The intriguing interplay between topology and superconductivity has attracted significant attention, given its potential for realizing topological superconductivity. In the quantum anomalous Hall insulators (QAHIs)-based junction, the supercurrents are carried by the chiral edge states, characterized by a $2Φ_0$ magnetic flux periodicity ($Φ_0 = h/2e$ is the flux quantum, $h$ the Planck constant, and $e$ the electron charge). However, experimental observations indicate the presence of bulk carriers in QAHI samples due to magnetic dopants. In this study, we reveal a systematic transition from edge-state to bulk-state dominant supercurrents as the chemical potential varies from the bulk gap to the conduction band. This results in an evolution from a $2Φ_0$-periodic oscillation pattern to an asymmetric Fraunhofer pattern. Furthermore, a novel Fraunhoher-like pattern emerges due to the coexistence of chiral edge states and bulk states caused by magnetic {\color{black}domains}, even when the chemical potential resides within the gap. These findings not only advance the theoretical understanding but also pave the way for the experimental discovery of the chiral Josephson effect based on QAHI doped with magnetic impurities.
Anharmonicity and Charge-Noise Sensitivity of Fraunhofer Qubit
University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；New York University（纽约大学）；University of Maryland, College Park（马里兰大学帕克分校）；Ecole Polytechnique Federale de Lausanne（洛桑联邦理工学院）
Introduction of spin-orbit coupling (SOC) in a Josephson junction (JJ) gives rise to unusual Josephson effects. We investigate JJs based on a newly discovered heterodimensional superlattice V$_5$S$_8$ with a special form of SOC. The unique homointerface of our JJs enables elimination of extrinsic effects due to interfaces and disorder. We observe asymmetric Fraunhofer patterns with respect to both the perpendicular magnetic field and the current. The asymmetry is influenced by an in-plane magnetic field. Analysis of the pattern points to a nontrivial spatial distribution of the Josephson curre…
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 are recently reported, 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 Dira…
$ $The critical current of a Josephson junction is an oscillatory function of the enclosed magnetic flux $Φ$, because of quantum interference modulated with periodicity $h/2e$. We calculate these Fraunhofer oscillations in a two-dimensional (2D) ballistic superconductor--normal-metal--superconductor (SNS) junction. For a Fermi circle the amplitude of the oscillations decays as $1/Φ$ or faster. If the Fermi circle is strongly warped, as it is on a square lattice near the band center, we find that the amplitude decays slower $\propto 1/\sqrtΦ$ when the magnetic length $l_m=\sqrt{\hbar/eB}$ drops…
We fabricate superconductor-graphene-superconductor Josephson junctions with superconducting regions made of lead (Pb). The critical current through grapehene may be modulated by external magnetic field; the resulting Fraunhofer interference pattern shows several periods of oscillations, indicating that the junction is uniform. Deviations from the perfect Fraunhofer pattern are observed, and their cause is explained by a simulation that takes into account the sample design.
The effect of a magnetic field on Josephson current has been studied for a superconductor/normal-metal/superconductor (SNS) system, where N is a two-dimensional electron gas in a confining potential. It is found that the dependence of Josephson currents on the magnetic field are sensitive to the width of the normal metal. If the normal metal is wide and contains many channels (subbands), the current on a weak magnetic field shows a dependence similar to a Fraunhofer-pattern in SIS system and, as the field gets strong, it shows another type of oscillatory dependence on the field resulting from …
We calculate the beating of $h/2e$ and $h/e$ periodic oscillations of the flux-dependent critical supercurrent $I_c(Φ)$ through a quantum spin-Hall insulator between two superconducting electrodes. A conducting pathway along the superconductor connects the helical edge channels via a non-helical channel, allowing an electron incident on the superconductor along one edge to be Andreev reflected along the opposite edge. In the limit of small Andreev reflection probability the resulting even-odd effect is described by $I_c\propto|\cos(eΦ/\hbar)+f|$, with $|f|\ll 1$ proportional to the probability…
We investigate patterns of critical current as a function of perpendicular and in-plane magnetic fields in superconductor-semiconductor-superconductor (SNS) junctions based on InAs/InGaAs heterostructures with an epitaxial Al layer. This material system is of interest due to its exceptionally good superconductor-semiconductor coupling, as well as large spin-orbit interaction and g-factor in the semiconductor. Thin epitaxial Al allows the application of large in-plane field without destroying superconductivity. For fields perpendicular to the junction, flux focusing results in aperiodic node sp…
Unconventional superconductivity arising from the interplay between strong spin-orbit coupling and magnetism is an intensive area of research. One form of unconventional superconductivity arises when Cooper pairs subjected to a magnetic exchange coupling acquire a finite momentum. Here, we report on a signature of finite momentum Cooper pairing in the 3D topological insulator Bi2Se3. We apply in-plane and out-of-plane magnetic fields to proximity-coupled Bi2Se3 and find that the in-plane field creates a spatially oscillating superconducting order parameter in the junction as evidenced by the e…
We consider recent experiments on wide superconductor-quantum spin Hall insulator (QSHI)-superconductor Josephson junctions, which have shown preliminary evidence of proximity-induced superconductivity at the edge-modes of the QSHI system based on an approximate analysis of the observed Fraunhofer spectra of the Josephson critical current as a function of the applied magnetic field. Using a completely independent exact numerical method involving a non-linear constrained numerical optimization, we calculate the supercurrent profiles, comparing our results quantitatively with the experimental Fr…
The $4π$ Josephson Effect is a distinguishing feature of a topological Josephson junction. However, stringent conditions make it hard to observe in experiments. Here we numerically study the transient transport properties in a topological Josephson junction. We show that the $4π$ Josephson current can be sustained for a significant time (around several $μs$ with suitable conditions). Furthermore, we compare the behaviors of Josephson current in different conditions, identifying three main regimes: First, when both the superconducting wires of the Josephson junction lie in the topologically non…
We show that a spin-polarized Landau level in a two-dimensional electron gas can carry a spin-triplet supercurrent between two spin-singlet superconductors. The supercurrent results from the interplay of Andreev reflection and Rashba spin-orbit coupling at the normal--superconductor (NS) interface. We contrast the current-phase relationship and the Fraunhofer oscillations of the spin-triplet and spin-singlet Josephson effect in the lowest Landau level, and find qualitative differences.
We investigate Josephson junctions on the surface of a three-dimensional topological insulator in planar, step, and edge geometries. The elliptical nature of the Dirac cone representing the side surface states of the topological insulator results in a scaling factor in the Josephson current in a step junction as compared to the planar junction. In edge junctions, the contribution of the Andreev bound states to the Josephson current vanishes due to spin-momentum locking of the surface states. Furthermore, we consider a junction with a ferromagnetic insulator between the superconducting regions.…
Non-Gaussian fluctuations of the electrical current can be detected with a Josephson junction placed on-chip with the noise source. We present preliminary measurements with an NIS junction as a noise source, and a Josephson junction in the thermal escape regime as a noise detector. It is shown that the Josephson junction detects not only the average noise, which manifests itself as an increased effective temperature, but also the noise asymmetry. A theoretical description of the thermal escape of a Josephson junction in presence of noise with a non-zero third cumulant is presented, together wi…
We analyzed multimode Josephson junctions with exciton-polaritons (polaritonic Josephson junctions) when several coupling mechanisms of fundamental and excited states are present. The applied method is based on Keldysh-Green function formalism and takes into account polariton pseudospin. We found that mean value of circular polarization degree in intrinsic Josephson oscillations and microscopic quantum self-trapping follow an oscillator behavior whose renormalizes due to intermode interactions. The effect of an additional transfer of particles over junction barrier occurring in multimode appro…
We report an experimental study on the tuning of supercurrent in a ballistic graphene-based Josephson junction by applying a control voltage to a transverse normal channel. In this four-terminal geometry, the control voltage changes the occupation of Andreev states in the Josephson junction, thereby tuning the magnitude of the supercurrent. As a function of gate voltage, we find two different regimes characterized by a double-step distribution and a hot-electron distribution, respectively. Our work opens new opportunities to design highly controllable Josephson junctions for tunable supercondu…
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.
Quasiparticle poisoning and diabatic transitions may significantly narrow the window for the experimental observation of the $4π$-periodic $dc$ Josephson effect predicted for topological Josephson junctions. Here, we show that switching current measurements provide accessible and robust signatures for topological superconductivity which persist in the presence of quasiparticle poisoning processes. Such measurements provide access to the phase-dependent subgap spectrum and Josephson currents of the topological junction when incorporating it into an asymmetric SQUID together with a conventional …
The response of superconductor-normal-metal-superconductor junctions to magnetic field is complicated and non-universal because all trajectories contributing to supercurrent have a different effective area, and therefore acquire arbitrary magnetic phases. We design an hourglass-shaped Josephson junction where due to the junction symmetry the magnetic phase of every trajectory is approximately equal. By doing so we are able to increase a critical field of the Josephson junction to many flux quanta per junction area. We then analyse how breaking the symmetry condition increases the sensitivity o…
We present direct measurements of the current-phase relation for lateral Josephson junctions with a graphene barrier, obtained by a phase-sensitive SQUID interferometry technique. We find that the current-phase relation is forward skewed with respect to the commonly observed sinusoidal behavior for short junctions in the quasi-ballistic transport regime, consistent with predictions for the behavior of Dirac fermions in a Josephson junction. The skewness increases with critical current and decreases sharply with increasing temperature.
We theoretically study a Josephson junction formed by two finite-size $s$-wave SCs on a topological insulator under a magnetic field. At certain conditions, the junction hosts the chiral Majorana modes enclosing the two finite-size SCs. The interplay of the extended chiral Majorana modes and the states inside the junction can results in nontrivial topological effects such as the $2n π$ fractional AC Josephson effects predicted in Ref.~\cite{ChoiSim} We show that the $2n π$ fractional AC Josephson effects can occur in a realistic situation, such as the presence of the midgap states, without req…
We have studied experimentally the escape dynamics in underdamped capacitively shunted and unshunted Josephson junctions with submicroampere critical currents below 0.5 K temperatures. In the shunted junctions, thermal activation process was preserved up to the highest temperature where the escape in the unshunted junctions exhibits the phase diffusion. Our observations in the shunted junctions are in good agreement with the standard thermal activation escape, unlike the results in the unshunted junctions.
We propose a scheme to implement the two-qubit quantum phase gate with Josephson-junction charge qubits in a thermal cavity. In this scheme, the photon-number-dependent parts in the time evolution operator are canceled at the special time. Thus the scheme is insensitive to the thermal field. We also demonstrate that the scheme can be used to generate maximally entangled state of many Josephson-junction charge qubits
The concept of coupled robust field induced Josephson junctions placed in complex electromagnetic environments is presented. Such structures are made by polarization of superconducting nanostructures by magnetic fields. The methodology of modeling of structures and possible implementations is introduced. The presented scheme is expected to implement and describe both classical and quantum computers with use of Josephson junction and artificial evolution. In such cases one can obtain unexpected new topologies of circuits that can contribute in enhancement of known and used circuit schemes. Furt…
We investigate the Josephson radiation of nanowire (NW)-based Josephson junctions in a parallel magnetic field. The Josephson junction made of an InAs NW with superconducting Al leads shows the emission spectra which follow the Josephson frequency $f_{J}$ over the range 4-8 GHz at zero magnetic field. We observe an apparent deviation of the emission spectra from the Josephson frequency which is accompanied by a strong enhancement of the switching current above a magnetic field of $\sim 300$ mT. The observed modulations can be understood to reflect trivial changes in the superconducting circuit…
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)]
We theoretically investigate the mapping of the supercurrent distribution in a planar superconductor-normal-superconductor junction in the presence of a perpendicular magnetic field via the scanning gate microscopy technique. We find that the distribution of counter-propagating supercurrents aligned in Josephson vortices can be mapped by the change of the critical current induced by the tip of the scanning probe, if the flux in the junction is set close to maxima of the Fraunhofer pattern. Instead, when the magnetic field drives the junction to a supercurrent minimum in the Fraunhofer pattern,…
We show that the time reversal symmetry inevitably breaks in a superconducting Josephson junction formed by two superconductors with different pairing symmetries dubbed as i-Josephson junction. While the leading conventional Josephson coupling vanishes in such an i-Josephson junction, the second order coupling from tunneling always generates chiral superconductivity orders with broken time reversal symmetry. Josephson frequency in the i-junction is doubled, namely $ω= 4eV /h$. The result provides a way to engineer topological superconductivity such as the d + id' -wave superconducting state ch…
We investigate the influence of gauge fields induced by strain on the supercurrent passing through the graphene-based Josephson junctions. We show in the presence of a constant pseudomagnetic field ${\bf B}_S$ originated from an arc-shape elastic deformation, the Josephson current is monotonically enhanced. This is in contrast with the oscillatory behavior of supercurrent (known as Fraunhofer pattern) caused by real magnetic fields passing through the junction. The absence of oscillatory supercurrent originates from the fact that strain-induced gauge fields have opposite directions at the two …
We report electronic transport measurements of graphene contacted by NbTiN electrodes, which at low temperature remain superconducting up to at least 11 Tesla. In devices with a single superconducting contact, we find a more than twofold enhancement of the conductance at zero bias, which we interpret in terms of reflectionless tunneling. In devices with two superconducting contacts, we observe the Josephson effect, bipolar supercurrents and Fraunhofer patterns.
Charge formations on superconducting layers and creation of the longitudinal plasma wave in the stack of intrinsic Josephson junctions change crucially the superconducting current through the stack. Investigation of the correlations of superconducting currents in neighboring Josephson junctions and the charge correlations in neighboring superconducting layers allows us to predict the additional features in the current--voltage characteristics. The charge autocorrelation functions clearly demonstrate the difference between harmonic and chaotic behavior in the breakpoint region. Use of the corre…
We review experiments on small-capacitance Josephson junctions. When the Josephson junction is fabricated in the configuration of dc superconducting quantum interference device (SQUID), the Josephson coupling can be tuned IN SITU with an external magnetic field. The electrical transport properties of one-dimensional arrays of small-capacitance dc SQUIDs have been investigated in order to study the superconductor-insulator transition. The arrays have also been used to bias a single Josephson junction, and a clear Coulomb blockade of Cooper-pair tunneling has been observed in the single junction…
We use a tight-binding Bogoliubov-de Gennes (BdG) formalism to self-consistently calculate the proximity effect, Josephson current, and local density of states in ballistic graphene SNS Josephson junctions. Both short and long junctions, with respect to the superconducting coherence length, are considered, as well as different doping levels of the graphene. We show that self-consistency does not notably change the current-phase relationship derived earlier for short junctions using the non-selfconsistent Dirac-BdG formalism but predict a significantly increased critical current with a stronger…
We derive a generic phenomenological model of a Majorana Josephson junction that accounts for avoided crossing of Andreev states, and investigate its dynamics at constant bias voltage to reveal an unexpected pattern of any-π Josephson effect in the limit of slow decoherence.
Coupling of Josephson-phase and spin-waves is theoretically studied in a superconductor/ferromagnetic insulator/superconductor (S/FI/S) junction. Electromagnetic (EM) field inside the junction and the Josephson current coupled with spin-waves in FI are calculated by combining Maxwell and Landau-Lifshitz-Gilbert equations. In the S/FI/S junction, it is found that the current-voltage (I-V) characteristic shows two resonant peaks. Voltages at the resonant peaks are obtained as a function of the normal modes of EM field, which indicates a composite excitation of the EM field and spin-waves in the …
This work deals with two pressing issues in the design and operation of Josephson qubits -- loss of coherence and measurement. (Longer abstract follows in the work.)
We perform extensive analysis of graphene Josephson junctions embedded in microwave circuits. By comparing a diffusive junction at 15 mK with a ballistic one at 15 mK and 1 K, we are able to reconstruct the current-phase relation.
Setting up strong Josephson coupling in van der Waals materials in close proximity to superconductors offers several opportunities both to inspect fundamental physics and to develop novel cryogenic quantum technologies. Here we show evidence of Josephson coupling in a planar few-layer black Phosphorus junction. The planar geometry allows us to probe the junction behavior by means of external gates, at different carrier concentrations. Clear signatures of Josephson coupling are demonstrated by measuring supercurrent flow through the junction at milli Kelvin temperatures. Manifestation of Fraunh…
Experiments on one-dimensional small capacitance Josephson Junction arrays are described. The arrays have a junction capacitance that is much larger than the stray capacitance of the electrodes, which we argue is important for observation of Coulomb blockade. The Josephson energy can be tuned in situ and an evolution from Josephson-like to Coulomb blockade behavior is observed. This evolution can be described as a superconducting to insulating, quantum phase transition. In the Coulomb blockade state, hysteretic current-voltage characteristics are described by a dynamic model which is dual to t…
Josephson junctions and SQUIDs with graphene or other 2D materials as the weak link between superconductors have become a hot topic of research in recent years, with respect to both fundamental physics and potential applications. We have previously reported ultra-wide Josephson junctions (up to 80 μm wide) based on CVD graphene where the critical current was found to be uniformly distributed in the direction perpendicular to the current. In this paper, we demonstrate that the unusually large Josephson penetration depth λ_J that this corresponds to is enabled by the unique geometric structure o…
The Josephson current between an s-wave and a spin-triplet superconductor Sr$_2$RuO$_4$ (SRO) is studied theoretically. In spin-singlet / spin-triplet superconductor junctions, there is no Josephson current proportional to $\sin ϕ$ in the absence of the spin-flip scattering near junction interfaces, where $ϕ$ is a phase-difference across junctions. Thus a dominant term of the Josephson current is proportional to $\sin 2ϕ$ . The spin-orbit scattering at the interfaces gives rise to the Josephson current proportional to $\cosϕ$, which is a direct consequence of the chiral paring symmetry in SRO.
We propose a realization of the superconducting diode effect in flux biased superconducting circuits of Josephson junctions. So far the observation of the superconducting diode effect has been limited to rather exotic material platforms. In theoretical proposals, it relied on a non-sinusoidal form of the current phase relation of Josephson junctions. Here, we show how the diode effect can be engineered in superconducting circuits without any such requirements. The only necessary ingredients are standard sinusoidal Josephson junctions and flux bias lines that are readily available in scalable i…
We theoretically investigate heat transport in temperature-biased Josephson tunnel junctions in the presence of an in-plane magnetic field. In full analogy with the Josephson critical current, the phase-dependent component of the heat flux through the junction displays coherent diffraction. Thermal transport is analyzed in three prototypical junction geometries highlighting their main differences. Notably, minimization of the Josephson coupling energy requires the quantum phase difference across the junction to undergo π-slips in suitable intervals of magnetic flux. An experimental setup suite…
We present a detailed study of photonic heat transport across a Josephson junction coupled to two arbitrary linear circuits having different temperatures. First, we consider the linear approximation, in which a nonlinear Josephson potential is replaced by a quadratic one and the junction acts as an inductor. Afterwards, we discuss the effects of junction anharmonicity. We separately consider the weak-coupling limit, in which the Bloch band structure of the junction energy spectrum plays an important role, and the opposite strong-coupling regime. We apply our general results to two specific mod…
We discuss dephasing by the dissipative electromagnetic environment and by measurement in circuits consisting of small Josephson junctions. We present quantitative estimates and determine in which case the circuit might qualify as a quantum bit. Specifically, we analyse a three junction Cooper pair pump and propose a measurement to determine the decoherence time $τ_ϕ$.
Topological Josephson junctions (JJs), which contain Majorana bound states, are expected to exhibit 4$π$-periodic current-phase relation, thereby resulting in doubled Shapiro steps under microwave irradiation. We performed numerical calculations of dynamical properties of topological JJs using a modified resistively and capacitively shunted junction model and extensively investigated the progressive evolution of Shapiro steps as a function of the junction parameters and microwave power and frequency. Our calculation results indicate that the suppression of odd-integer Shapiro steps, i.e., evid…
Control of the Josephson current by varying a gate current has recently been demonstrated in both 4-terminal and 3-terminal junctions. We show that, when the the gates are weakly coupled to the Josephson junction, the Josephson current versus gate current (or versus gate voltage) relation is the same for both the 4- and 3- terminal geometries. At low temperature, the supercurrent switches abruptly as a function of the gate voltage, but only slowly as a function of the gate current.
One of the consequences of Cooper pairs having a finite momentum in the interlayer of a Josephson junction, is $π$-junction behavior. The finite momentum can either be due to an exchange field in ferromagnetic Josephson junctions, or due to the Zeeman effect. Here, we report the observation of Zeeman effect induced 0-$π$ transitions in Bi$_{1-x}$Sb$_x$, 3D Dirac semimetal-based Josephson junctions. The large g-factor of the Zeeman effect from a magnetic field applied in the plane of the junction allows tuning of the Josephson junctions from 0- to $π$- regimes. This is revealed by sign changes …
We study the thermodynamic properties of topological Josephson junctions using a quantum spin Hall (QSH) insulator-based junction as an example. In particular, we propose that phase-dependent measurements of the heat capacity offer an alternative to Josephson-current measurements to demonstrate key topological features. Even in an equilibrium situation, where the fermion parity is not conserved, the heat capacity exhibits a pronounced double peak in its phase dependence as a signature of the protected zero-energy crossing in the Andreev spectrum. This double-peak feature is robust against chan…
We present measurements of the current-phase relation (CPR) of Superconductor-Ferromagnet-Superconductor (SFS) Josephson junctions as a function of temperature. The CPR is determined by incorporating the junction into a superconducting loop coupled to a dc SQUID, allowing measurement of the junction phase difference. Junctions fabricated with a thin (~ 22 nm) barrier of Cu0.47Ni0.53 sandwiched between Nb electrodes exhibit a re-entrant critical current with temperature, vanishing at T =T_pi ~ 2-4 K. We find that the critical current is negative for T < T_pi, indicating that the junction is a p…
We investigate experimentally the physics of quantum phase slips in one-dimensional Josephson Junction chains. These quantum phase-slips are induced by quantum phase fluctuations occurring on single junctions of the chain. In our experiment we can tune the strength of these fluctuations as each chain junction is realized in form of a SQUID leading to tunable Josephson coupling. We determine the ground state of the chain via switching current measurements of the chain shunted by a large Josephson junction. Our results can be well fitted with a tight binding Hamiltonian taking into account quant…
We discuss heat transport in thermally-biased long Josephson tunnel junctions in the presence of an in-plane magnetic field. In full analogy with the Josephson critical current, the phase-dependent component of the heat current through the junction displays coherent diffraction. Thermal transport is analyzed as a function of both the length and the damping of the junction, highlighting deviations from the standard Fraunhofer pattern characteristic of short junctions. The heat current diffraction patterns show features strongly related to the formation and penetration of Josephson vortices, i.e…
We calculate the electrical currents through a superconductor - insulator - superconductor junction which is also weakly coupled to a normal metal side probe. The voltage $V$ applied to the normal metal terminal controls the occupation of Andreev energy levels $E_n$, and therefore controls the Josephson current flowing through these levels. Whenever the probe voltage crosses an Andreev level, the Josephson current changes abruptly by an amount equal to the current flowing through the Andreev level. The differential conductance along the normal metal terminal permits spectroscopy of the Andreev…
A non-band theory is developed to describe the superconductor-insulator (SI) transtition in resistively shunted, single Josephson junctions. The $I-V$ characteristic is formulated by a Landauer-like formula and evaluated by the path-integral transfer-matrix method. The result is consistent with the recent experiments at around 80 $mK$. However, the insulator phase shrinks with decreasing temperature indicating that the single Josephson junction becomes all superconducting at absolute zero temperature, as long as dissipation is present.
Wide mesoscopic superconducting - normal-metal - superconducting (S-N-S) junctions exhibit Andreev bound states which carry substantial supercurrents, even at temperatures for which the equilibrium Josephson effect is exponentially small --- the currents carried by different states can cancel each other. This cancellation is incomplete whenever the junctions are driven out of equilibrium, e.g., by a dc voltage. This leads to phenomena similar to the usual dc and ac Josephson effects, but dominated by the second harmonic of the Josephson frequency, which may explain some striking recent experim…
Superconducting circuits incorporating Josephson tunnel junctions are widely used for fundamental research as well as for applications in fields such as quantum information and magnetometry. The quantum coherent nature of Josephson junctions makes them especially suitable for metrology applications. Josephson junctions suffice to form two sides of the quantum metrology triangle, relating frequency to either voltage or current, but not its base, which directly links voltage to current. We propose a five Josephson tunnel junction circuit in which simultaneous pumping of flux and charge results i…
