We develop a general microscopic theory of dc Josephson effect in hybrid SNS structures with ballistic electrodes and spin-active NS interfaces. We establish a direct relation between the spectrum of Andreev levels and the Josephson current which contains complete information about non-trivial interplay between Andreev reflection and spin-dependent interface scattering. The system exhibits a rich structure of properties sensitive to spin-dependent barrier transmissions, spin-mixing angles, relative magnetization orientation of interfaces and the kinematic phase of scattered electrons. We analyze the current-phase relations and identify the conditions for the presence of a pi-junction state in the systems under consideration. We also analyze resonant enhancement of the supercurrent in gate-voltage-driven nanojunctions. As compared to the non-magnetic case, this effect can be strongly modified by spin-dependent scattering at NS interfaces.
We discuss how to control dc Josephson current by influencing the structure and nonequilibrium population of Andreev levels via external electrostatic gates, external current injection and electromagnetic radiation. In particular we will consider the "giant" Josephson current in "long" SIS tunnel junctions and the regular and anomalous nonequilibrium Josephson currents in three terminal SNS junctions. We will briefly discuss applications to the Josephson field effect transistor (JOFET) and to the newly invented Josephson interference transistor (JOINT).
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.
Simultaneous breaking of inversion- and time-reversal symmetry in Josephson junction leads to a possible violation of the $I(φ)=-I(-φ)$ equality for the current-phase relation. This is known as anomalous Josephson effect and it produces a phase shift $φ_0$ in sinusoidal current-phase relations. In ballistic Josephson junctions with non-sinusoidal current phase relation the observed phenomenology is much richer, including the supercurrent diode effect and the magnetochiral anisotropy of Josephson inductance. In this work, we present measurements of both effects on arrays of Josephson junctions …
The paper develops the theory of the ballistic SNS sandwich, in which the Josephson effect exists without the proximity effect. The theory takes into account restrictions imposed by the charge conservation law and the incommensurability of the superconducting gap with the Andreev level energy spacing. This resulted in revisions of some conclusions of previous works. In the one-dimensional case the Josephson phase of the ground state of the ballistic SNS sandwich is not necessarily zero but may have any value from 0 to $π$. If this value is $π$ this is a $π$ junction, which was well known befor…
We present simultaneous measurements of Josephson inductance and DC transport characteristics of ballistic Josephson junctions based upon an epitaxial Al-InAs heterostructure. The Josephson inductance at finite current bias directly reveals the current-phase relation. The proximity-induced gap, the critical current and the average value of the transparency $\barτ$ are extracted without need for phase bias, demonstrating, e.g.,~a near-unity value of $\barτ=0.94$. Our method allows us to probe the devices deeply in the non-dissipative regime, where ordinary transport measurements are featureless…
We discuss how complex-oxide heterostructures that include high-Tc superconducting cuprates can be used to realize an array of sub-millimeter cavities that support Josephson plasmon polaritons. These cavities have several attractive features for new types of light matter interaction studies and we show that they promote "ultrastrong" coupling between THz frequency radiation and Josephson plasmons. Cavity electrodynamics of Josephson plasmons allows to manipulate the superconducting order-parameter phase coherence. As an example, we discuss how it could be used to cool superconducting phase flu…
We analyze the dc Josephson effect in a ballistic superconductor/half-metal/superconductor junction by means of the Bogoliubov de Gennes equations. We study the role of spin-active interfaces and compare how different superconductor symmetries, including d-wave pairing, affect the Josephson current. We analyze the critical current as a function of junction width, temperature, and spin-flip strength and direction. In particular, we demonstrate that the temperature dependence of the supercurrent in the dxy symmetry case differs qualitatively from the s and dx2-y2 symmetries. Moreover, we have de…
We study the nonequilibrium Josephson current in a long two-dimensional ballistic SNS-junction with a normal reservoir coupled to the normal part of the junction. The current for a given superconducting phase difference $ϕ$ oscillates as a function of voltage applied between the normal reservoir and the SNS-junction. The period of the oscillations is $π\hbar v_F/L$, with $L$ the length of the junction, and the amplitude of the oscillations decays as $V^{-3/2}$ for $eV \gg \hbar v_{F}/L$ and zero temperature. The critical current $I_c$ shows a similar oscillating, decaying behavior as a functio…
We investigate Josephson junctions among conventional superconducting wires, in the presence of externally applied Zeeman fields and supercurrents. We demonstrate that the critical Josephson current and the current-phase relation of the junction depends on the relative orientation of the applied Zeeman fields and supercurrents. The controllability of the Josephson current relies on the stabilization of conventional superconductivity in high magnetic fields, due to the restoration of the opposite momentum opposite spin projection resonance at the Fermi level. We assert that our results can lead…
We study Andreev reflection and the Josephson effect in a ballistic monolayer of black phosphorous, known as phosphorene. Due to the anisotropic band structure of this system, the supercurrent changes with an order of magnitude when comparing tunneling along two perpendicular directions in the monolayer. We show that the main reason for this effect is a large difference in the number of transverse modes in Andreev bound states. The oscillatory behavior of the supercurrent as a function of the length and chemical potential of the junction also differs substantially depending on the orientation …
We present a detailed study of nonequilibrium Josephson currents and conductance in ballistic multiterminal SNS-devices. Nonequilibrium is created by means of quasiparticle injection from a normal reservoir connected to the normal part of the junction. By applying a voltage at the normal reservoir the Josephson current can be suppressed or the direction of the current can be reversed. For a junction longer than the thermal length, $L\ggξ_T$, the nonequilibrium current increases linearly with applied voltage, saturating at a value equal to the equilibrium current of a short junction. The conduc…
The stationary Josephson effect is studied theoretically in the situation when there is externally injected transport supercurrent which flows in the banks parallel to the contact interface. Coexistence of this supercurrent with the order parameter phase difference between the banks of the contact results in the appearance of quasiparticles in the weak link, which create the current, localized in the vicinity of the contact and counter-flowing to the transport supercurrent. We review the results of our previous study of weak links between current-carrying conventional and unconventional (d-wav…
We theoretically analyze non-local effects in electron transport across three-terminal ballistic normal-superconducting-normal (NSN) structures with spin-active interfaces. Subgap electrons entering S-electrode from one N-metal may form Cooper pairs with their counterparts penetrating from another N-metal. This phenomenon of crossed Andreev reflection is highly sensitive to electron spins and yields a rich variety of properties of non-local conductance which we describe non-perturbatively at arbitrary interface transmissions, voltages and temperatures. Our results can be applied to hybrid stru…
The microscopic theory of current carrying states in the ballistic superconducting microchannel is presented. The effects of the contact length L on the Josephson current are investigated. For the temperatures T close to the critical temperature T_c the problem is treated selfconsistently, with taking into account the distribution of the order parameter $Δ(r)$ inside the contact. The closed integral equation for $Δ$ in strongly inhomogeneous microcontact geometry ($L\lesssim ξ_{0}, ξ_{0}$ is the coherence length at T=0) replaces the differential Ginzburg-Landau equation. The critical current $…
We study quantum transport in ballistic $s_\pm$-wave superconductors where coupling between the two bands is included, and apply our model to three possible probes for detecting the internal phase shift of such a pairing state: tunneling spectroscopy in a N$|s_\pm$-wave junction, crossed Andreev reflection in a two-lead N$|s_\pm$-wave$|$N system, and Josephson current in a s-wave$|$I$|s_\pm$-wave Josephson junction. Whereas the first two probes are insensitive to the superconducting phase in the absence of interband coupling, the Josephson effect is intrinsically phase-dependent, and is moreov…
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…
We investigate a Josephson junction in an electron-hole superfluid in a double layer TMD heterostructure. Observation of a critical tunneling current is a clear signature of superfluidity. In addition, we find the BCS-BEC crossover physics in the narrow barrier region controls the critical current across the entire system. The corresponding critical velocity, which is measurable in this system, has a maximum when the excitations pass from bosonic to fermionic. Remarkably, this occurs for the density at the boundary of the BEC to BCS-BEC crossover regime determined from the condensate fraction.…
We develop a detailed microscopic theory describing dc Josephson effect and Andreev bound states in superconducting junctions with a half-metal. In such systems the supercurrent is caused by triplet pairing states emerging due to spin-flip scattering at the interfaces between superconducting electrodes and the half-metal. For sufficiently clean metals we provide a detailed non-perturbative description of the Josephson current at arbitrary transmissions and spin-flip scattering parameters for both interfaces. Our analysis demonstrates that the behavior of both the Josephson current and Andreev …
We calculate the phase, the temperature and the junction length dependence of the supercurrent for ballistic graphene Josephson-junctions. For low temperatures we find non-sinusoidal dependence of the supercurrent on the superconductor phase difference for both short and long junctions. The skewness, which characterizes the deviation of the current-phase relation from a simple sinusoidal one, shows a linear dependence on the critical current for small currents. We discuss the similarities and differences with respect to the classical theory of Josephson junctions, where the weak link is formed…
We present fully self-consistent calculations of the thermodynamic properties of three-dimensional clean SNS Josephson junctions, where S is an s-wave short-coherence-length superconductor and N is a clean normal metal. The junction is modeled on an infinite cubic lattice such that the transverse width of the S is the same as that of the N, and its thickness is tuned from the short to long limit. Both the reduced order parameter near the SN boundary and the short coherence length depress the critical Josephson current $I_c$, even in short junctions. This is contrasted with recent measurements …
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 demonstrate long-range superconducting correlations in a several micrometer-long carbon nanotube encapsulated in a van der Waals stack between hBN and NbSe$_2$. We show that a substantial supercurrent flows through the nanotube section beneath the NbSe$_2$ crystal as well as through the 2 $μ$m-long section not in contact with it. As expected for superconductors of nanoscopic cross section, the current-induced breakdown of superconductivity is characterized by resistance steps due to the nucleation of phase slip centers. All elements of our hybrid device are active building blocks of several…
We report a unique experimental approach to create topological superconductors by inducing superconductivity into epitaxial metallic thin film with strong spin-orbit coupling. Utilizing molecular beam epitaxy technique under ultra-high vacuum condition, we are able to achieve (111) oriented single phase of gold (Au) thin film grown on a well-oriented vanadium (V) s-wave superconductor film with clean interface. We obtained atomically smooth Au thin films with thicknesses even down to below a nanometer showing near-ideal surface quality. The as-grown V/Au bilayer heterostructure exhibits superc…
Recently, a quantum anomalous Hall insulator (QAHI)/superconductor heterostructure has been realized and shows half-quantized conductance plateaus in two-terminal conductance measurements [Q. L. He \textit{et al.}, Science {\bf357}, 294 (2017)]. The half-quantized conductance plateaus are considered as a solid evidence of chiral Majorana edge modes. However, there is a strong debate over the origin of the half-quantized conductance plateaus. In this work, we propose a Josephson junction based on the QAHI/superconductor heterostructure to identify the existence of chiral Majorana edge modes. We…
We consider the one-dimensional (1D) topological superconductor that may form in a planar superconductor-metal-superconductor Josephson junction in which the metal is is subjected to spin orbit coupling and to an in-plane magnetic field. This 1D topological superconductor has been the subject of recent theoretical and experimental attention. We examine the effect of perpendicular magnetic field and a supercurrent driven across the junction on the position and structure of the Majorana zero modes that are associated with the topological superconductor. In particular, we show that under certain …
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 …
Highly transmissive ballistic junctions are demonstrated between Nb and the two-dimensional electron gas formed at an InAs/AlSb heterojunction. A reproducible fabrication protocol is presented yielding high critical supercurrent values. Current-voltage characteristics were measured down to 0.4 K and the observed supercurrent behavior was analyzed within a ballistic model in the clean limit. This investigation allows us to demonstrate an intrinsic interface transmissivity approaching 90%. The reproducibility of the fabrication protocol makes it of interest for the experimental study of InAs-bas…
We study a Josephson junction made with a spin-textured bridge, when both Rashba and Zeeman interactions combine to generate a magneto-electric coupling between the superconducting current and the in-plane magnetic texture in the normal region. In particular, we unambiguously obtain the so-called anomalous current-phase relation $j=j_{c}\sinφ+j_{a}\cosφ$ in a two-dimensional ballistic Josephson junction close to the critical temperature of the heterostructure, when an anomalous current $j_{a}\neq0$ subsists even at zero phase-difference between the superconductors, and is responsible for the c…
Josephson junctions with graphene as the weak link between superconductors have been intensely studied in recent years, with respect to both fundamental physics and potential applications. However, most of the previous work was based on mechanically exfoliated graphene, which is not compatible with mass production. Here we present our research using graphene grown by chemical vapour deposition (CVD) as the weak link of Josephson junctions. We demonstrate that CVD-graphene-based Josephson junctions with Nb electrodes can work effectively without any thermal hysteresis from 1.5 K down to a base …
Utilizing a full microscopic Bogoliubov-de Gennes (BdG) approach, we study the equilibrium charge and spin currents in ballistic $SFSFS$ Josephson systems, where $F$ is a uniformly magnetized ferromagnet and $S$ is a conventional $s$-wave superconductor. From the spatially varying spin currents, we also calculate the associated equilibrium spin transfer torques. Through variations in the relative phase differences between the three $S$ regions, and magnetization orientations of the ferromagnets, our study demonstrates tunability and controllability of the spin and charge supercurrents. The spi…
We present an experimental and theoretical investigation of coherent current transport in wide ballistic superconductor-two dimensional electron gas-superconductor junctions. It is found experimentally that upon increasing the junction length, the subharmonic gap structure in the current-voltage characteristics is shifted to lower voltages, and the excess current at voltages much larger than the superconducting gap decreases. Applying a theory of coherent multiple Andreev reflection, we show that these observations can be explained in terms of transport through Andreev resonances.
The magneto-electrostatic tailoring of the supercurrent in quantum point contact ballistic Josephson junctions is demonstrated. An etched InAs-based heterostructure is laterally contacted to superconducting niobium leads and the existence of two etched side gates permits, in combination with the application of a perpendicular magnetic field, to modify continuously the magnetic interference pattern by depleting the weak link. For wider junctions the supercurrent presents a Fraunhofer-like interference pattern with periodicity h/2e whereas by shrinking electrostatically the weak link, the period…
We study the proximity effect in superconductor (S), antiferromagnetic (AF) bilayers, and report the fabrication and measurement of the first trilayer S/AF/S Josephson junctions. The disordered f.c.c. alloy γ-Fe50Mn50 was used as the AF, and the S is Nb. Micron and sub-micron scale junctions were measured, and the scaling of $J_C (d_AF)$ gives a coherence length in the AF of 2.4 nm, which correlates with the coherence length due to suppression of $T_C$ in the bilayer samples. The diffusion constant for FeMn was found to be 1.7 \times 10$^{-4}$ m$^2$ s$^-1$, and the density of states at the Fer…
We fabricate Josephson field-effect-transistors in germanium quantum wells contacted by superconducting aluminum and demonstrate supercurrents carried by holes that extend over junction lengths of several micrometers. In superconducting quantum point contacts we observe discretization of supercurrent, as well as Fabry-Perot resonances, demonstrating ballistic transport. The magnetic field dependence of the supercurrent follows a clear Fraunhofer-like pattern and Shapiro steps appear upon microwave irradiation. Multiple Andreev reflections give rise to conductance enhancement and evidence a tra…
Edge-contacted superconductor-graphene-superconductor Josephson junction have been utilized to realize topological superconductivity, which have shown superconducting signatures in the quantum Hall regime. We perform the first-principles calculations to interpret electronic couplings at the superconductor-graphene edge contacts by investigating various aspects in hybridization of molybdenum d orbitals and graphene $π$ orbitals. We also reveal that interfacial oxygen defects play an important role in determining the doping type of graphene near the interface.
We solve the Dirac-Bogoliubov-De-Gennes equation in an impurity-free superconductor-normal-superconductor (SNS) junction, to determine the maximal supercurrent that can flow through an undoped strip of graphene with heavily doped superconducting electrodes. The result is determined by the superconducting gap and by the aspect ratio of the junction (length L, small relative to the width W and to the superconducting coherence length). Moving away from the Dirac point of zero doping, we recover the usual ballistic result in which the Fermi wave length takes over from L. The product of critical cu…
Motivated by a recent experiment directly measuring the current-phase relation (CPR) in graphene under the influence of a superconducting proximity effect, we here study the temperature dependence of the CPR in ballistic graphene SNS Josephson junctions within the the self-consistent tight-binding Bogoliubov-de Gennes (BdG) formalism. By comparing these results with the standard Dirac-BdG method, where rigid boundary conditions are assumed at the SN interfaces, we show on a crucial importance of both proximity effect and depairing by current for the CPR. The proximity effect grows with tempera…
The Josephson effect in ballistic point contacts between single-band and multi-band superconductors was investigated. It was found that in the case of Josephson junctions formed by a single-band and an $s_\pm$-wave two-band superconductor as well as by a single-band and a three-band superconductor the junctions become frustrated, demonstrating the $ϕ$-contact properties. Depending on the ground state of a three-band superconductor with broken time-reversal symmetry (BTRS), the Josephson junction can have from one to three energy minima, some of which can be locally stable. We also study the be…
We consider the steady-state nonequilibrium behavior of mesoscopic superconducting wires connected to normal-metal reservoirs. Going beyond the diffusive limit, we utilize the quasiclassical theory and perform a self-consistent calculation that guarantees current conservation through the entire system. Going from the ballistic to the diffusive limit, we investigate several crucial phenomena such as charge imbalance, momentum-resolved nonequilbrium distributions, and the current-to-superflow conversion. Connecting to earlier results for the diffusive case, we find that superconductivity can bre…
A Josephson junction made of a generic magnetic material sandwiched between two conventional superconductors is studied in the ballistic semi-classic limit. The spectrum of Andreev bound states is obtained from the single-valuedness of a particle-hole spinor over closed orbits generated by electron-hole reflections at the interfaces between superconducting and normal materials. The semiclassical quantization condition is shown to depend only on the angle mismatch between initial and final spin directions along such closed trajectories. For the demonstration, an Andreev-Wilson loop in the compo…
Ballistic Josephson junctions are studied in the presence of a spin-splitting field and spin-orbit coupling. A generic expression for the quasi-classical Green's function is obtained and with its help we analyze several aspects of the proximity effect between a spin-textured normal metal (N) and singlet superconductors (S). In particular, we show that the density of states may show a zero-energy peak which is a generic consequence of the spin-dependent couplings in heterostructures. In addition we also obtain the spin current and the induced magnetic moment in a SNS structure and discuss possi…
Short ballistic graphene Josephson junctions sustain superconducting current with a non-sinusoidal current-phase relation up to a critical current threshold. The current-phase relation, arising from proximitized superconductivity, is gate-voltage tunable and exhibits peculiar skewness observed in high quality graphene superconductors heterostructures with clean interfaces. These properties make graphene Josephson junctions promising sensitive quantum probes of microscopic fluctuations underlying transport in two-dimensions. We show that the power spectrum of the critical current fluctuations h…
Graphene is a relatively new material (2004) made of atomic layers of carbon arranged in a honeycomb lattice. Josephson junction devices are made from graphene by depositing two parallel superconducting leads on a graphene flake. These devices have hysteretic current-voltage characteristics with a supercurrent branch and Shapiro steps appear when irradiated with microwaves. These properties motivate us to investigate the presence of quantum metastable states similar to those found in conventional current-biased Josephson junctions. We present work investigating the nature of these metastable s…
$ $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…
Revisiting the adiabatic limit in ballistic multiterminal Josephson junctions
Université Grenoble-Alpes, CNRS, Grenoble INP, Institut NEEL（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、格勒诺布尔理工学院、NEEL研究所）；The Pennsylvania State University（宾夕法尼亚州立大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）
Measurement of multiple Andreev reflection (MAR) in a Josephson junction made from an InAs heterostructure with epitaxial aluminum is used to quantify the highly transparent semiconductor-superconductor interface, indicating near-unity transmission. The observed temperature dependence of MAR does not follow a conventional BCS form, but instead agrees with a model in which the density of states in the quantum well acquires an effective induced gap, in our case 180 μeV, close to that of the epitaxial superconductor. Carrier density dependence of MAR is investigated using a depletion gate, reveal…
We investigate transport properties of ballistic magnetic Josephson junctions and establish that suppression of supercurrent is an intrinsic property of the junctions, even in absence of disorder. By studying the role of ferromagnet thickness, magnetization, and crystal orientation we show how the supercurrent decays exponentially with thickness and identify two mechanisms responsible for the effect: (i) large exchange splitting may gap out minority or majority carriers leading to the suppression of Andreev reflection in the junction, (ii) loss of synchronization between different modes due to…
The superconducting proximity effect in semiconductor nanowires has recently enabled the study of new superconducting architectures, such as gate-tunable superconducting qubits and multiterminal Josephson junctions. As opposed to their metallic counterparts, the electron density in semiconductor nanosystems is tunable by external electrostatic gates providing a highly scalable and in-situ variation of the device properties. In addition, semiconductors with large $g$-factor and spin-orbit coupling have been shown to give rise to exotic phenomena in superconductivity, such as $φ_0$ Josephson jun…
We combine electron beam lithography and masked anodization of epitaxial aluminium to define tunnel junctions via selective oxidation, alleviating the need for wet-etch processing or direct deposition of dielectric materials. Applying this technique to define Josephson junctions in proximity induced superconducting Al-InAs heterostructures, we observe multiple Andreev reflections in transport experiments, indicative of a high quality junction. We further compare the mobility and density of Hall-bars defined via wet etching and anodization. These results may find utility in uncovering new fabri…
Specific features of the equilibrium current-carrying state of a Josephson tunnel junction between diffusive superconductors are studied theoretically in the 1D geometry. It is found that the Josephson current induces localized states of electron excitations in the vicinity of the tunnel barrier, which are a continuous analog of Andreev levels in a ballistic junction. The depth of the corresponding ``potential well'' is much greater than the separation between an Andreev level and the continuous energy spectrum boundary for the same transmissivity of the barrier. In contrast to a ballistic jun…
