ac Josephson Effect in a Single Quantum Channel

Josephson dynamics and Shapiro steps at high transmissions: current bias regime

We investigate Josephson dynamics of highly transparent superconducting nanojunctions at subgap voltages and temperatures. In this limit, intrinsic dissipation in such junctions turns out to be sub-Ohmic, which yields a linear dependence of the average voltage on the bias current I slightly exceeding the critical one Ic. We demonstrate a strong impact of intrinsic sub-Ohmic dissipation on integer Shapiro steps appearing on the I-V curve in the presence of external microwave radiation.

Machine-learning prediction of the formation of atomic gold wires by mechanically controlled break junctions

One of the challenging issues in the formation of atomic wires in break-junction experiments is the formation of stable monoatomic chains of reasonable length. To address this issue, in this study, we present a combination of unsupervised and supervised machine learning models trained on the experimentally measured conductance traces, with a goal to develop a microscopic understanding. Applying a machine learning model to two independent data sets from two different samples containing 72 000 and 90 000 conductance-displacement traces of single-atomic junctions, respectively, we first obtain the optimum conditions of bias and the stretching rate for the formation of chains of length > 4 Å. A deep learning method is subsequently applied for the classification of individual breaking traces, leading to the identification of trace features related to long-chain formation. Further investigation by ab initio molecular dynamics simulations provides a molecular-level understanding of the problem.

Upper Critical Field and Tunneling Spectroscopy of Underdoped Na(Fe,Co)As Single Crystals

A comprehensive study of superconducting properties of underdoped NaFe0.979Co0.021As single crystals by a combination of upper critical field measurements and incoherent multiple Andreev reflection effect (IMARE) spectroscopy is presented. The Hc2(T) temperature dependences are measured at magnetic fields up to 16 T with in-plane and out-of-plane field directions and considered within single-band and two-band models in order to estimate the Hc2(0) value. In IMARE spectroscopy probes, the magnitude, characteristic ratio, and temperature dependence of the superconducting order parameters (ΔL,S(T)) are determined locally and directly. A possible k-space anisotropy of the large superconducting gap is demonstrated. We show that usage of a quadruple of λij0 coupling constants obtained in the IMARE experiment can significantly reduce the number of free parameters required to fit the Hc2(T) dependence within a two-band approach (from six to two).

Gate-Defined Josephson Weak-Links in Monolayer WTe2

Systems combining superconductors with topological insulators offer a platform for the study of Majorana bound states and a possible route to realize fault tolerant topological quantum computation. Among the systems being considered in this field, monolayers of tungsten ditelluride (WTe2 ) have a rare combination of properties. Notably, it has been demonstrated to be a quantum spin Hall insulator (QSHI) and can easily be gated into a superconducting state. Measurements on gate-defined Josephson weak-link devices fabricated using monolayer WTe2 are reported. It is found that consideration of the 2D superconducting leads are critical in the interpretation of magnetic interference in the resulting junctions. The reported fabrication procedures suggest a facile way to produce further devices from this technically challenging material and the results mark the first step toward realizing versatile all-in-one topological Josephson weak-links using monolayer WTe2 .

Superfluid Signatures in a Dissipative Quantum Point Contact

We measure superfluid transport of strongly interacting fermionic lithium atoms through a quantum point contact with local, spin-dependent particle loss. We observe that the characteristic non-Ohmic superfluid transport enabled by high-order multiple Andreev reflections transitions into an excess Ohmic current as the dissipation strength exceeds the superfluid gap. We develop a model with mean-field reservoirs connected via tunneling to a dissipative site. Our calculations in the Keldysh formalism reproduce the observed nonequilibrium particle current, yet do not fully explain the observed loss rate or spin current.

Direct Observation of the Spin Exciton in Andreev Spectroscopy of Iron-Based Superconductors

Quasiparticle excitations provide viable information on the physics of unconventional superconductors. Higgs and Leggett modes are some of the classic examples. Another important bosonic excitation is the spin exciton originating from the sign-changing superconducting gap structure. Here we report a direct observation of the temperature-dependent spin exciton in the Andreev spectra of iron-based superconductors. Combined with the other experimental evidence, our observation confirms the extended s-wave (s±) order parameter symmetry and indirectly proves the spin-fluctuation mechanism of Cooper pairing.

Photon-Assisted Tunneling of High-Order Multiple Andreev Reflections in Epitaxial Nanowire Josephson Junctions

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 of 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 energies, which depend on MAR order, n, in agreement with a recently suggested modification of the classical Tien-Gordon equation. The scaling of the quantized energy spacings with microwave frequency provides independent confirmation of the effective charge, ne, transferred by the nth-order tunneling process. The measurements suggest PAT as a powerful method for assigning the origin of low-energy spectral features in hybrid Josephson devices.

Phase tuning of multiple Andreev reflections of Dirac fermions and the Josephson supercurrent in Al–MoTe 2 –Al junctions

When an electron in a metal N is incident on the interface with a superconductor, it undergoes an Andreev reflection. A positive charge (a hole) is reflected back to N, while an electron pair (Cooper pair) is created in the superconductor. If N is sandwiched between two superconductors to form a junction, multiple Andreev reflections occur. As a result, multiple Cooper pairs are shuttled across the junction, but only a fraction of them retain phase coherence to define a supercurrent. In a Dirac semimetal, the reflections are observed with exceptional clarity. By tuning the quantum phase across the junction, we show that the supercurrent is tightly choreographed with the Andreev reflections. This allows the coherent fraction to be found.

When an electron is incident on a superconductor from a metal, it is reflected as a hole in a process called Andreev reflection. If the metal N is sandwiched between two superconductors S in an SNS junction, multiple Andreev reflections (MARs) occur. We have found that, in SNS junctions with high transparency (τ → 1) based on the Dirac semimetal MoTe₂, the MAR features are observed with exceptional resolution. By tuning the phase difference φ between the bracketing Al superconductors, we establish that the MARs coexist with a Josephson supercurrent Is=IA sinφ. As we vary the junction voltage V, the supercurrent amplitude IA varies in step with the MAR order n, revealing a direct relation between them. Two successive Andreev reflections serve to shuttle a Cooper pair across the junction. If the pair is shuttled coherently, it contributes to Is. The experiment measures the fraction of pairs shuttled coherently vs. V. Surprisingly, superconductivity in MoTe₂ does not affect the MAR features.

Multiple Andreev reflections effect spectroscopy of LiFeAs single crystals: three superconducting order parameters and their temperature evolution

The structure of the superconducting order parameter of LiFeAs is studied by incoherent multiple Andreev reflections effect (IMARE) spectroscopy. The high transparent superconductor–thin normal metal–superconductor (SnS) contacts are created by a planar “break-junction” technique. Below $$T_c \approx 17.5$$ T c ≈ 17.5  K, the obtained I(V) and dI(V)/dV characteristics of SnS junctions show a presence of at least three bulk superconducting order parameters in LiFeAs. We directly determine the magnitudes, characteristic ratios, and temperature dependences of the superconducting gaps and discuss their symmetry.

Signatures of Interactions in the Andreev Spectrum of Nanowire Josephson Junctions

We performed microwave spectroscopy of an InAs nanowire between superconducting contacts implementing a finite-length, multichannel 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 noninteracting 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.

Microscopic Theory of the Current-Voltage Characteristics of Josephson Tunnel Junctions

Deep theoretical understanding of the electrical response of Josephson junctions is indispensable regarding both recent discoveries of new kinds of superconductivity and technological advances such as superconducting quantum computers. Here, we study the microscopic theory of the dc current-biased I-V characteristics of Josephson tunnel junctions. We derive an analytical formula of the I-V characteristics of generic junctions. We identify subharmonics of the I-V characteristics and their underlying mechanism as the feedback effect of intrinsic ac currents generated by voltage pulses in the past. We apply our theory to analytically solve the Werthamer equation and describe various dc current-biased I-V characteristics as a function of softening of the superconducting gap. Strikingly, we identify voltage staircases of the I-V characteristics in a genuine Josephson junction without ac current bias or qubit dynamics. Our general analytical formalism opens new avenues for a microscopic understanding of I-V characteristics of Josephson junctions that have been limited to phenomenological models so far.

Quantized critical supercurrent in SrTiO3-based quantum point contacts

Superconductivity in SrTiO3 occurs at remarkably low carrier densities and therefore, unlike conventional superconductors, can be controlled by electrostatic gates. Here, we demonstrate nanoscale weak links connecting superconducting leads, all within a single material, SrTiO3. Ionic liquid gating accumulates carriers in the leads, and local electrostatic gates are tuned to open the weak link. These devices behave as superconducting quantum point contacts with a quantized critical supercurrent. This is a milestone toward establishing SrTiO3 as a single-material platform for mesoscopic superconducting transport experiments that also intrinsically contains the necessary ingredients to engineer topological superconductivity.

Collapse of the Josephson Emission in a Carbon Nanotube Junction in the Kondo Regime

We probe the high frequency emission of a carbon nanotube based Josephson junction and compare it to its dc Josephson current. The ac emission is probed by coupling the carbon nanotube to an on-chip detector (a superconductor-insulator-superconductor junction), via a coplanar waveguide resonator. The measurement of the photoassisted current of the detector gives direct access to the signal emitted by the carbon nanotube. We focus on the gate regions that exhibit Kondo features in the normal state and demonstrate that when the dc supercurrent is enhanced by the Kondo effect, the ac Josephson effect is strongly reduced. This result is compared to numerical renormalization group theory and is attributed to a transition between the singlet ground state and the doublet excited state which is enabled only when the junction is driven out-of-equilibrium by a voltage bias.

Missing Shapiro steps in topologically trivial Josephson junction on InAs quantum well

Josephson junctions hosting Majorana fermions have been predicted to exhibit a 4π periodic current phase relation. One experimental consequence of this periodicity is the disappearance of odd steps in Shapiro steps experiments. Experimentally, missing odd Shapiro steps have been observed in a number of materials systems with strong spin-orbit coupling and have been interpreted in the context of topological superconductivity. Here we report on missing odd steps in topologically trivial Josephson junctions fabricated on InAs quantum wells. We ascribe our observations to the high transparency of our junctions allowing Landau-Zener transitions. The probability of these processes is shown to be independent of the drive frequency. We analyze our results using a bi-modal transparency distribution which demonstrates that only few modes carrying 4π periodic current are sufficient to describe the disappearance of odd steps. Our findings highlight the elaborate circumstances that have to be considered in the investigation of the 4π Josephson junctions in relationship to topological superconductivity.

Role of Quasiparticles in an Electric Circuit with Josephson Junctions

Although Josephson junctions can be viewed as highly nonlinear impedances for superconducting quantum technologies, they also possess internal dynamics that may strongly affect their behavior. Here, we construct a computational framework that includes a microscopic description of the junction (full fledged treatment of both the superconducting condensate and the quasiparticles) in the presence of a surrounding electrical circuit. Our approach generalizes the standard resistor capacitor Josephson model to arbitrary junctions (including, e.g., multiterminal geometries and/or junctions that embed topological or magnetic elements) and arbitrary electric circuits treated at the classical level. By treating the superconducting condensate and quasiparticles on equal footings, we capture nonequilibrium phenomena such as multiple Andreev reflection. We show that the interplay between the quasiparticle dynamics and the electrical environment leads to the emergence of new phenomena. In a RC circuit connected to single channel Josephson junction, we find out-of-equilibrium current-phase relations that are strongly distorted with respect to the (almost sinusoidal) equilibrium one, revealing the presence of the high harmonic ac Josephson effect. In an RLC circuit connected to a junction, we find that the shape of the resonance is strongly modified by the quasiparticle dynamics: close to resonance, the current can be smaller than without the resonator. Our approach provides a route for the quantitative modeling of superconducting-based circuits.

Enhanced Shot Noise of Multiple Andreev Reflections in a Carbon Nanotube Quantum Dot in SU(2) and SU(4) Kondo regimes

The sensitivity of shot noise to the interplay between Kondo correlations and superconductivity is investigated in a carbon nanotube quantum dot connected to superconducting electrodes. Depending on the gate voltage, the SU(2) and SU(4) Kondo unitary regimes can be clearly identified. We observe enhancement of the shot noise via the Fano factor in the superconducting state. Its divergence at low bias voltage, which is more pronounced in the SU(4) regime than in the SU(2) one, is larger than what is expected from proliferation of multiple Andreev reflections predicted by the existing theories. Our result suggests that the Kondo effect is responsible for this strong enhancement.

Spin-Orbit Interaction and Induced Superconductivity in a One-Dimensional Hole Gas

Low dimensional semiconducting structures with strong spin-orbit interaction (SOI) and induced superconductivity attracted great interest in the search for topological superconductors. Both the strong SOI and hard superconducting gap are directly related to the topological protection of the predicted Majorana bound states. Here we explore the one-dimensional hole gas in germanium silicon (Ge-Si) core-shell nanowires (NWs) as a new material candidate for creating a topological superconductor. Fitting multiple Andreev reflection measurements shows that the NW has two transport channels only, underlining its one-dimensionality. Furthermore, we find anisotropy of the Landé g-factor that, combined with band structure calculations, provides us qualitative evidence for the direct Rashba SOI and a strong orbital effect of the magnetic field. Finally, a hard superconducting gap is found in the tunneling regime and the open regime, where we use the Kondo peak as a new tool to gauge the quality of the superconducting gap.

Selective-Area Superconductor Epitaxy to Ballistic Semiconductor Nanowires

Semiconductor nanowires such as InAs and InSb are promising materials for studying Majorana zero modes and demonstrating non-Abelian particle exchange relevant for topological quantum computing. While evidence for Majorana bound states in nanowires has been shown, the majority of these experiments are marked by significant disorder. In particular, the interfacial inhomogeneity between the superconductor and nanowire is strongly believed to be the main culprit for disorder and the resulting "soft superconducting gap" ubiquitous in tunneling studies of hybrid semiconductor-superconductor systems. Additionally, a lack of ballistic transport in nanowire systems can create bound states that mimic Majorana signatures. We resolve these problems through the development of selective-area epitaxy of Al to InSb nanowires, a technique applicable to other nanowires and superconductors. Epitaxial InSb-Al devices generically possess a hard superconducting gap and demonstrate ballistic 1D superconductivity and near-perfect transmission of supercurrents in the single mode regime, requisites for engineering and controlling 1D topological superconductivity. Additionally, we demonstrate that epitaxial InSb-Al superconducting island devices, the building blocks for Majorana-based quantum computing applications, prepared using selective-area epitaxy can achieve micron-scale ballistic 1D transport. Our results pave the way for the development of networks of ballistic superconducting electronics for quantum device applications.

Anomalous Fraunhofer Patterns in Gated Josephson Junctions Based on the Bulk-Insulating Topological Insulator BiSbTeSe2

One-dimensional Majorana modes are predicated to form in Josephson junctions based on three-dimensional topological insulators (TIs). While observations of supercurrents in Josephson junctions made on bulk-insulating TI samples have been reported recently, the Fraunhofer patters observed in such TI-based Josephson junctions, which sometimes present anomalous features, are still not well-understood. Here, we report our study of highly gate-tunable TI-based Josephson junctions made of one of the most bulk-insulating TI materials, BiSbTeSe₂, and Al. The Fermi level can be tuned by gating across the Dirac point, and the high transparency of the Al-BiSbTeSe₂ interface is evinced by a high characteristic voltage and multiple Andreev reflections, with peak indices reaching 12. Anomalous Fraunhofer patterns with missing lobes were observed in the entire range of gate voltage. We found that, by employing an advanced fitting procedure to use the maximum entropy method in a Monte Carlo algorithm, the anomalous Fraunhofer patterns are explained as a result of inhomogeneous supercurrent distributions on the TI surface in the junction. Besides establishing a highly promising fabrication technology, this work clarifies one of the important open issues regarding TI-based Josephson junctions.

Non-equilibrium charge and spin transport in superconducting-ferromagnetic-superconducting point contacts

The conventional Josephson effect may be modified by introducing spin-active scattering in the interface layer of the junction. Here, we discuss a Josephson junction consisting of two s-wave superconducting leads coupled over a classical spin that precesses with the Larmor frequency due to an external magnetic field. This magnetically active interface results in a time-dependent boundary condition with different tunnelling amplitudes for spin-up and -down quasi-particles and where the precession produces spin-flip scattering processes. As a result, the Andreev states develop sidebands and a non-equilibrium population that depend on the details of the spin precession. The Andreev states carry a steady-state Josephson charge current and a time-dependent spin current, whose current-phase relations could be used to characterize the precessing spin. The spin current is supported by spin-triplet correlations induced by the spin precession and creates a feedback effect on the classical spin in the form of a torque that shifts the precession frequency. By applying a bias voltage, the Josephson frequency adds another complexity to the situation and may create resonances together with the Larmor frequency. These Shapiro resonances manifest as torques and, under suitable conditions, are able to reverse the direction of the classical spin in sub-nanosecond time. Another characteristic feature is the subharmonic gap structure in the DC charge current displaying an even-odd effect attributable to precession-assisted multiple Andreev reflections.This article is part of the theme issue 'Andreev bound states'.

Theory of Andreev bound states in S-F-S junctions and S-F proximity devices

Andreev bound states are an expression of quantum coherence between particles and holes in hybrid structures composed of superconducting and non-superconducting metallic parts. Their spectrum carries important information on the nature of the pairing, and determines the current in Josephson devices. Here, I focus on Andreev bound states in systems involving superconductors and ferromagnets with strong spin-polarization. I provide a general framework for non-local Andreev phenomena in such structures in terms of coherence functions, and show how the latter link wave function and Green-function based theories.This article is part of the theme issue 'Andreev bound states'.

Josephson effect in junctions of conventional and topological superconductors

We present a theoretical analysis of the equilibrium Josephson current-phase relation in hybrid devices made of conventional s-wave spin-singlet superconductors (S) and topological superconductor (TS) wires featuring Majorana end states. Using Green's function techniques, the topological superconductor is alternatively described by the low-energy continuum limit of a Kitaev chain or by a more microscopic spinful nanowire model. We show that for the simplest S-TS tunnel junction, only the s-wave pairing correlations in a spinful TS nanowire model can generate a Josephson effect. The critical current is much smaller in the topological regime and exhibits a kink-like dependence on the Zeeman field along the wire. When a correlated quantum dot (QD) in the magnetic regime is present in the junction region, however, the Josephson current becomes finite also in the deep topological phase as shown for the cotunneling regime and by a mean-field analysis. Remarkably, we find that the S-QD-TS setup can support φ0-junction behavior, where a finite supercurrent flows at vanishing phase difference. Finally, we also address a multi-terminal S-TS-S geometry, where the TS wire acts as tunable parity switch on the Andreev bound states in a superconducting atomic contact.

Observation of Electron Coherence and Fabry-Perot Standing Waves at a Graphene Edge

Electron surface states in solids are typically confined to the outermost atomic layers and, due to surface disorder, have negligible impact on electronic transport. Here, we demonstrate a very different behavior for surface states in graphene. We probe the wavelike character of these states by Fabry-Perot (FP) interferometry and find that, in contrast to theoretical predictions, these states can propagate ballistically over micron-scale distances. This is achieved by embedding a graphene resonator formed by gate-defined p-n junctions within a graphene superconductor-normal-superconductor structure. By combining superconducting Aharanov-Bohm interferometry with Fourier methods, we visualize spatially resolved current flow and image FP resonances due to p-n-p cavity modes. The coherence of the standing-wave edge states is revealed by observing a new family of FP resonances, which coexist with the bulk resonances. The edge resonances have periodicity distinct from that of the bulk states manifest in a repeated spatial redistribution of current on and off the FP resonances. This behavior is accompanied by a modulation of the multiple Andreev reflection amplitude on-and-off resonance, indicating that electrons propagate ballistically in a fully coherent fashion. These results, which were not anticipated by theory, provide a practical route to developing electron analog of optical FP resonators at the graphene edge.

Nontrivial Chern Numbers in Three-Terminal Josephson Junctions

Recently, it has been predicted that the Andreev bound state spectrum of four-terminal Josephson junctions may possess zero-energy Weyl singularities. Using one superconducting phase as a control parameter, these singularities are associated with topological transitions between time-reversal symmetry broken phases with different Chern numbers. Here we show that such topological transitions may also be tuned with a magnetic flux through the junction area in a three-terminal geometry.

Transport Properties of an Electron-Hole Bilayer in Contact with a Superconductor Hybrid Junction

We investigate the transport properties of a junction consisting of an electron-hole bilayer in contact with normal and superconducting leads. The electron-hole bilayer is considered as a semimetal with two electronic bands. We assume that in the region between the contacts the system hosts an exciton condensate described by a BCS-like model with a gap Γ in the quasiparticle density of states. We first discuss how the subgap electronic transport through the junction is mainly governed by the interplay between two kinds of reflection processes at the interfaces: the standard Andreev reflection at the interface between the superconductor and the exciton condensate, and a coherent crossed reflection at the semimetal-exciton-condensate interface that converts electrons from one layer into the other. We show that the differential conductance of the junction shows a minimum at voltages of the order of Γ/e. Such a minimum can be seen as a direct hallmark of the existence of the gapped excitonic state.

Critical analysis of soft point contact Andreev reflection spectra between superconducting films and pressed In

We present a critical analysis of an alternative technique of point contact Andreev reflection (PCAR) spectroscopy used to extract energy resolved information of superconductors which is based on making 'soft-contacts' between superconductors and indium. This technique is not sensitive to mechanical vibrations and hence can be used in a cryogen free platform increasing its accessibility to users having no access to cryogenic liquids. Through our experiments on large number of superconducting films we show that the PCAR spectra below the T _c of In show sub-harmonic gap structures consistent with the theory of multiple Andreev reflection (MAR) and a zero bias conductance (ZBC) anomaly associated with the Josephson supercurrent. Furthermore, we demonstrate that large contact resistance with low transparency ballistic contacts in the PCAR regime are required to obtain reliable spectroscopic data. One limitation of the technique arises for low contact resistance junctions where the superconducting proximity effect (SPE) reduces the value of the superconducting energy gap.

Anomalous Inner-Gap Structure in Transport Characteristics of Superconducting Junctions with Degraded Interfaces

Quantitative description of charge transport across tunneling and break-junction devices with novel superconductors encounters some problems not present or not as severe for traditional superconducting materials. In this work, we explain unexpected features in related transport characteristics as an effect of a degraded nanoscaled sheath at the superconductor surface. A model capturing the main aspects of the ballistic charge transport across hybrid superconducting structures with normally conducting nanometer-thick interlayers is proposed. The calculations are based on a scattering formalism taking into account Andreev electron-into-hole (and inverse) reflections at normal metal-superconductor interfaces as well as transmission and backscattering events in insulating barriers between the electrodes. Current-voltage characteristics of such devices exhibit a rich diversity of anomalous (from the viewpoint of the standard theory) features, in particular shift of differential-conductance maxima at gap voltages to lower positions and appearance of well-defined dips instead expected coherence peaks. We compare our results with related experimental data.

Signatures of evanescent transport in ballistic suspended graphene-superconductor junctions

In Dirac materials, the low energy excitations behave like ultra-relativistic massless particles with linear energy dispersion. A particularly intriguing phenomenon arises with the intrinsic charge transport behavior at the Dirac point where the charge density approaches zero. In graphene, a 2-D Dirac fermion gas system, it was predicted that charge transport near the Dirac point is carried by evanescent modes, resulting in unconventional “pseudo-diffusive” charge transport even in the absence of disorder. In the past decade, experimental observation of this phenomenon remained challenging due to the presence of strong disorder in graphene devices which limits the accessibility of the low carrier density regime close enough to the Dirac point. Here we report transport measurements on ballistic suspended graphene-Niobium Josephson weak links that demonstrate a transition from ballistic to pseudo-diffusive like evanescent transport below a carrier density of ~10¹⁰ cm⁻². Approaching the Dirac point, the sub-harmonic gap structures due to multiple Andreev reflections display a strong Fermi energy-dependence and become increasingly pronounced, while the normalized excess current through the superconductor-graphene interface decreases sharply. Our observations are in qualitative agreement with the long standing theoretical prediction for the emergence of evanescent transport mediated pseudo-diffusive transport in graphene.

Charge of a quasiparticle in a superconductor

Nonlinear charge transport in superconductor-insulator-superconductor (SIS) Josephson junctions has a unique signature in the shuttled charge quantum between the two superconductors. In the zero-bias limit Cooper pairs, each with twice the electron charge, carry the Josephson current. An applied bias VSD leads to multiple Andreev reflections (MAR), which in the limit of weak tunneling probability should lead to integer multiples of the electron charge ne traversing the junction, with n integer larger than 2Δ/eVSD and Δ the superconducting order parameter. Exceptionally, just above the gap eVSD ≥ 2Δ, with Andreev reflections suppressed, one would expect the current to be carried by partitioned quasiparticles, each with energy-dependent charge, being a superposition of an electron and a hole. Using shot-noise measurements in an SIS junction induced in an InAs nanowire (with noise proportional to the partitioned charge), we first observed quantization of the partitioned charge q = e*/e = n, with n = 1-4, thus reaffirming the validity of our charge interpretation. Concentrating next on the bias region eVSD ~ 2Δ, we found a reproducible and clear dip in the extracted charge to q ~ 0.6, which, after excluding other possibilities, we attribute to the partitioned quasiparticle charge. Such dip is supported by numerical simulations of our SIS structure.

Josephson contacts of neutral strongly interacting fermions

Contacts between superconductors are explored via their ultracold atomic gas analogs [Also see Reports by Husmann et al. and Valtolina et al. ]

Tunneling Processes into Localized Subgap States in Superconductors

We combine scanning-tunneling-spectroscopy experiments probing magnetic impurities on a superconducting surface with a theoretical analysis of the tunneling processes between (superconducting) tip and substrate. We show that the current through impurity-induced Shiba bound states is carried by single-electron tunneling at large tip-substrate distances and Andreev reflections at smaller distances. The single-electron current requires relaxation processes, allowing us to extract information on quasiparticle transitions and lifetimes.

Josephson junction on one edge of a two dimensional topological insulator affected by magnetic impurity

The current-phase relation in a Josephson junction formed by putting two s-wave superconductors on the same edge of a two dimensional topological insulator is investigated. We consider the case in which the junction length is finite and magnetic impurity exists. The similarities and differences with respect to a conventional Josephson junction are discussed. Both the 2π- and 4π-period current-phase relations (I2π(ϕ),I4π(ϕ)) are studied. There is a sharp jump at ϕ = π and ϕ = 2π for I2π and I4π, respectively, in the clean junction. For I2π, the sharp jump is robust against the impurity strength and distribution. However, for I4π, an impurity makes the jump at ϕ = 2π smooth. The critical (maximum) current Ic,2π of I2π is given and we find it will be increased by an asymmetrical distribution of the impurity.

Topological superconducting state of lead nanowires in an external magnetic field

Superconductors with an odd number of bands crossing the Fermi energy have topologically protected Andreev states at interfaces, including Majorana states in one-dimensional geometries. We propose here that repeated indentation of a Pb tip on a Pb substrate can lead to nanowires such that the resulting superconducting system has novel topological properties. We have analyzed a number of conductance curves obtained in different nanowires, and observe, in a few cases, very peculiar dependence of the critical current on magnetic field. In these cases, the form of multiple Andreev reflections observed at finite voltages are compatible with topological superconductivity. The nanowires give a low number of 1D channels, large spin orbit coupling, and a sizable Zeeman energy, provided that the applied magnetic field is higher than the Pb bulk critical field.

ac Josephson effect in finite-length nanowire junctions with Majorana modes

It has been predicted that superconducting junctions made with topological nanowires hosting Majorana bound states (MBS) exhibit an anomalous 4π-periodic Josephson effect. Finding an experimental setup with these unconventional properties poses, however, a serious challenge: for finite-length wires, the equilibrium supercurrents are always 2π periodic as anticrossings of states with the same fermionic parity are possible. We show, however, that the anomaly survives in the transient regime of the ac Josephson effect. Transients are, moreover, protected against decay by quasiparticle poisoning as a consequence of the quantum Zeno effect, which fixes the parity of Majorana qubits. The resulting long-lived ac Josephson transients may be effectively used to detect MBS.

Supercurrent and multiple Andreev reflections in an InSb nanowire Josephson junction

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 in the current bias configuration and multiple Andreev reflection characteristics in the voltage bias configuration. The temperature dependence and the magnetic field dependence of the critical current and the multiple Andreev reflection characteristics of the junction are also studied. Furthermore, we extract the excess current from the measurements and study its temperature and magnetic field dependences. The successful observation of the superconductivity in the InSb nanowire-based Josephson junction device indicates that InSb nanowires provide an excellent material system for creating and observing novel physical phenomena such as Majorana fermions in solid-state systems.

Nonequilibrium transport through a spinful quantum dot with superconducting leads

We study the nonlinear cotunneling current through a spinful quantum dot contacted by two superconducting leads. Applying a general nonequilibrium Green function formalism to an effective Kondo model, we study the rich variation in the IV characteristics with varying asymmetry in the tunnel coupling to source and drain electrodes. The current is found to be carried, respectively, by multiple Andreev reflections in the symmetric limit, and by spin-induced Yu-Shiba-Rusinov bound states in the strongly asymmetric limit. The interplay between these two mechanisms leads to qualitatively different IV characteristics in the crossover regime of intermediate symmetry, consistent with recent experimental observations of negative differential conductance and repositioned conductance peaks in subgap cotunneling spectroscopy.

RSFQ TECHNOLOGY: PHYSICS AND DEVICES

Rapid Single-Flux-Quantum (RSFQ) logic, based on the representation of digital bits by single quanta of magnetic flux in superconducting loops, may combine several-hundred-GHz speed with extremely low power dissipation (close to 10-18 Joule/bit) and very simple fabrication technology. The drawbacks of this technology include the necessity of deep (liquid-helium-level) cooling of RSFQ circuits and the rudimentary level of the currently available fabrication and testing facilities. The objective of this paper is to review RSFQ device physics and also discuss in brief the prospects of future development of this technology in the light of the tradeoff between its advantages and handicaps.

Nonequilibrium Josephson effect through helical edge states

We study Josephson junctions between superconductors connected through the helical edge states of a two-dimensional topological insulator in the presence of a magnetic barrier. As the equilibrium Andreev bound states of the junction are 4π periodic in the superconducting phase difference, it was speculated that, at finite dc bias voltage, the junction exhibits a fractional Josephson effect with half the Josephson frequency. Using the scattering matrix formalism, we show that his effect is absent in the average current. However, clear signatures can be seen in the finite-frequency current noise. Furthermore, we discuss other manifestations of the Majorana bound states forming at the edges of the superconductors.

Josephson-current-induced conformational switching of a molecular quantum dot

We discuss the behavior of a two-level system coupled to a quantum dot contacted by superconducting source and drain electrodes, representing a simple model for the conformational degree of freedom of a molecular dot or a break junction. The Josephson current is shown to induce conformational changes, including a complete reversal. For small bias voltage, periodic conformational motions induced by Landau-Zener transitions between Andreev states are predicted.

Measurement of the current-phase relation of superconducting atomic contacts

We have probed the current-phase relation of an atomic contact placed with a tunnel junction in a small superconducting loop. The measurements are in quantitative agreement with the predictions of a resistively shunted SQUID model in which the Josephson coupling of the contact is calculated using the independently determined transmissions of its conduction channels.

Kondo-enhanced Andreev tunneling in InAs nanowire quantum dots

We report measurements of the nonlinear conductance of InAs nanowire quantum dots coupled to superconducting leads. We observe a clear alternation between odd and even occupation of the dot, with subgap peaks at |V(sd)| = Delta/e markedly stronger (weaker) than the quasiparticle tunneling peaks at |V(sd)| = 2Delta/e for odd (even) occupation. We attribute the enhanced Delta peak to an interplay between Kondo correlations and Andreev tunneling in dots with an odd number of spins, and we substantiate this interpretation by a poor man's scaling analysis.

Crossover from Josephson to multiple Andreev reflection currents in atomic contacts

The basic current-carrying mechanism through a superconducting weak link embedded in a resistive environment undergoes a continuous crossover, as the voltage increases, from Josephson Cooper pair transfer exciting electromagnetic modes in the environment to multiple Andreev reflections leading to the creation of quasiparticles. We corroborate these ideas through measurements of the dc current-voltage characteristics of superconducting atomic contacts containing channels of arbitrary and adjustable transmission. We present a simple model, in the spirit of the classical resistively shunted junction model, that accounts well for the observed characteristics.

Alternating current Josephson effect and resonant superconducting transport through vibrating Nb nanowires

In 1962, Josephson made a celebrated prediction: when a constant voltage is applied across a thin insulator separating two superconductors, it will generate an oscillating current. These oscillations are ubiquitous in superconducting weak links of various geometries, and analogues have been found in other macroscopic quantum systems, such as superfluids and gaseous Bose-Einstein condensates. The interplay between the oscillating current and external microwave radiation of matching frequency (Shapiro steps) or with internal electrodynamic resonances (Fiske effect) appear as changes in the current-voltage characteristics of superconducting tunnel junctions and provide further insight into the phenomenon. Here, we report measurements and theoretical studies suggesting that Josephson current oscillations interact with atomic-scale mechanical motion as well. We formed a niobium dimer nanowire that acts as a weak link between two superconducting (bulk) niobium electrodes. We find features in the differential conductance through the dimer which we believe correspond to excitations of the dimer vibrational modes by Josephson oscillations and support our results with theoretical simulations.

Dynamics of spin transport in voltage-biased Josephson junctions

We investigate spin transport in voltage-biased spin-active Josephson junctions. The interplay of spin filtering, spin mixing, and multiple Andreev reflection leads to nonlinear voltage dependence of the dc and ac spin current. We compute the voltage characteristics of the spin current (IS) for superconductor-ferromagnet-superconductor Josephson junctions. The subharmonic gap structure of IS(V) is shown to be sensitive to the degree of spin mixing generated by the ferromagnetic interface, and exhibits a pronounced even-odd effect associated with spin transport during multiple Andreev reflection processes. For strong spin mixing both the magnitude and the direction of the dc spin current can be sensitively controlled by the bias voltage.

Gate-controlled superconductivity in a diffusive multiwalled carbon nanotube

We have investigated electrical transport in a diffusive multiwalled carbon nanotube contacted using superconducting leads made of an Al/Ti sandwich structure. We find proximity-induced superconductivity with measured critical currents up to I(cm)=1.3 nA, tunable by the gate voltage down to 10 pA. The supercurrent branch displays a finite zero bias resistance which varies as R(0) proportional to I(cm){-alpha} with alpha=0.74. Using IV characteristics of junctions with phase diffusion, a good agreement is obtained with the Josephson coupling energy in the long, diffusive junction model of A. D. Zaikin and G. F. Zharkov [Sov. J. Low Temp. Phys. 7, 184 (1981)].