The emergence of zero energy states in non-topological superconductors represents an inevitable problem that obscures the proper identification of zero energy Majorana bound states (MBSs) and prevents their use as topologically protected qubits. In this Research Letter we investigate long superconductor-normal-superconductor junctions where trivial zero energy states, robust over a large range of parameters, appear as a result of helicity and confinement in the normal region. We demonstrate that both equilibrium supercurrents and critical currents are sensitive to variations in the length of the superconductor regions in the topological phase hosting MBSs, but, remarkably, no such length dependence exists when robust, but trivial, zero energy states are present. This strikingly different response originates from the non-local nature of the MBSs and we, therefore, propose it as a simple protocol for distinguishing between trivial and topological zero energy states.
We report on the fabrication and electrical transport properties of superconducting junctions made of β-Ag$_{2}$Se topological insulator (TI) nanowires in contact with Al superconducting electrodes. The temperature dependence of the critical current indicates that the superconducting junction belongs to a short and diffusive junction regime. As a characteristic feature of the narrow junction, the critical current decreases monotonously with increasing magnetic field. The stochastic distribution of the switching current exhibits the macroscopic quantum tunneling behavior, which is robust up to …
We report the emergence of zero-energy states in the trivial phase of a short nanowire junction with strong spin-orbit coupling and magnetic field, formed by strong coupling between the nanowire and two superconductors. The zero-energy states appear in the junction when the superconductors induce a large energy shift in the nanowire, such that the junction naturally forms a quantum dot, a process that is highly tunable by the superconductor width. Most importantly, we demonstrate that the zero-energy states produce a $π$-shift in the phase-biased supercurrent, which can be used as a simple too…
We present a novel technique for the realization of suspended Josephson junctions based on InAs semiconductor nanowires. The devices are assembled using a technique of drop-casting guided by dielectrophoresis that allows to finely align the nanostructures on top of the electrodes. The proposed architecture removes the interaction between the nanowire and the substrate which is known to influence disorder and the orientation of the Rashba vector. The relevance of this approach in view of the implementation of Josephson junctions based on High-Temperature Superconductors is discussed.
We report on the fabrication and measurements of planar mesoscopic Josephson junctions formed by InAs nanowires coupled to superconducting Nb terminals. The use of Si-doped InAs-nanowires with different bulk carrier concentrations allowed to tune the properties of the junctions. We have studied the junction characteristics as a function of temperature, gate voltage, and magnetic field. In junctions with high doping concentrations in the nanowire Josephson supercurrent values up to 100\,nA are found. Owing to the use of Nb as superconductor the Josephson coupling persists at temperatures up to …
We have studied the effects of optical-frequency light on proximitized InAs/Al Josephson junctions based on highly n-doped InAs nanowires at varying incident photon flux and at three different photon wavelengths. The experimentally obtained IV curves were modeled using a shunted junction model which takes scattering at the contact interfaces into account. The Josephson junctions were found to be surprisingly robust, interacting with the incident radiation only through heating, whereas above the critical current our devices showed non-thermal effects resulting from photon exposure. Our work pro…
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.
The effect of quantum fluctuations on the current-voltage characteristics of Josephson junctions and superconducting nanowires is studied in the underdamped limit. Quantum fluctuations induce transitions between a Coulomb--blockade and a supercurrent branch, and can significantly modify the shape of current-voltage characteristics in the case of a highly resistive environment. Owing to the phase-charge duality, our results can be directly extended to the opposite overdamped limit.
We theoretically study a Josephson junction based on a semiconducting nanowire subject to a time-dependent flux bias. We establish a general density matrix approach for the dynamical response of the Majorana junction and calculate the resulting flux-dependent susceptibility using both microscopic and effective low-energy descriptions for the nanowire. We find that the diagonal component of the susceptibility, associated with the dynamics of the Majorana states populations, dominates over the standard Kubo contribution for a wide range of experimentally relevant parameters. The diagonal term, t…
We theoretically study superconducting islands based on semiconductor-nanowire Josephson junctions and take into account the presence of subgap quasiparticle excitations in the spectrum of the junction. Our method extends the standard model Hamiltonian for a superconducting charge qubit and replaces the Josephson potential by the Bogoliubov--de Gennes Hamiltonian of the nanowire junction, projected onto the relevant low-energy subgap subspace. This allows to fully incorporate the coherent dynamics of subgap levels in the junction. The combined effect of spin-orbit coupling and Zeeman energy in…
We theoretically study transport properties of nanowires with the Dresselhaus [110] spin-orbit coupling under the in-plane Zeeman potential and the proximity-induced s-wave pair potential. In the topologically nontrivial phase, the nanowire hosts the Majorana fermions at its edges and the number of the Majorana bound states is equal to the number propagating channels (Nc). When we attach a normal metal to the superconductor, such Majorana bound states penetrate into the dirty normal segment and form the Nc resonant transmission channels there. We show that chiral symmetry of the electronic sta…
We measured the Josephson radiation emitted by an InSb semiconductor nanowire junction utilizing photon assisted quasiparticle tunneling in an AC-coupled superconducting tunnel junction. We quantify the action of the local microwave environment by evaluating the frequency dependence of the inelastic Cooper-pair tunneling of the nanowire junction and find the zero frequency impedance $Z(0)=492\,Ω$ with a cutoff frequency of $f_0=33.1\,$GHz. We extract a circuit coupling efficiency of $η\approx 0.1$ and a detector quantum efficiency approaching unity in the high frequency limit. In addition to t…
We study theoretically the critical current in semiconductor nanowire Josephson junction with strong spin-orbit interaction. The critical current oscillates by an external magnetic field. We reveal that the oscillation of critical current depends on the orientation of magnetic field in the presence of spin-orbit interaction. We perform a numerical simulation for the nanowire by using a tight-binding model. The Andreev levels are calculated as a function of phase difference $φ$ between two superconductors. The DC Josephson current is evaluated from the Andreev levels in the case of short juncti…
Josephson junctions based on semiconductor nanowires are potential building blocks for electrically tunable qubit structures, e.g. the gatemon or the Andreev qubit. However, an actual realization requires the thorough investigation of the intrinsic excitation spectrum. Here, we demonstrate the fabrication of low-loss superconducting microwave circuits that combine high quality factors with a well-controlled gate architecture by utilizing a flip-chip approach. This platform is then used to perform single-tone and two-tone experiments on Andreev states in in-situ grown InAs/Al core/half-shell na…
We report the fabrication of strongly coupled nanohybrid superconducting junctions using PbS semiconductor nanowires and Pb0.5In0.5 superconducting electrodes. The maximum supercurrent in the junction reaches up to ~15 μA at 0.3 K, which is the highest value ever observed in semiconductor-nanowire-based superconducting junctions. The observation of microwave-induced constant voltage steps confirms the existence of genuine Josephson coupling through the nanowire. Monotonic suppression of the critical current under an external magnetic field is also in good agreement with the narrow junction mod…
Topological quantum computation using non-Abelian Majorana zero modes localized in proximitized semiconductor nanowires requires careful electrostatic control of wire-junctions so as to manipulate and braid the zero modes enabling anyonic fault-tolerant gate operations. We theoretically investigate the topological superconducting properties of such elementary wire-junctions, the so-called T junctions, finding that the existence of the junction may nonperturbatively affect the Majorana behavior by introducing spurious non-topological subgap states mimicking zero-modes. We propose a possible sol…
We study a Josephson junction in a Kitaev chain with particle-hole symmetric nearest neighbor interactions. When the phase difference across the junction is $π$, we show analytically that the full spectrum is fourfold degenerate up to corrections that vanish exponentially in the system size. The Majorana bound states at the ends of the chain are known to survive interactions. Our result proves that the same is true for the zero-energy quasiparticle localized at the junction. We further study finite size corrections numerically, and show how repulsive interactions lead to stronger end-to-end co…
Half a century ago Brian Josephson made a series of striking predictions related to a tunnelling barrier sandwiched between two superconductors. One particular prediction, later became known as the a.c.-Josephson effect, said that under a finite d.c. bias the tunnelling current contains an a.c. supercurrent component, oscillating at microwave frequency. This prediction was experimentally verified through observation of the junction current-voltage characteristics modified by the interaction with the electromagnetic radiation, and direct detection of the microwave radiation emitted from the jun…
We demonstrate an original method -- based on controlled oxidation -- to create high-quality tunnel junctions between superconducting Al reservoirs and InAs semiconductor nanowires. We show clean tunnel characteristics with a current suppression by over $4$ orders of magnitude for a junction bias well below the Al gap $Δ_0 \approx 200\,μ{\rm eV}$. The experimental data are in close agreement with the BCS theoretical expectations of a superconducting tunnel junction. The studied devices combine small-scale tunnel contacts working as thermometers as well as larger electrodes that provide a proof…
We report on the fabrication and measurements of a superconducting junction of a single-crystalline Au nanowire, connected to Al electrodes. Current-Voltage characteristic curve shows clear supercurrent branch below the superconducting transition temperature of Al and quantized voltage plateaus on application of microwave radiation, as expected from Josephson relations. Highly transparent (0.95) contacts very close to an ideal limit of 1 are formed at the interface between the normal metal (Au) and the superconductor (Al). The very high transparency is ascribed to the single crystallinity of a…
A semiconducting nanowire proximitized by an $s$-wave superconductor can be tuned into a topological state by an applied magnetic field. This quantum phase transition is marked by the emergence of Majorana zero modes at the ends of the wire. The fusion of Majorana modes at a junction between two nanowires results in a $4π$-periodic Josephson effect. We elucidate how the $4π$-periodicity arises across the topological phase transition in a highly-transparent short nanowire junction. Owing to a high transmission coefficient, Majorana zero modes coming from different wires are strongly coupled, wi…
We numerically study crossed Andreev reflection (CAR) in a topological insulator nanowire T-junction where one lead is proximitized by a superconductor. We perform realistic simulations based on the 3D BHZ model and compare the results with those from an effective 2D surface model, whose computational cost is much lower. Both approaches show that CAR should be clearly observable in a wide parameter range, including perfect CAR in a somewhat more restricted range. Furthermore, it can be controlled by a magnetic field and is robust to disorder. Our effective 2D implementation allows to model sys…
We develop and study theoretically a minimal model of semiconductor nanowire Josephson junction that incorporates Zeeman and spin-orbit effects. The DC Josephson current is evaluated from the phase-dependent energies of Andreev levels. Upon changing the magnetic field applied, the critical current oscillates manifesting cusps that signal the $0$-$π$ transition. Without spin-orbit interaction, the oscillations and positions of cusps are regular and do not depend on the direction of magnetic field. In the presence of spin-orbit interaction, the magnetic field dependence of the current becomes an…
We have studied mesoscopic Josephson junctions formed by highly $n$-doped InAs nanowires and superconducting Ti/Pb source and drain leads. The current-voltage properties of the system are investigated by varying temperature and external out-of-plane magnetic field. Superconductivity in the Pb electrodes persists up to $ \sim 7$ K and with magnetic field values up to 0.4 T. Josephson coupling at zero backgate voltage is observed up to 4.5 K and the critical current is measured to be as high as 615 nA. The supercurrent suppression as a function of the magnetic field reveals a diffraction pattern…
Josephson junctions based on InAs semiconducting nanowires and Nb superconducting electrodes are fabricated in-situ by a special shadow evaporation scheme for the superconductor electrode. Compared to other metallic superconductors such as Al, Nb has the advantage of a larger superconducting gap which allows operation at higher temperatures and magnetic fields. Our junctions are fabricated by shadow evaporation of Nb on pairs of InAs nanowires grown selectively on two adjacent tilted Si (111) facets and crossing each other at a small distance. The upper wire relative to the deposition source a…
We performed microwave spectroscopy of an InAs nanowire between superconducting contacts implementing a finite-length, multi-channel Josephson weak link. Certain features in the spectra, such as the splitting by spin-orbit interactions of the transition lines among Andreev states, have been already understood in terms of non-interacting models. However, we identify here additional transitions, which evidence the presence of Coulomb interactions. By combining experimental measurements and model calculations, we reach a qualitative understanding of these very rich Andreev spectra.
Typical measurements of nanowire devices rely on end-to-end measurements to reveal mesoscopic phenomena such as quantized conductance or Coulomb blockade. However, creating nanoscale tunnel junctions allows one to directly measure other properties such as the density of states or electronic energy distribution functions. In this paper, we demonstrate how to realize uniform tunnel junctions on InSb nanowires, where the low invasiveness preserves ballistic transport in the nanowires. The utility of the tunnel junctions is demonstrated via measurements using a superconducting tunneling probe, whi…
We study the energy spectrum and the electromagnetic response of Andreev bound states in short Josephson junctions made of semiconducting nanowires. We focus on the joint effect of Zeeman and spin-orbit coupling on the Andreev level spectra. Our model incorporates the penetration of the magnetic field in the proximitized wires, which substantially modifies the spectra. We pay special attention to the occurrence of fermion parity switches at increasing values of the field and to the magnetic field dependence of the absorption strength of microwave-induced transitions. Our calculations can be us…
We report a systematic experimental study of mesoscopic conductance fluctuations in superconductor/normal/superconductor (SNS) devices Nb/InAs-nanowire/Nb. These fluctuations far exceed their value in the normal state and strongly depend on temperature even in the low-temperature regime. This dependence is attributed to high sensitivity of perfectly conducting channels to dephasing and the SNS fluctuations thus provide a sensitive probe of dephasing in a regime where normal transport fails to detect it. Further, the conductance fluctuations are strongly non-linear in bias voltage and reveal su…
We report on half-integer Shapiro steps observed in an InAs nanowire Josephson junction. We observed the Shapiro steps of the short ballistic InAs nanowire Josephson junction and found anomalous half-integer steps in addition to the conventional integer steps. The half-integer steps disappear as the temperature increases or transmission of the junction decreases. These experimental results agree closely with numerical calculation of the Shapiro response for the skewed current phase relation in a short ballistic Josephson junction.
Gate-tunable semiconductor-superconductor nanowires with superconducting leads form exotic Josephson junctions that are a highly desirable platform for two types of qubits: those with topological superconductivity (Majorana qubits) and those based on tunable anharmonicity (gatemon qubits). Controlling their behavior, however, requires understanding their electrostatic environment and electronic structure. Here we study gated InAs nanowires with epitaxial aluminum shells. By measuring current-phase relations (CPR) and comparing them with analytical and numerical calculations, we show that we ca…
Epitaxially grown, high quality semiconductor InSb nanowires are emerging material systems for the development of high performance nanoelectronics and quantum information processing and communication devices, and for the studies of new physical phenomena in solid state systems. Here, we report on measurements of a superconductor-normal conductor-superconductor junction device fabricated from an InSb nanowire with aluminum based superconducting contacts. The measurements show a proximity induced supercurrent flowing through the InSb nanowire segment, with a critical current tunable by a gate, i…
Both axial and radial junction nanowire solar cells have their challenges and advantages. However, so far, there is no review that explicitly provides a detailed comparative analysis of both axial and radial junction solar cells. This article reviews some of the recent results on axial and radial junction nanowire solar cells with an attempt to perform a comparative study between the optical and device behavior of these cells. In particular, we start by reviewing different results on how the absorption can be tuned in axial and radial junction solar cells. We also discuss results on some of th…
Signatures of Majorana fermion bound states in one-dimensional topological insulator (TI) nanowires with proximity effect induced superconductivity are studied. The phase diagram and energy spectra are calculated for single TI nanowires and it is shown that the nanowires can be in the topological invariant phases of winding numbers $W=0, \pm 1$, and $\pm 2$ corresponding to the cases with zero, one and two pairs of Majorana fermions in the single TI nanowires. It is also shown that the topological winding numbers, i.e., the numbers of pairs of Majorana fermions in the TI nanowires can be extra…
The basis for superconducting electronics can broadly be divided between two technologies: the Josephson junction and the superconducting nanowire. While the Josephson junction (JJ) remains the dominant technology due to its high speed and low power dissipation, recently proposed nanowire devices offer improvements such as gain, high fanout, and compatibility with CMOS circuits. Despite these benefits, nanowire-based electronics have largely been limited to binary operations, with devices switching between the superconducting state and a high-impedance resistive state dominated by uncontrolled…
We experimentally studied the Josephson supercurrent in Nb/InN-nanowire/Nb junctions. Large critical currents up to 5.7 $μ$A have been achieved, which proves the good coupling of the nanowire to the superconductor. The effect of a magnetic field perpendicular to the plane of the Josephson junction on the critical current has been studied. The observed monotonous decrease of the critical current with magnetic field is explained by the magnetic pair-breaking effect in planar Josephson junctions of ultra-narrow width [J. C. Cuevas and F. S. Bergeret, Phys. Rev. Lett. 99, 217002 (2007)]
Semiconductor/superconductor hybrids exhibit a range of phenomena that can be exploited for the study of novel physics and the development of new technologies. Understanding the origin the energy spectrum of such hybrids is therefore a crucial goal. Here, we study Josephson junctions defined by shadow epitaxy on InAsSb/Al nanowires. The devices exhibit gate-tunable supercurrents at low temperatures and multiple Andreev reflections (MARs) at finite voltage bias. Under microwave irradiation, photon assisted tunneling (PAT) of MARs produces characteristic oscillating sidebands at quantized energi…
Majorana Josephson junctions in nanowire systems exhibit a pseudo-$4π$ period current-phase relation in the clean limit. In this work, we study how this current-phase relation responds to a tilted magnetic field in a disordered Majorana Josephson junction within the Bogoliubov-de Gennes approach. We show that the tilted magnetic field induces a $ϕ_0$ phase shift to the current-phase relation. Most importantly, we find that this $ϕ_0$-junction behavior is robust even in the presence of disorders.
The Josephson effect is a fundamental quantum phenomenon consisting in the appearance of a dissipationless supercurrent in a weak link between two superconducting (S) electrodes. While the mechanism leading to the Josephson effect is quite general, i.e., Andreev reflections at the interface between the S electrodes and the weak link, the precise physical details and topology of the junction drastically modify the properties of the supercurrent. Specifically, a strong enhancement of the critical supercurrent $I_C$ is expected to occur when the topology of the junction allows the emergence of Ma…
We propose a method to distinguish between trivial and topological, Majorana, zero-energy states in both short and long superconductor-normal-superconductor junctions based on Rashba nanowires using phase-biased equilibrium transport measurements. In particular, we show how the sawtooth profile of the supercurrent, due to the Majorana oscillation suppression in the topological phase for sufficiently long superconductor regions, leads to a strong signal in its zero-frequency susceptibility for a phase difference of $ϕ=π$. This signal is notably insensitive to the chemical potential in the norma…
We investigate transport though normal-superconductor nanowire junctions in the presence of spin-orbit coupling and magnetic field. As the Zeeman field crosses the critical bulk value B_c of the topological transition, a Majorana bound state (MBS) is formed, giving rise to a sharp zero-bias anomaly (ZBA) in the tunneling differential conductance. We identify novel features beyond this picture in wires with inhomogeneous depletion, like the appearance of two MBSs inside a long depleted region for B<B_c. The resulting ZBA is in most cases weakly split and may coexist with Andreev bound states ne…
Hybrid InSb nanowire-superconductor devices are promising for investigating Majorana modes and topological quantum computation in solid-state devices. An experimental realisation of ballistic, phase-coherent superconductor-nanowire hybrid devices is a necessary step towards engineering topological superconducting electronics. Here, we report on a low-temperature transport study of Josephson junction devices fabricated from InSb nanowires grown by molecular-beam epitaxy and provide a clear evidence for phase-coherent, ballistic charge transport through the nanowires in the junctions. We demonst…
A numerical method to obtain the spectrum of smooth normal-superconductor junctions in nanowires, able to host Majorana zero modes, is presented. Softness in the potential and superconductor interfaces yields opposite effects on the protection of Majorana modes. While a soft potential is a hindrance for protection, a soft superconductor gap transition greatly favors it. Our method also points out the possibility of extended Majorana states when propagating modes are active far from the junction, although this requires equal incident fluxes in all open channels.
Enhanced photocurrent is demonstrated in a junction-less photodetector with nanowires embedded in its channel. The fabricated photodetector consists of a large area for efficient absorption of incident light with energy band engineering achieved in nanowires. The structure design consists of a set of two symmetrically positioned gates, primary and secondary, that are located over the nanowires. Each gate is used for biasing and control of the charge flow. We find that detectors with narrower nanowires controlled by their secondary gate generate larger photocurrents under similar illumination c…
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 evaporated islands of superconductor tin on InAs SAG nanowires, by using in-situ shadowing with high aspect-ratio pre-fabricated SiOx dielectric walls. Our technique al…
We have investigated electronic cooling of suspended nanowires with SINIS tunnel junction coolers. The suspended samples consist of a free standing nanowire suspended by four narrow ($\sim$ 200 nm) bridges. We have compared two different cooler designs for cooling the suspended nanowire. We demonstrate that cooling of the nanowire is possible with a proper SINIS cooler design.
We study Josephson junctions made of semiconducting nanowires with Rashba spin-orbit coupling, where superconducting correlations are induced by the proximity effect. In the presence of a suitably directed magnetic field, the system displays the anomalous Josephson effect: a nonzero supercurrent in the absence of a phase bias between two superconductors. We show that this anomalous current can be increased significantly by tuning the nanowire into the helical regime. In particular, in a short junction, a large anomalous current is a signature for topologically nontrivial superconductivity in t…
We demonstrate that a suspended nanowire forming a weak link between two superconductors can be cooled to its motional ground state by a supercurrent flow. The predicted cooling mechanism has its origins in magnetic field induced inelastic tunneling of the macroscopic superconducting phase associated with the junction. Furthermore, we show the voltage-drop over the junction is proportional to the average population of the vibrational modes in the stationary regime, a phenomena which can be used to probe the level of cooling.
We propose a new orbital controlled model to explain the gate field induced switching of current in a semiconducting PbS-nanowire junction. A single particle scattering formalism in conjunction with a posteriori density functional approach involving hybrid functional is used to study the electronic current; both first and higher order Stark effects are explicitly treated in our model. Our calculation reveals that after a threshold gate-voltage, orbital mixing produces p-components at the S atoms in the participating orbitals. This results in an inter-layer orbital interaction that allows elect…
A semiconductor nanowire based superconductor-normal-superconductor (SNS) junction is modeled theoretically. A magnetic field is applied along the nanowire axis, parallel to the current. The Bogoliubov-de Gennes equations for Andreev bound states are solved while considering the electronic subbands due to radial confinement in the N-section. The energy-versus-phase curves of the Andreev bound states shift in phase as the N-section quasiparticles with orbital angular momentum couple to the axial field. A similar phase shift is observed in the continuum current of the junction. The quantum mecha…
Supercurrent and multiple Andreev reflections in Ge hut nanowire Josephson Junctions
Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（凝聚态物理国家重点实验室和中国科学院物理研究所）
One of the most promising platforms for one-dimensional topological superconductivity is based on semiconducting nanowires with strong spin-orbit coupling (SOC), where s-wave superconductivity is induced by proximity effect and an external Zeeman field drives the system into the topological superconducting phase with Majorana bound states (MBSs) at the end of the wire. During last years this idea has led to a great number of important experiments in hybrid superconductor-semiconductor systems, where the main signature is an emergent zero-bias peak (ZBP) in the differential conductance as the Z…
We report fabrication and measurement of a device where closely-placed two parallel InAs nanowires (NWs) are contacted by source and drain normal metal electrodes. Established technique includes selective deposition of double nanowires onto a previously defined gate region. By tuning the junction with the finger bottom gates, we confirmed the formation of parallel double quantum dots, one in each NW, with a finite electrostatic coupling between each other. With the fabrication technique established in this study, devices proposed for more advanced experiments, such as Cooper-pair splitting and…
