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 the nanowires forming the junction triggers a topological transition, where the subgap levels evolve from finite-energy Andreev bound states into near-zero energy Majorana bound states. The interplay between the microscopic energy scales governing the nanowire junction (the Josephson energy, the Majorana coupling and the Majorana energy splitting), with the charging energy of the superconducting island, gives rise to a great variety of physical regimes. Based on this interplay of different energy scales, we fully characterize the microwave response of the junction, from the Cooper pair box to the transmon regimes, and show how the presence of Majoranas can be detected through distinct spectroscopic features. In split-junction geometries, the plasma mode couples to the phase-dispersing subgap levels resulting from Majorana hybridization via a Jaynes--Cummings-like interaction. As a consequence of this interaction, higher order plasma excitations in the junction inherit Majorana properties, including the $4π$ effect.
We study coherent transport through a semiconductor nanowire in the presence of spin-orbit coupling and Zeeman splitting due to an applied magnetic field. By employing analytical and numerical techniques we develop a theory for the Josephson effect in the superconductor-semiconductor nanowire-superconductor structure. We show that Josephson current through the clean semiconductor nanowire exhibits a number of interesting features due to the interplay between the Zeeman splitting and spin-orbit coupling. We also study effect how disorder in the nanowire affects Andreev bound-state energy spectr…
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 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 investigate the properties of a weak link between two Rashba-based superconducting nanowires with geometric misalignment. By applying an external magnetic field the system can be driven into a topological non-trivial regime. We demonstrate that the Josephson current can be modulated in amplitude and sign through the variation of the applied field and, remarkably, via the angle controlling the spin-orbit locking mismatch at the interface of the nanowires. The proposed setup with misaligned coplanar nanowires provides the building block configuration for the manipulation of coherent transport…
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 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 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 …
A superconductor-semiconducting nanowire-superconductor heterostructure in the presence of spin orbit coupling and magnetic field can support a supercurrent even in the absence of phase difference between the superconducting electrodes. We investigate this phenomenon, the anomalous Josephson effect, employing a model capable of describing many bands in the normal region. We discuss geometrical and symmetry conditions required to have finite anomalous supercurrent and in particular we show that this phenomenon is enhanced when the Fermi level is located close to a band opening in the normal reg…
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…
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 present a quantitative characterization of an electrically tunable Josephson junction defined in an InAs nanowire proximitized by an epitax-ially-grown superconducting Al shell. The gate-dependence of the number of conduction channels and of the set of transmission coefficients are extracted from the highly nonlinear current-voltage characteristics. Although the transmissions evolve non-monotonically, the number of independent channels can be tuned, and configurations with a single quasi-ballistic channel achieved.
We investigate theoretically the Josephson junction of semiconductor nanowire with strong spin-orbit (SO) interaction in the presence of magnetic field. By using a tight-binding model, the energy levels $E_n$ of Andreev bound states are numerically calculated as a function of phase difference $φ$ between two superconductors in the case of short junctions. The DC Josephson current is evaluated from the Andreev levels. In the absence of SO interaction, a $0$-$π$ transition due to the magnetic field is clearly observed. In the presence of SO interaction, the coexistence of SO interaction and Zeem…
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 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 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 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.
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…
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…
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…
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 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…
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 n…
At a superconductor (S)-normal metal (N) junction pairing correlations can "leak-out" into the N region. This proximity effect [1, 2] modifies the system transport properties and can lead to supercurrent flow in SNS junctions [3]. Recent experimental works showed the potential of semiconductor nanowires (NWs) as building blocks for nanometre-scale devices [4-7], also in combination with superconducting elements [8-12]. Here, we demonstrate an InAs NW Josephson transistor where supercurrent is controlled by hot-quasiparticle injection from normal-metal electrodes. Operational principle is based…
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…
We theoretically study the DC Josephson effect of a semiconductor nanowire (NW) with strong spin-orbit interaction when a magnetic field is applied parallel to the NW. We adopt a model of single scatterer in a quasi-one-dimensional system for the case of short junctions where the size of normal region is much smaller than the coherent length. In the case of single conduction channel in the model, we obtain analytical expressions for the energy levels of Andreev bound states, $E_n$, and supercurrent $I$, as a function of phase difference $φ$ between two superconductors. We show the 0-$π$ transi…
We study the key features of the Josephson transport through a curved semiconducting nanowire. Based on numerical simulations and analytical estimates within the framework of the Bogoliubov-de Gennes equations we find the ground-state phase difference $φ_0$ between the superconducting leads tuned by the spin splitting field $h$ driving the system from the topologically trivial to the nontrivial superconducting state. The phase $φ_0$ vanishes for rather small $h$, grows in a certain field range around the topological transition, and then saturates at large $h$ in the Kitaev regime. Both the sub…
We study a Majorana island coupled to a bulk superconductor via a Josephson junction and to multiple external normal leads. In the absence of the Josephson coupling, the system displays a topological Kondo state, which had been largely studied recently. However, we find that this state is unstable even to small Josephson coupling, which instead leads at low temperature $T$ to a new fixed point. Most interesting is the case of three external leads, forming a minimal electronic realization of the long sought two-channel Kondo effect. While the $T=0$ conductance corresponds to simple resonant And…
We present an extensive experimental and theoretical study of the proximity effect in InAs nanowires connected to superconducting electrodes. We fabricate and investigate devices with suspended gate-controlled nanowires and nonsuspended nanowires, with a broad range of lengths and normal-state resistances. We analyze the main features of the current-voltage characteristics: the Josephson current, excess current, and subgap current as functions of length, temperature, magnetic field, and gate voltage, and compare them with theory. The Josephson critical current for a short-length device, L = 30…
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…
Dispersive charge sensing is realized in hybrid semiconductor-superconductor nanowires in gate-defined single- and double-island device geometries. Signal-to-noise ratios (SNRs) were measured both in the frequency and time domain. Frequency-domain measurements were carried out as a function of frequency and power and yield a charge sensitivity of $1 \times 10^{-3} e/\sqrt{\rm Hz}$ for an 11 MHz measurement bandwidth. Time-domain measurements yield SNR > 1 for 20 $μ$s integration time. At zero magnetic field, photon-assisted tunneling was detected dispersively in a double-island geometry, indic…
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…
We report on the switching current distributions in nano-hybrid Josephson junctions made of InAs semiconductor nanowires. Temperature dependence of the switching current distribution can be understood by motion of Josephson phase particle escaping from a tilted washboard potential, fitted well to the macroscopic quantum tunneling, thermal activation and phase diffusion models, depending on temperature. Application of gate voltage to tune the Josephson coupling strength enables us to adjust the effective temperature for the escaping process, which would be promising for developing gate-tunable …
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…
A method was devised to construct a generalized dual field theory in the quantum field theory. As a simple example using this method, we examined the duality between coherent quantum phase slip and the Josephson effect in single junction systems and nanowires. The this method was proved to be reliable within the Villain approximation.
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…
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…
Phase slips in a one-dimensional closed array of Josephson junctions hybridize the persistent current states (PCS) and plasmon branches of excitations. The interference between phase slips passing through different junctions of the array makes the hybridization sensitive to the charges of the superconducting islands comprising the array. This in turn results in the Aharonov-Casher effect for plasmons, which in absence of phase slips are insensitive to island charges.
We have performed the first experiments in a superconductor - normal metal - superconductor single electron transistor in which there is an extra superconducting strip partially overlapping the normal metal island in good metal-to-metal contact. Superconducting proximity effect gives rise to current peaks at voltages below the quasiparticle threshold. We interpret these peaks in terms of the Josephson-quasiparticle process and discuss their connection with the proximity induced energy gap in the normal metal island.
We study inhomogeneous Cooper pairs distribution and localization effects in tree-like networks of superconducting islands coupled via Josephson weak links. Using a generalized Feynman's approach, reminiscent of the Bose-Hubbard model, we demonstrate that the Cooper pairs fraction which localizes on a specific network's island is limited by the network topology and, if present, by the repulsive interaction. These findings contribute to clarify the interplay between confinement effects induced by the network's topology and interaction and shed some light on recent experiments dealing with netwo…
In the presence of Rashba spin-orbit coupling, magnetic field can drive a proximitized nanowire into a topological superconducting phase. We study transport properties of such nanowires in the Coulomb blockade regime. The associated with the topological superconductivity Majorana modes significantly modify transport and lead to single-electron coherent transmission through the nanowire - a non-local signature of topological superconductivity. In this work, we focus on the case of strong hybridization of the Majorana modes with the normal leads. The induced by hybridization broadening of the Ma…
Exotic superconductors, such as high T$_C$, topological, and heavy-fermion superconductors, require phase sensitive measurements to determine the underlying pairing. Here we investigate the proximity-induced superconductivity in nanowires of SnTe, where an $s\pm is^{\prime}$ superconducting state is produced that lacks the time-reversal and valley-exchange symmetry of the parent SnTe. This effect, in conjunction with a ferroelectric distortion of the lattice at low temperatures, results in a marked alteration of the properties of Josephson junctions fabricated using SnTe nanowires. This work e…
Nanoscale superconductor-semiconductor hybrid devices are assembled from InAs semiconductor nanowires individually contacted by aluminum-based superconductor electrodes. Below 1 K, the high transparency of the contacts gives rise to proximity-induced superconductivity. The nanowires form superconducting weak links operating as mesoscopic Josephson junctions with electrically tunable coupling. The supercurrent can be switched on/off by a gate voltage acting on the electron density in the nanowire. A variation in gate voltage induces universal fluctuations in the normal-state conductance which a…
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…
