A nonmonotonic dependence of the critical Josephson supercurrent on the injection current through a normal metal/ferromagnet weak link from a single domain ferromagnetic strip has been observed experimentally in nanofabricated planar crosslike S-N/F-S Josephson structures. This behavior is explained by 0-pi and pi-0 transitions, which can be caused by the suppression and Zeeman splitting of the induced superconductivity due to interaction between N and F layers, and the injection of spin-polarized current into the weak link. A model considering both effects has been developed. It shows the qualitative agreement between the experimental results and the theoretical model in terms of spectral supercurrent-carrying density of states of S-N/F-S structure and the spin-dependent double-step nonequilibrium quasiparticle distribution.
Nonlocal supercurrent was observed in mesoscopic planar SNS Josephson junction with additional normal metal electrodes when nonequilibrium quasiparticles were injected from the normal metal electrode in one of the superconducting banks of the Josephson junction in the absence of net transport current through the junction. We claim that the effect observed is due to a supercurrent counterflow appearing to compensate the quasiparticle flow in the SNS weak link. We have measured SNS junction response for different distances from the quasiparticle injector to the SNS junction at temperatures far b…
We consider a mesoscopic normal metal, where the spin degeneracy is lifted by a ferromagnetic exchange field or Zeeman splitting, coupled to two superconducting reservoirs. As a function of the exchange field or the distance between the reservoirs, the supercurrent through this device oscillates with an exponentially decreasing envelope. This phenomenon is similar to the tuning of a supercurrent by a non-equilibrium quasiparticle distribution between two voltage-biased reservoirs. We propose a device combining the exchange field and non-equilibrium effects, which allows us to observe a range o…
The thermopower of mesoscopic normal metal/superconductor structures has been measured at low temperatures. Effect of supercurrent present in normal part of the structure was studied in two cases: when it was created by applied external magnetic field and when it was applied directly using extra superconducting electrodes. Temperature and magnetic field dependencies of thermopower are compared to the numerical simulations based on the quasiclassical theory of the superconducting proximity effect.
The distinctive quasiparticle distribution existing under nonequilibrium in a superconductor-insulator-normal metal-insulator-superconductor (SINIS) mesoscopic line is proposed as a novel tool to control the supercurrent intensity in a long Josephson weak link. We present a description of this system in the framework of the diffusive-limit quasiclassical Green-function theory and take into account the effects of inelastic scattering with arbitrary strength. Supercurrent enhancement and suppression, including a marked transition to a $π$-junction are striking features leading to a fully tunable…
In this paper we study the effect of a Zeeman field on the supercurrent of a mesoscopic SNS junction. It is shown that the supercurrent suppression is due to a redistribution of current-carrying states in energy space. A dramatic consequence is that (part of the) the suppressed supercurrent can be recovered with a suitable non-equilibrium distribution of quasiparticles.
We study mesoscopic fluctuations and weak localization correction to the supercurrent in Josephson junctions with coherent diffusive electron dynamics in the normal part. Two kinds of junctions are considered: a chaotic dot coupled to superconductors by tunnel barriers and a diffusive junction with transparent normal--superconducting interfaces. The amplitude of current fluctuations and the weak localization correction to the average current are calculated as functions of the ratio between the superconducting gap and the electron dwell energy, temperature, and superconducting phase difference …
Recent experiments have demonstrated the nonequilibrium control of the supercurrent through diffusive phase-coherent normal-metal weak links. The experimental results have been accurately described by the quasiclassical Green's function technique in the Keldysh formalism. Taking into account the geometry of the structure, different energy scales and the nonidealities at the interfaces allows us to obtain a quantitative agreement between the theory and the experimental results in both the amplitude and the phase dependence of the supercurrent, with no or very few fitting parameters. Here we dis…
In the classical Josephson effect the phase difference across the junction is well defined, and the supercurrent is reduced only weakly by phase diffusion. For mesoscopic junctions with small capacitance the phase undergoes large quantum fluctuations, and the current is also decreased by Coulomb blockade effects. We discuss the behavior of the current-voltage characteristics in a large range of parameters comprising the phase diffusion regime with coherent Josephson current as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.
We study spin-polarized quasiparticle transport in a mesoscopic superconductor with a spin- splitting field in the presence of co-flowing supercurrent. In such a system, the nonequilibrium state is characterized by charge, spin, energy and spin energy modes. Here we show that in the presence of both spin splitting and supercurrent, all these modes are mutually coupled. As a result, the supercurrent can convert charge imbalance, that in the presence of spin splitting decays on a relatively short scale, to a long-range spin accumulation decaying only via inelastic scattering. This effect enables…
We study coherent current states in the mesoscopic superconducting weak link simultaneously subjected to the order parameter phase difference on the contact and to the tangential to the junction interface superfluid velocity in the banks. The Josephson current-phase relation controlled by the external transport current is obtained. At phase difference close to pi the nonlocal nature of the Josephson phase-dependent current results in the appearance of two vortexlike states in the vicinity of the contact.
The Ginzburg-Landau theory is used to model the order parameter of a finite-size mesoscopic ring to investigate the effects of the onset of screening currents on the transport of incoming ones. The magnetic flux breaks the symmetry of currents between input and output stubs by means of an induced spatial ordering upon diamagnetic and paramagnetic supercurrents circulating in the ring. The distribution of those screening currents drives the interference of incoming/outgoing supercurrents resulting into a sinusoidal variation of resistance as a function of the magnetic flux even if the density o…
We study Josephson effect in a ballistic graphene strip of length $L$ smaller than the superconducting coherence length and arbitrary width $W$. We find that the dependence of the critical supercurrent $I_{c}$ on $W$ is drastically different for different types of the edges. For \textit{smooth} and \textit{armchair} edges at low concentration of the carriers $I_{c}$ decreases monotonically with decreasing $W/L$ and tends to a constant minimum for a narrow strip $W/L\lesssim1$. The minimum supercurrent is zero for smooth edges but has a finite value $eΔ_{0}/\hbar$ for the armchair edges. At hig…
We present magnetization measurements of mesoscopic superconducting niobium loops containing a ferromagnetic (PdNi) pi-junction. The loops are prepared on top of the active area of a micro Hall-sensor based on high mobility GaAs/AlGaAs heterostructures. We observe asymmetric switching of the loop between different magnetization states when reversing the sweep direction of the magnetic field. This provides evidence for a spontaneous current induced by the intrinsic phase shift of the pi-junction. In addition, the presence of the spontaneous current near zero applied field is directly revealed b…
We report for the first time enhancement of the supercurrent by means of injection in a mesoscopic three terminal planar SNSNS device made of Al on GaAs. When a current is injected from one of the superconducting Al electrodes at an injection bias $V=Δ(T)/e$, the DC Josephson current between the other two superconducting electrodes has a maximum, giving evidence for an enhancement due to a non-equilibrium injection into bound Andreev states of the underlying semiconductor. The effect persists to temperatures where the equilibrium supercurrent has vanished.
We examine the thermopower Q of a mesoscopic normal-metal (N) wire in contact to superconducting (S) segments and show that even with electron-hole symmetry, Q may become finite due to the presence of supercurrents. Moreover, we show how the dominant part of Q can be directly related to the equilibrium supercurrents in the structure. In general, a finite thermopower appears both between the N reservoirs and the superconductors, and between the N reservoirs themselves. The latter, however, strongly depends on the geometrical symmetry of the structure.
Mesoscopic superconducting-normal-metal-superconducting (S-N-S) junctions with a large separation between the superconducting electrodes (i.e. wide junctions) exhibit nonequilibrium supercurrents, even at temperatures for which the equilibrium Josephson effect is exponentially small. The second harmonic of the Josephson frequency dominates these currents, as observed in recent experiments. A simple description of these effects, in the spirit of the Resistively-Shunted-Junction model, is suggested here. It is used to calculate dc I-V characteristics, and to examine the effects of various types …
We show that at zero temperature the supercurrent through the superconductor - ferromagnetic metal - superconductor junctions does not decay exponentially with the thickness $L$ of the junction. At large $L$ it has a random sample-specific sign which can change with a change in temperature. In the case of mesoscopic junctions the phase of the order parameter in the ground state is a random sample-specific quantity. In the case of junctions of large area the ground state phase difference is $\pm π/2$.
We consider the charge and spin effects in low dimensional superconducting weak links. The first part of the review deals with the effects of electron-electron interaction in Superconductor/Luttinger liquid/Superconductor junctions. The experimental realization of this mesoscopic hybrid system can be the individual single wall carbon nanotube that bridges the gap between two bulk superconductors. The dc Josephson current through a Luttinger liquid in the limits of perfectly and poorly transmitting junctions is evaluated. The relationship between the Josephson effect in a long SNS junction and …
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…
In a mesoscopic superconductor - normal metal - superconductor (SNS) heterostructure the quasiparticle distribution can be driven far from equilibrium by a voltage applied across the normal metal. This reduces the supercurrent between the superconducting electrodes, which creates the possibility to use these SNS junctions as fast switches and transistors. We describe the system in the framework of the quasiclassical theory and find good agreement with recent experiments. We propose further experimental tests, for instance the voltage-dependence of the current-phase-relation, which includes a t…
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…
Within the framework of the generalized time-dependent Ginzburg-Landau equations, we studied the influence of the magnetic self-field induced by the currents inside a superconducting sample driven by an applied transport current. The numerical simulations of the resistive state of the system show that neither material inhomogeneity nor a normal contact smaller than the sample width are required to produce an inhomogeneous current distribution inside the sample, which leads to the emergence of a kinematic vortex-antivortex pair (vortex street) solution. Further, we discuss the behaviors of the …
We report on the fabrication and characterization of a two-terminal mesoscopic interferometer based on three V/Cu/V Josephson junctions having nanoscale cross-section. The junctions have been arranged in a double-ring geometry realized by metallic thin film deposition through a suspended mask defined by electron beam lithography. Although a significant amount of asymmetry between the critical current of each junction is observed we show that the interferometer is able to suppress the supercurrent to a level lower than 6 parts per thousand, being here limited by measurement resolution. The pres…
We consider mesoscopic four-terminal Josephson junctions and study emergent topological properties of the Andreev subgap bands. We use symmetry-constrained analysis for Wigner-Dyson classes of scattering matrices to derive band dispersions. When scattering matrix of the normal region connecting superconducting leads is energy-independent, the determinant formula for Andreev spectrum can be reduced to a palindromic equation that admits a complete analytical solution. Band topology manifests with an appearance of the Weyl nodes which serve as monopoles of finite Berry curvature. The correspondin…
We analysed the electron-hole or, in another words, branch imbalance (BI) and the related electric potential $V_{imb}$ which may arise in a mesoscopic superconductor/normal metal (S/N) structure under non-equilibrium conditions in the presence of a supercurrent. Non-equilibrium conditions can be created in different ways: a) a quasiparticle current flowing between the N reservoirs; b) a temperature gradient between the N reservoirs and no quasiparticle current. It is shown that the voltage $V_{imb}$ oscillates with the phase difference $ϕ$. In a cross-geometry structure the voltage $V_{imb}$ a…
A Josephson diode is a non-reciprocal circuit element that supports a larger dissipationless supercurrent in one direction than in the other. In this work, we propose and theoretically study a class of Josephson diodes based on supercurrent interferometers containing mesoscopic Josephson junctions, such as point contacts or quantum dots, which are not diodes themselves but possess non-sinusoidal current-phase relations. We show that such Josephson diodes have several important advantages, like being electrically tunable and requiring neither Zeeman splitting nor spin-orbit coupling, only time-…
In the new van der Waals Kondo-lattice Fe$_3$GeTe$_2$, itinerant ferromagnetism and heavy fermionic behaviour coexist. Both the key properties of such a system namely a spin-polarized Fermi surface and a low Fermi momentum are expected to significantly alter Andreev reflection dominated transport at a contact with a superconducting electrode, and display unconventional proximity-induced superconductivity. We observed interplay between Andreev reflection and Kondo resonance at mesoscopic interfaces between superconducting Nb and Fe$_3$GeTe$_2$. Above the critical temperature ($T_c$) of Nb, the …
New vortex solutions to the Landau-Ginzburg equations are described. These configurations, which extend the well known Abrikosov and giant magnetic vortex ones, consist of a succession of ring-like supercurrent vortices organised in a concentric pattern, possibly bound to a giant magnetic vortex then lying at their center. The dynamical and thermodynamic stability of these annular vortices is an important open issue on which hinges the direct experimental observation of such configurations. Nevertheless, annular vortices should affect indirectly specific dynamic properties of mesoscopic superc…
We analyze an interplay between the proximity effect and quantum interference of electrons in hybrid structures superconductor-normal metal-superconductor which contain several insulating barriers. We demonstrate that the dc Josephson current in these structures may change qualitatively due to quantum interference of electrons scattered at different interfaces. In junctions with few conducting channels mesoscopic fluctuations of the supercurrent are significant and its amplitude can be strongly enhanced due to resonant effects. In the many channel limit averaging over the scattering phase effe…
The Josephson effect is a fundamental quantum phenomenon consisting in the appearance of a dissipationless supercurrent in a weak link between two superconducting (S) electrodes. While the mechanism leading to the Josephson effect is quite general, i.e., Andreev reflections at the interface between the S electrodes and the weak link, the precise physical details and topology of the junction drastically modify the properties of the supercurrent. Specifically, a strong enhancement of the critical supercurrent $I_C$ is expected to occur when the topology of the junction allows the emergence of Ma…
We investigate nonlocal coherent transport in ballistic four-terminal Josephson structures (where bulk superconductors (terminals) are connected through a clean normal layer, e.g., a two-dimensional electron gas). Coherent anisotropic superposition of macroscopic wave functions of the superconductors in the normal region produces phase slip lines (2D analogs to phase slip centres) and time-reversal symmetry breaking 2D vortex states in it, as well as such effects as phase dragging and magnetic flux transfer. The tunneling density of local Andreev states in the normal layer was shown to contain…
We study theoretically the Josephson current-phase relationship in a chaotic quantum dot coupled to superconductors by ballistic contacts. In this regime, strong proximity effect induces superconductivity in the quantum dot that leads to a significant modification in the electron density of states and formation of multiple sub-gaps. The magnitude of the resulting supercurrent depends on the phase difference of the superconducting order parameter in the leads and shows strongly anharmonic skewed behavior. We find that when the Thouless energy on the dot exceeds the superconducting energy gap, t…
The distinctive quasiparticle distribution existing under nonequilibrium in a superconductor-insulator-normal metal-insulator-superconductor (SINIS) mesoscopic line is proposed as a novel tool to control the supercurrent intensity in a long Josephson weak link. We present a description of this system in the framework of the diffusive-limit quasiclassical Green-function theory and take into account the effects of inelastic scattering with arbitrary strength. Supercurrent enhancement and suppression, including a marked transition to a $π$-junction are striking features leading to a fully tunable…
The iron-chalcogenide high temperature superconductor Fe(Se,Te) (FST) has been reported to exhibit complex magnetic ordering and nontrivial band topology which may lead to novel superconducting phenomena. However, the recent studies have so far been largely concentrated on its band and spin structures while its mesoscopic electronic and magnetic response, crucial for future device applications, has not been explored experimentally. Here, we used scanning superconducting quantum interference device microscopy for its sensitivity to both local diamagnetic susceptibility and current distribution …
A nondissipative supercurrent state of a Josephson junction is metastable with respect to the formation of a finite-resistance state. This transition is driven by fluctuations, thermal at high temperatures and quantum at low temperatures. We evaluate the life time of such a state due to quantum fluctuations in the limit when the supercurrent is approaching the critical current. The decay probability is determined by the instanton action for the superconducting phase difference across the junction. At low temperatures, dynamics of the phase is massive and is determined by the effective capacita…
We report on the fabrication and measurements of planar mesoscopic Josephson junctions formed by InAs nanowires coupled to superconducting Nb terminals. The use of Si-doped InAs-nanowires with different bulk carrier concentrations allowed to tune the properties of the junctions. We have studied the junction characteristics as a function of temperature, gate voltage, and magnetic field. In junctions with high doping concentrations in the nanowire Josephson supercurrent values up to 100\,nA are found. Owing to the use of Nb as superconductor the Josephson coupling persists at temperatures up to …
We examine the thermopower Q of a mesoscopic normal-metal (N) wire in contact to superconducting (S) segments and show that even with electron-hole symmetry, Q may become finite due to the presence of supercurrents. Moreover, we show how the dominant part of Q can be directly related to the equilibrium supercurrents in the structure. We also discuss the thermopower arising due to an anomalous kinetic coefficient which is finite in the presence of supercurrent and in some situations gives the dominant contribution. In general, a finite thermopower appears both between the N reservoirs and the s…
The macroscopic quantum interference effects in ballistic Josephson microstructures are investigated. The studied system consists of four bulk superconductors (terminals) which are weakly coupled through the mesoscopic rectangular normal metal (two dimensional electron gas). We show that nonlocal electrodynamics of ballistic systems leads to specific current-phase relations for the mesoscopic multiterminal Josephson junction. The nonlocal coupling of supercurrents produces the "dragging" effect for phases of the superconducting order parameter in different terminals. The composite Josephson ju…
It was recently demonstrated the possibility to tune, through the application of a control gate voltage, the superconducting properties of mesoscopic devices based on Bardeen-Cooper-Schrieffer metals. In spite of the several experimental evidence obtained on different materials and geometries, a description of the microscopic mechanism at the basis of such unconventional effect has not been provided yet. This work discusses the technological potential of gate control of superconductivity in metallic superconductors and revises the experimental results which provide information regarding a poss…
We study fractional Josephson effect in a particle-number conserving system consisting of a quasi-one-dimensional superconductor coupled to a nanowire or an edge carrying $e/m$ fractional charge excitations with $m$ being an odd integer. We show that, due to the topological ground-state degeneracy in the system, the periodicity of the supercurrent on magnetic flux through the superconducting loop is non-trivial which provides a possibility to detect topological phases of matter by the $dc$ supercurrent measurement. Using a microscopic model for the nanowire and quasi-one-dimensional supercondu…
For a general model of a mesoscopic multi-level quantum dot, we determine the necessary conditions for the existence of an anomalous Josephson current with spontaneously broken time-reversal symmetry. They correspond to a finite spin-orbit coupling, a suitably oriented Zeeman field, and the dot being a chiral conductor. We provide analytical expressions for the anomalous supercurrent covering a wide parameter regime.
Graphene-based Josephson junctions provide a novel platform for studying the proximity effect due to graphene's unique electronic spectrum and the possibility to tune junction properties by gate voltage. Here we describe graphene junctions with a mean free path of several micrometres, low contact resistance and large supercurrents. Such devices exhibit pronounced Fabry-Pérot oscillations not only in the normal-state resistance but also in the critical current. The proximity effect is mostly suppressed in magnetic fields below 10mT, showing the conventional Fraunhofer pattern. Unexpectedly, som…
We design magnetic traps for atoms based on the average magnetic field of vortices induced in a type-II superconducting thin film. This magnetic field is the critical ingredient of the demonstrated vortex-based atom traps, which operate without transport current. We use Bean's critical-state method to model the vortex field through mesoscopic supercurrents induced in the thin strip. The resulting inhomogeneous magnetic fields are studied in detail and compared to those generated by multiple normally-conducting wires with transport currents. Various vortex patterns can be obtained by programmin…
Josephson junctions (JJs), where both time-reversal and inversion symmetry are broken, exhibit a phase shift $ϕ_0$ in their current-phase relation. This allows for an anomalous supercurrent to flow in the junction even in the absence of a phase bias between the superconductors. We show that a finite phase shift also manifests in the so-called Andreev interferometers - a device that consists of a mesoscopic conductor coupled to the $ϕ_0$-junction. Due to the proximity effect, the resistance of this conductor is phase-sensitive - it oscillates by varying the phase of the JJ. As a result, the qua…
We theoretically investigate the temperature-to-phase conversion (TPC) process occurring in dc superconducting quantum interferometers based on superconductor--normal metal--superconductor (SNS) mesoscopic Josephson junctions. In particular, we predict the temperature-driven rearrangement of the phase gradients in the interferometer under the fixed constraints of fluxoid quantization and supercurrent conservation. This allows sizeable phase variations across the junctions for suitable structure parameters and temperatures. We show that the TPC can be a basis for sensitive single-photon sensors…
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…
Graphene Josephson diodes from inherent asymmetric disorder
Istituto Nanoscienze–CNR, NEST-Scuola Normale Superiore（意大利国家研究委员会纳米科学研究所，NEST-比萨高等师范学院）；Department of Physics and Astronomy, University of Florence（佛罗伦萨大学物理与天文学系）；CNR-SPIN（意大利国家研究委员会自旋物理学研究所）；Center for Nanotechnology Innovation, Laboratorio NEST, Istituto Italiano di Tecnologia（意大利理工学院NEST实验室纳米技术创新中心）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（国立材料研究所电子与光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（国立材料研究所材料纳米架构研究中心）
Field-controlled breaking and restoration of parity-time symmetry in Josephson interference
Institute of Physics, Academia Sinica（中央研究院物理研究所）；Department of Engineering and System Science, National Tsing Hua University（国立清华大学工程与系统科学系）；Nanoscience and Technology Program, Taiwan International Graduate Program, Academia Sinica（中央研究院台湾国际研究生学院纳米科技计划）；Department of Physics, National Sun Yat-Sen University（国立中山大学物理系）；Program on Key Materials, Academy of Innovative Semiconductor and Sustainable Manufacturing (AISSM), National Cheng Kung University（国立成功大学创新半导体与永续制造学院关键材料计划）；Department of Physics, National Cheng Kung University（国立成功大学物理系）；Taiwan Consortium of Emergent Crystalline Materials (TCECM), National Science and Technology Council（国家科学及技术委员会台湾新兴晶体材料联盟）
