconductor hybrid morphologies and device geometries., Comment: Published in Nano Letters: https://pubs.acs.org/doi/10.1021/acs.nanolett.1c02487

Unlocking the full potential of nanocrystals in electronic devices requires scalable and deterministic manufacturing techniques. A platform offering promising alternative paths to scalable production is microtomy, the technique of cutting thin lamellae with large areas containing embedded nanostructures. This platform has so far not been used for fabrication of electronic quantum devices. Here, we combine microtomy with vapor-liquid-solid growth of III/V nanowires to create a scalable platform that can deterministically transfer large arrays of single and fused nanocrystals - offering single unit control and free choice of target substrate. We fabricate electronic devices on cross-sectioned InAs nanowires with good yield and demonstrate their ability to exhibit quantum phenomena such as conductance quantization, single electron charging, and wave interference. Finally, we devise how the platform can host rationally designed semiconductor/superconductor networks relevant for emerging quantum technologies.

Cooper pair splitting (CPS) is a way to create spatially separated, entangled electron pairs. To this day, CPS is often identified in experiments as a spatial current correlation. However, such correlations can arise even in the absence of CPS, when a quantum dot is strongly coupled to the superconductor, and a subgap Shiba state is formed. Here, we present a detailed experimental characterization of those spatial current correlations, as the tunnel barrier strength between the quantum dot and the neighboring normal electrode is tuned. The correlation of the non-local signal and the barrier strength reveals a competition between CPS and the non-local probing of the Shiba state. We describe our experiment with a simple transport model, and obtain the tunnel couplings of our device by fitting the model's prediction to the measured conductance correlation curve. Furthermore, we use our theory to extract the contribution of CPS to the non-local signal., Comment: 12 pages, 3 figures

Gate-controlled supercurrent (GCS) in superconductor nanobridges has recently attracted attention as a means to create superconducting field effect transistors. Despite the clear advantage for applications with low power consumption and high switching speeds, the microscopic mechanism of the field effect is still under debate. In this work, we realize GCS for the first time in an epitaxial superconductor, which is created as a shell on an InAs nanowire. We show that the supercurrent in the epitaxial Al layer can be switched to the normal state by applying $\simeq\pm$ 23$\,$V on a bottom gate insulated from the nanowire by a crystalline hBN layer. Our extensive study on the temperature and magnetic field dependencies of GCS suggests that hot electron injection alone cannot explain our experimental findings.

Little-Parks oscillations of a hollow superconducting cylinder are of interest for flux-driven topological superconductivity in single Rashba nanowires. The oscillations are typically symmetric in the orientation of the applied magnetic flux. Using double InAs nanowires coated by an epitaxial superconducting Al shell which, despite the non-centro-symmetric geometry, behaves effectively as one hollow cylinder, we demonstrate that a small misalignment of the applied parallel field with respect to the axis of the nanowires can produce field-asymmetric Little-Parks oscillations. These are revealed by the simultaneous application of a magnetic field perpendicular to the misaligned parallel field direction. The asymmetry occurs in both the destructive regime, in which superconductivity is destroyed for half-integer quanta of flux through the shell, and in the non-destructive regime, where superconductivity is depressed but not fully destroyed at these flux values., Comment: 9 pages, 3 figures

We demonstrate direct transport between two opposing sets of Yu-Shiba-Rusinov (YSR) subgap states realized in a double quantum dot. This sub-gap transport relies on intrinsic quasiparticle relaxation, but the tunability of the device allows us to explore also an additional relaxation mechanism based on charge transferring Andreev reflections. The transition between these two relaxation regimes is identified in the experiment as a marked gate-induced stepwise change in conductance. We present a transport calculation, including YSR bound states and multiple Andreev reflections alongside with quasiparticle relaxation, due to a weak tunnel coupling to a nearby normal metal, and obtain excellent agreement with the data.

We characterize parallel double quantum dot Josephson junctions based on closely-grown double nanowires bridged by in-situ deposited superconductors. The parallel double dot behavior occurs despite the closeness of the nanowires and the potential risk of nanowire clamping during growth. By tuning the charge filling and lead couplings, we map out the simplest parallel double quantum dot Yu-Shiba-Rusinov phase diagram. Our quasi-independent two-wire hybrids show promise for the realization of exotic topological phases., Comment: 8 pages, 4 figures

Coupling individual atoms via tunneling fundamentally changes the state of matter: electrons bound to atomic cores become delocalized resulting in a change from an insulating to a metallic state, as it is well known from the canonical example of solids. A chain of atoms could lead to more exotic states if the tunneling takes place via the superconducting vacuum and can induce topologically protected excitations like Majorana or parafermions. Toward the realization of such artificial chains, coupling a single atom to the superconducting vacuum is well studied, but the hybridization of two sites via the superconductor was not yet reported. The peculiar vacuum of the BCS condensate opens the way to annihilate or generate two electrons from the bulk resulting in a so-called Andreev molecular state. By employing parallel nanowires with an Al superconductor shell, two artificial atoms were created at a minimal distance with an epitaxial superconducting link between. Hybridization via the BCS vacuum was observed between the two artificial atoms for the first time, as a demonstration of an Andreev molecular state., Comment: References were updated

Parallel one-dimensional semiconductor channels connected by a superconducting strip constitute the core platform in several recent quantum device proposals that rely e.g. on Andreev processes or topological effects. In order to realize these proposals, the actual material systems must have high crystalline purity and the coupling between the different elements should be controllable in terms of their interfaces and geometry. We present a strategy for synthesizing double InAs nanowires by the vapor-liquid-solid mechanism using III-V molecular beam epitaxy. A superconducting layer is deposited onto nanowires without breaking vacuum, ensuring pristine interfaces between the superconductor and the two semiconductor nanowires. The method allows for a high yield of merged as well as separate parallel nanowires, with full or half-shell superconductor coatings. We demonstrate their utility in complex quantum devices by electron transport measurements.

In recent years, the notion of Quantum Materials has emerged as a powerful unifying concept across diverse fields of science and engineering, from condensed-matter and cold atom physics to materials science and quantum computing. Beyond traditional quantum materials such as unconventional superconductors, heavy fermions, and multiferroics, the field has significantly expanded to encompass topological quantum matter, two-dimensional materials and their van der Waals heterostructures, Moire materials, Floquet time crystals, as well as materials and devices for quantum computation with Majorana fermions. In this Roadmap collection we aim to capture a snapshot of the most recent developments in the field, and to identify outstanding challenges and emerging opportunities. The format of the Roadmap, whereby experts in each discipline share their viewpoint and articulate their vision for quantum materials, reflects the dynamic and multifaceted nature of this research area, and is meant to encourage exchanges and discussions across traditional disciplinary boundaries. It is our hope that this collective vision will contribute to sparking new fascinating questions and activities at the intersection of materials science, condensed matter physics, device engineering, and quantum information, and to shaping a clearer landscape of quantum materials science as a new frontier of interdisciplinary scientific inquiry., Comment: 93 pages, 27 figures

Cooper pairing and Coulomb repulsion are antagonists, producing distinct energy gaps in superconductors and Mott insulators. When a superconductor exchanges unpaired electrons with a quantum dot, its gap is populated by a pair of electron-hole symmetric Yu-Shiba-Rusinov excitations between doublet and singlet many-body states. The fate of these excitations in the presence of a strong Coulomb repulsion in the superconductor is unknown, but of importance in applications such as topological superconducting qubits and multi-channel impurity models. Here we couple a quantum dot to a superconducting island with a tunable Coulomb repulsion. We show that a strong Coulomb repulsion changes the singlet many-body state into a two-body state. It also breaks the electron-hole energy symmetry of the excitations, which thereby lose their Yu-Shiba-Rusinov character., Comment: Supplementary Information available as an ancillary file with this submission. Raw experimental data available at https://doi.org/10.17894/ucph.e17975c9-c12c-412b-b046-aca7526cb8ed

Serial double quantum dots created in semiconductor nanostructures provide a versatile platform for investigating two-electron spin quantum states, which can be tuned by electrostatic gating and an external magnetic field. In this work, we directly measure the supercurrent reversal between adjacent charge states of an InAs nanowire double quantum dot with superconducting leads, in good agreement with theoretical models. In the even charge parity sector, we observe a supercurrent blockade with increasing magnetic field, corresponding to the spin singlet to triplet transition. Our results demonstrate a direct spin to supercurrent conversion, the superconducting equivalent of the Pauli spin blockade. This effect can be exploited in hybrid quantum architectures coupling the quantum states of spin systems and superconducting circuits., Comment: Published version. Supplementary Information is available as ancillary file, raw data and calculations can be downloaded from https://doi.org/10.5281/zenodo.3978236

The strong coupling of a superconductor to a spinful quantum dot results in Yu-Shiba-Rusinov (YSR) discrete subgap excitations. In isolation and at zero temperature, the excitations are $\delta$ resonances. In transport experiments, however, they show as broad differential conductance peaks. We obtain the lineshape of the peaks and their temperature dependence in superconductor-quantum-dot-metal (S-QD-N) nanowire-based devices. Unexpectedly, we find that the peaks shift in energy with temperature, with the shift magnitude and sign depending on ground state parity and bias voltage. Additionally, we empirically find a power-law scaling of the peak area versus temperature. These observations are not explained by current models.

Semiconductor-superconductor hybrids are widely used for realising complex quantum phenomena such as topological superconductivity and spins coupled to Cooper pairs. Accessing exotic regimes at high magnetic fields and increasing operating temperatures beyond the state-of-the-art requires new, epitaxially matched semiconductor-superconductor materials. The challenge is to generate favourable conditions for heterostructure formation between materials with the desired inherent properties. Here, we harness increased knowledge of metal-on-semiconductor growth to develop InAs nanowires with epitaxially matched, single crystal, atomically flat Pb films along the entire nanowire. These highly ordered heterostructures have a critical temperature of 7 K and a superconducting gap of 1.25 meV, which remains hard at 8.5 T, thereby more than doubling the available parameter space. Additionally, InAs/Pb island devics exhibit magnetic field-driven transitions from Cooper pair to single electron charging; a pre-requisite for use in topological quantum computation. Introducing semiconductor-Pb hybrids potentially enables access to entirely new regimes for an array of quantum systems.

Electronic excitations above the ground state must overcome an energy gap in superconductors with spatially-homogeneous s-wave pairing. In contrast, inhomogeneous superconductors such as those with magnetic impurities or weak links, or heterojunctions containing normal metals or quantum dots, can host subgap electronic excitations that are generically known as Andreev bound states (ABSs). With the advent of topological superconductivity, a new kind of ABS with exotic qualities, known as Majorana bound state (MBS), has been discovered. We review the main properties of ABSs and MBSs, and the state-of-the-art techniques for their detection. We focus on hybrid superconductor-semiconductor nanowires, possibly coupled to quantum dots, as one of the most flexible and promising experimental platforms. We discuss how the combined effect of spin-orbit coupling and Zeeman field in these wires triggers the transition from ABSs into MBSs. We show theoretical progress beyond minimal models in understanding experiments, including the possibility of different types of robust zero modes that may emerge without a band-topological transition. We examine the role of spatial non-locality, a special property of MBS wavefunctions that, together with non-Abelian braiding, is the key to realizing topological quantum computation., Comment: Review. 23 pages, 8 figures, 1 table. Shareable published version by Springer Nature at https://rdcu.be/b7DWT (free to read but not to download)

Uniform, defect-free crystal interfaces and surfaces are crucial ingredients for realizing high-performance nanoscale devices. A pertinent example is that advances in gate-tunable and topological superconductivity using semiconductor/superconductor electronic devices are currently built on the hard proximity-induced superconducting gap obtained from epitaxial indium arsenide/aluminium heterostructures. Fabrication of devices requires selective etch processes; these exist only for InAs/Al hybrids, precluding the use of other, potentially superior material combinations. We present a crystal growth platform -- based on three-dimensional structuring of growth substrates -- which enables synthesis of semiconductor nanowire hybrids with in-situ patterned superconductor shells. This platform eliminates the need for etching, thereby enabling full freedom in choice of hybrid constituents. We realise and characterise all the most frequently used architectures in superconducting hybrid devices, finding increased yield and electrostatic stability compared to etched devices, along with evidence of ballistic superconductivity. In addition to aluminium, we present hybrid devices based on tantalum, niobium and vanadium. This is the submitted version of the manuscript. The accepted, peer reviewed version is available from Advanced Materials: http://doi.org/10.1002/adma.201908411 Previous title: Shadow lithography for in-situ growth of generic semiconductor/superconductor devices

Various promising qubit concepts have been put forward recently based on engineered superconductor (SC) subgap states like Andreev bound states, Majorana zero modes or the Yu-Shiba-Rusinov (Shiba) states. The coupling of these subgap states via a SC strongly depends on their spatial extension and is an essential next step for future quantum technologies. Here we investigate the spatial extension of a Shiba state in a semiconductor quantum dot coupled to a SC for the first time. With detailed transport measurements and numerical renormalization group calculations we find a remarkable more than 50 nm extension of the zero energy Shiba state, much larger than the one observed in very recent scanning tunneling microscopy (STM) measurements. Moreover, we demonstrate that its spatial extension increases substantially in magnetic field., Comment: 11 pages, 7 figures

The Cooper-pair transistor (CPT), a small superconducting island enclosed between two Josephson weak links, is the atomic building block of various superconducting quantum circuits. Utilizing gate-tunable semiconductor channels as weak links, the energy scale associated with the Josephson tunneling can be changed with respect to the charging energy of the island, tuning the extent of its charge fluctuations. Here, we directly demonstrate this control by mapping the energy level structure of a CPT made of an indium arsenide nanowire (NW) with a superconducting aluminum shell. We extract the device parameters based on the exhaustive modeling of the quantum dynamics of the phase-biased nanowire CPT and directly measure the even-odd parity occupation ratio as a function of the device temperature, relevant for superconducting and prospective topological qubits., Comment: Published version. Supplementary Information is available as ancillary file, raw data and calculations can be downloaded from http://doi.org/10.4121/uuid:5d54f11b-6774-4ae4-96cf-25e6a91927e2

Parity control of superconducting islands hosting Majorana zero modes (MZMs) is required to operate topological qubits made from proximitized semiconductor nanowires. We, therefore, study parity effects in hybrid InAs-Al single-Cooper-pair transistors (SCPTs) as a first step. In particular, we investigate the gate-charge supercurrent modulation and observe a consistent 2$e$-periodic pattern indicating a general lack of low-energy subgap states in these nanowires at zero magnetic field. In a parallel magnetic field, an even-odd pattern develops with a gate-charge spacing that oscillates as a function of field demonstrating that the modulation pattern is sensitive to the presence of a single subgap state. In addition, we find that the parity lifetime of the SCPT decreases exponentially with magnetic field as the subgap state approaches zero energy. Our work highlights the important role that intentional quasiparticle traps and superconducting gap engineering would play in topological qubits that require quenching of the island charge dispersion., Comment: 8 pages, 4 figures, supplemental material included as ancillary file

Recent years have brought an explosion of activities in the research of topological aspects of condensed-matter systems. Topologically non-trivial phases of matter are typically accompanied by protected surface states or exotic degenerate excitations such as Majorana end states or Haldane's localized spinons. Topologically protected degeneracies can, however, also appear in the bulk. An intriguing example is provided by Weyl semimetals, where topologically protected electronic band degeneracies and exotic surface states emerge even in the absence of interactions. Here we demonstrate experimentally and theoretically that Weyl degeneracies appear naturally in an interacting quantum dot system, for specific values of the external magnetic field. These magnetic Weyl points are robust against spin-orbit coupling unavoidably present in most quantum dot devices. Our transport experiments through an InAs double dot device placed in magnetic field reveal the presence of a pair of Weyl points, exhibiting a robust ground state degeneracy and a corresponding protected Kondo effect., Comment: 6 pages, 3 figures. Supplementary Information can be downloaded as an ancillary pdf file

Quantum computation by non-Abelian Majorana zero modes (MZMs) offers an approach to achieve fault tolerance by encoding quantum information in the non-local charge parity states of semiconductor nanowire networks in the topological superconductor regime. Thus far, experimental studies of MZMs chiefly relied on single electron tunneling measurements which leads to decoherence of the quantum information stored in the MZM. As a next step towards topological quantum computation, charge parity conserving experiments based on the Josephson effect are required, which can also help exclude suggested non-topological origins of the zero bias conductance anomaly. Here we report the direct measurement of the Josephson radiation frequency in InAs nanowires with epitaxial aluminium shells. For the first time, we observe the $4\pi$-periodic Josephson effect above a magnetic field of $\approx 200\,$mT, consistent with the estimated and measured topological phase transition of similar devices., Comment: Published version. Supplementary Information is available as ancillary file, raw data and calculations can be downloaded from http://dx.doi.org/10.4121/uuid:1f936840-5bc2-40ca-8c32-1797c12cacb1

The combination of strong spin-orbit coupling, large $g$-factors, and the coupling to a superconductor can be used to create a topologically protected state in a semiconductor nanowire. Here we report on growth and characterization of hybrid epitaxial InAsSb/Al nanowires, with varying composition and crystal structure. We find the strongest spin-orbit interaction at intermediate compositions in zincblende InAs$_{1-x}$Sb$_{x}$ nanowires, exceeding that of both InAs and InSb materials, confirming recent theoretical studies \cite{winkler2016topological}. We show that the epitaxial InAsSb/Al interfaces allows for a hard induced superconducting gap and 2$e$ transport in Coulomb charging experiments, similar to experiments on InAs/Al and InSb/Al materials, and find measurements consistent with topological phase transitions at low magnetic fields due to large effective $g$-factors. Finally we present a method to grow pure wurtzite InAsSb nanowires which are predicted to exhibit even stronger spin-orbit coupling than the zincblende structure., Comment: 10 pages and 5 figures

Part of developing new strategies for fabrications of nanowire structures involves in many cases the aid of metal nanoparticles (NPs). It is highly beneficial if one can define both diameter and position of the initial NPs and make well-defined nanowire arrays. This sets additional requirement on the NPs with respect to being able to withstand a pre-growth annealing process (i.e. de- oxidation of the III-V semiconductor surface) in an epitaxy system. Recently, it has been demonstrated that Ag may be an alternative to using Au NPs as seeds for particle-seeded nanowire fabrication. This work brings light onto the effect of annealing of Au, Ag and Au-Ag alloy NP arrays in two commonly used epitaxial systems, the Molecular Beam Epitaxy (MBE) and the Metalorganic Vapor Phase Epitaxy (MOVPE). The NP arrays are fabricated with the aid of Electron Beam Lithography on GaAs 100 and 111B wafers and the evolution of the NPs with respect to shape, size and position on the surfaces are studied after annealing using Scanning Electron Microscopy (SEM). We find that while the Au NP arrays are found to be stable when annealed up to 600 $^{\circ}$C in a MOVPE system, a diameter and pitch dependent splitting of the particles are seen for annealing in a MBE system. The Ag NP arrays are less stable, with smaller diameters ($\leq$ 50 nm) dissolving during annealing in both epitaxial systems. In general, the mobility of the NPs is observed to differ between the two the GaAs 100 and 111B surfaces. While the initial pattern is found be intact on the GaAs 111B surface for a particular annealing process and particle type, the increased mobility of the NP on the 100 may influence the initial pre-defined positions at higher annealing temperatures. The effect of annealing on Au-Ag alloy NP arrays suggests that these NP can withstand necessary annealing conditions for a complete de-oxidation of GaAs surfaces., Comment: 31 pages, 8 figures

Gate-tunable semiconductor nanowires with superconducting leads have great potential for quantum computation and as model systems for mesoscopic Josephson junctions. The supercurrent, $I$, versus the phase, $\phi$, 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 behavior consistent with resonant tunneling through a single, highly transmitting mode. The gate dependence is consistent with modeled subband structure that includes an effective tunneling 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 and for Majorana readout proposals.

We present transport spectroscopy of sub-gap states in a bottom gated InAs nanowire coupled to a normal lead and a superconducting aluminium lead. The device shows clearly resolved sub-gap states which we can track as the coupling parameters of the system are tuned and as the gap is closed by means of a magnetic field. We systematically extract system parameters by using numerical renormalization group theory fits as a level of the quantum dot is tuned through a quantum phase transition electrostatically and magnetically. We also give an intuitive description of sub-gap excitations., Comment: 9 pages, 10 figures

The superconducting proximity effect in semiconductor nanowires has recently enabled the study of new superconducting architectures, such as gate-tunable superconducting qubits and multiterminal Josephson junctions. As opposed to their metallic counterparts, the electron density in semiconductor nanosystems is tunable by external electrostatic gates providing a highly scalable and in-situ variation of the device properties. In addition, semiconductors with large $g$-factor and spin-orbit coupling have been shown to give rise to exotic phenomena in superconductivity, such as $\varphi_0$ Josephson junctions and the emergence of Majorana bound states. Here, we report microwave spectroscopy measurements that directly reveal the presence of Andreev bound states (ABS) in ballistic semiconductor channels. We show that the measured ABS spectra are the result of transport channels with gate-tunable, high transmission probabilities up to $0.9$, which is required for gate-tunable Andreev qubits and beneficial for braiding schemes of Majorana states. For the first time, we detect excitations of a spin-split pair of ABS and observe symmetry-broken ABS, a direct consequence of the spin-orbit coupling in the semiconductor., Comment: Raw data and calculations are available at http://dx.doi.org/10.4121/uuid:8c4a0604-ac00-4164-a37a-dad8b9d2f580

We demonstrate experimentally that non-collinear intrinsic spin-orbit magnetic fields can be realized in a curved carbon nanotube two-segment device. Each segment, analyzed in the quantum dot regime, shows near four-fold degenerate shell structure allowing for identification of the spin-orbit coupling and the angle between the two segments. Furthermore, we determine the four unique spin directions of the quantum states for specific shells and magnetic fields. This class of quantum dot systems is particularly interesting when combined with induced superconducting correlations as it may facilitate unconventional superconductivity and detection of Cooper pair entanglement. Our device comprises the necessary elements., Comment: Supplemental material available at https://www.dropbox.com/s/ay3edjgg015uzrc/supplement.pdf?dl=1

Indium arsenide (InAs) nanowires (NWs) are a promising platform to fabricate quantum electronic devices, among others they have strong spin-orbit interaction (SOI). The controlled tuning of the SOI is desired in spin based quantum devices. In this study we investigate the possibility of tuning the SOI by electrostatic field, which is generated by a back gate and two side gates placed on the opposite sides of the NW. The strength of the SOI is analyzed by weak anti-localization effect. We demonstrate that the strength of SOI can be strongly tuned by a factor of 2 with the electric field across the NW, while the average electron density is kept constant. Furthermore a simple electrostatic model is introduced to calculate the expected change of SOI. Good agreement is found between the experimental results and the estimated Rashba type SOI generated by the gate-induced electric field., Comment: 7 pages, 3 figures

The determination and control of the electron $g$-factor in semiconductor quantum dots (QDs) are fundamental prerequisites in modern concepts of spintronics and spin-based quantum computation. We study the dependence of the $g$-factor on the orientation of an external magnetic field in quantum dots (QDs) formed between two metallic contacts on stacking fault free InAs nanowires. We extract the $g$-factor from the splitting of Kondo resonances and find that it varies continuously in the range between $|g^*| = 5$ and 15., Comment: 2 pages, 2 figures

Nanowire (NW) crystal growth via the vapour_liquid_solid mechanism is a complex dynamic process involving interactions between many atoms of various thermodynamic states. With increasing speed over the last few decades many works have reported on various aspects of the growth mechanisms, both experimentally and theoretically. We will here propose a general continuum formalism for growth kinetics based on thermodynamic parameters and transition state kinetics. We use the formalism together with key elements of recent research to present a more overall treatment of III_V NW growth, which can serve as a basis to model and understand the dynamical mechanisms in terms of the basic control parameters, temperature and pressures/beam fluxes. Self-catalysed GaAs NW growth on Si substrates by molecular beam epitaxy is used as a model system., Comment: 63 pages, 25 figures and 4 tables. Some details are explained more carefully in this version aswell as a new figure is added illustrating various facets of a WZ crystal

Light management is of great importance to photovoltaic cells, as it determines the fraction of incident light entering the device. An optimal pn-junction combined with an optimal light absorption can lead to a solar cell efficiency above the Shockley-Queisser limit. Here, we show how this is possible by studying photocurrent generation for a single core-shell p-i-n junction GaAs nanowire solar cell grown on a silicon substrate. At one sun illumination a short circuit current of 180 mA/cm^2 is obtained, which is more than one order of magnitude higher than what would be predicted from Lambert-Beer law. The enhanced light absorption is shown to be due to a light concentrating property of the standing nanowire as shown by photocurrent maps of the device. The results imply new limits for the maximum efficiency obtainable with III-V based nanowire solar cells under one sun illumination., Comment: 19 pages, 3 figures

The incorporation paths of Be in GaAs nanowires grown by the Ga-assisted method in molecular beam epitaxy has been investigated by electrical measurements of nanowires with different doping profiles. We find that Be atoms incorporate preferentially via the nanowire side facets, while the incorporation path through the Ga droplet is negligible. We also demonstrate that Be can diffuse into the volume of the nanowire giving an alternative incorporation path. This work is an important step towards controlled doping of nanowires and will serve as a help for designing future devices based on nanowires., Comment: 4 pages, 4 figures

Fullerene peapods, that is carbon nanotubes encapsulating fullerene molecules, can offer enhanced functionality with respect to empty nanotubes. However, the present incomplete understanding of how a nanotube is affected by entrapped fullerenes is an obstacle for peapods to reach their full potential in nanoscale electronic applications. Here, we investigate the effect of C60 fullerenes on electron transport via peapod quantum dots. Compared to empty nanotubes, we find an abnormal temperature dependence of Coulomb blockade oscillations, indicating the presence of a nanoelectromechanical coupling between electronic states of the nanotube and mechanical vibrations of the fullerenes. This provides a method to detect the C60 presence and to probe the interplay between electrical and mechanical excitations in peapods, which thus emerge as a new class of nanoelectromechanical systems., Comment: 7 pages, 3 figures. Published in Nature Communications. Free online access to the published version until Sept 30th, 2010, see http://www.nature.com/ncomms/journal/v1/n4/abs/ncomms1034.html

Understanding how the orbital motion of electrons is coupled to the spin degree of freedom in nanoscale systems is central for applications in spin-based electronics and quantum computation. We demonstrate this coupling of spin and orbit in a carbon nanotube quantum dot in the general multi-electron regime in presence of finite disorder. Further, we find a strong systematic dependence of the spin-orbit coupling on the electron occupation of the quantum dot. This dependence, which even includes a sign change is not demonstrated in any other system and follows from the curvature-induced spin-orbit split Dirac-spectrum of the underlying graphene lattice. Our findings unambiguously show that the spin-orbit coupling is a general property of nanotube quantum dots which provide a unique platform for the study of spin-orbit effects and their applications., Comment: High-res figures and supplement at http://www.fys.ku.dk/~tsand/TSJ_KGR2010.pdf

We have measured systematic repetitions of avoided crossings in low temperature three-terminal transport through a carbon nanotube with encapsulated C60 molecules. We show that this is a general effect of the hybridization of a host quantum dot with an impurity. The well-defined nanotube allows identification of the properties of the impurity, which we suggest to be a chain of C60 molecules inside the nanotube. This electronic coupling between the two subsystems opens the interesting and potentially useful possibility of contacting the encapsulated molecules via the tube., Comment: 6 pages, 3 figures

We observe two-fold shell filling in the spectra of closed one-dimensional quantum dots formed in single-wall carbon nanotubes. Its signatures include a bimodal distribution of addition energies, correlations in the excitation spectra for different electron number, and alternation of the spins of the added electrons. This provides a contrast with quantum dots in higher dimensions, where such spin pairing is absent. We also see indications of an additional fourfold periodicity indicative of K-K' subband shells. Our results suggest that the absence of shell filling in most isolated nanotube dots results from disorder or nonuniformity., Comment: 4 pages including 4 figures

We present a simple technique which uses a self-aligned oxide etch to suspend individual single-wall carbon nanotubes between metallic electrodes. This enables one to compare the properties of a particular nanotube before and after suspension, as well as to study transport in suspended tubes. As an example of the utility of the technique, we study quantum dots in suspended tubes, finding that their capacitances are reduced owing to the removal of the dielectric substrate., Comment: 3 pages, 4 figures

We report low-temperature transport experiments on single-wall nanotubes with metallic leads of varying contact quality, ranging from weak tunneling to almost perfect transmission. In the weak tunneling regime, where Coulomb blockade dominates, the nanotubes act as one-dimensional quantum dots. For stronger coupling to the leads the conductance can be strongly enhanced by inelastic cotunneling and the Kondo effect. For open contacts Coulomb blockade is completely suppressed, and the low-temperature conductance remains generally high, although we often see distinct dips in the conductance versus gate voltage which may result from resonant backscattering., Comment: 4 pages including 3 figures, for proceedings of the Moriond meeting 2001

The connection of electrical leads to wire-like molecules is a logical step in the development of molecular electronics, but also allows studies of fundamental physics. For example, metallic carbon nanotubes are quantum wires that have been found to act as one-dimensional quantum dots, Luttinger-liquids, proximity-induced superconductors and ballistic and diffusive one-dimensional metals. Here we report that electrically-contacted single-wall nanotubes can serve as powerful probes of Kondo physics, demonstrating the universality of the Kondo effect. Arising in the prototypical case from the interaction between a localized impurity magnetic moment and delocalized electrons in a metallic host, the Kondo effect has been used to explain enhanced low-temperature scattering from magnetic impurities in metals, and also occurs in transport through semiconductor quantum dots. The far higher tunability of dots (in our case, nanotubes) compared with atomic impurities renders new classes of Kondo-like effects accessible. Our nanotube devices differ from previous systems in which Kondo effects have been observed, in that they are one-dimensional quantum dots with three-dimensional metal (gold) reservoirs. This allows us to observe Kondo resonances for very large electron number (N) in the dot, and approaching the unitary limit (where the transmission reaches its maximum possible value). Moreover, we detect a previously unobserved Kondo effect, occurring for even values of N in a magnetic field., Comment: 7 pages, pdf only

We report measurements of the temperature and gate voltage dependence for individual bundles (ropes) of single-walled nanotubes. When the conductance is less than about e^2/h at room temperature, it is found to decrease as an approximate power law of temperature down to the region where Coulomb blockade sets in. The power-law exponents are consistent with those expected for electron tunneling into a Luttinger liquid. When the conductance is greater than e^2/h at room temperature, it changes much more slowly at high temperatures, but eventually develops very large fluctuations as a function of gate voltage when sufficiently cold. We discuss the interpretation of these results in terms of transport through a Luttinger liquid., Comment: 5 pages latex including 3 figures, for proceedings of IWEPNM 99 (Kirchberg)