In superconductor-normal-superconductor (SNS) junctions, dissipationless supercurrent is mediated via Andreev bound states (ABSs) controlled by the phase difference between the two superconductors. Theory has long predicted significant fluctuations, and thus a noise, of such supercurrent in equilibrium, due to the thermal excitation between the ABSs. Via the fluctuation-dissipation theorem (FDT), this leads paradoxically to a dissipative conductance even in the zero frequency limit. In this article, we directly measure the supercurrent noise in a phase-biased SNS ring inductively coupled to a superconducting resonator. Using the same setup, we also measure its admittance and quantitatively demonstrate the FDT for any phase. The dissipative conductance shows an 1/T temperature dependence, in contrast to the Drude conductance of unproximitized metal. This is true even at phase $π$ where the Andreev spectrum is gapless. Supported by linear response theory, we attribute this to the enhanced current correlation between the ABSs symmetrical across the Fermi level. Our results provide insight into the origin of noise in hydrid superconducting devices which may be useful for probing topologically protected ABSs.
We investigate the spin-flip effects on the Andreev bound states and the supercurrent in a superconductor/quantum-dot/superconductor system theoretically. The spin-flip scattering in the quantum dot can reverse the supercurrent flowing through the system, and one $π$-junction transition occurs. By controlling the energy level of quantum dot, the supercurrent is reversed back and another $π$-junction transition appears. The different influences of the spin-flip scattering and the intradot energy level on the supercurrent are interpreted in the picture of Andreev bound states.
We present an analytical result for the supercurrent across a superconductor/quantum-dot/superconductor junction. By converting the current integration into a special contour integral, we can express the current as a sum of the residues of poles. These poles are real and give a natural definition of the Andreev bound states. We also use the exact result to explain some features of the supercurrent transport behavior.
We analyze the transport through a narrow ballistic superconductor-normal- metal-superconductor Josephson contact with non-ideal transmission at the superconductor-normal-metal interfaces, e.g., due to insulating layers, effective mass steps, or band misfits (SIN interfaces). The electronic spectrum in the normal wire is determined through the combination of Andreev- and normal reflection at the SIN interfaces. Strong normal scattering at the SIN interfaces introduces electron- and hole-like resonances in the normal region which show up in the quasi-particle spectrum. These resonances have str…
We report conductance and supercurrent of InAs nanowires coupled to Al-superconducting electrodes with short channel lengths and good Ohmic contacts. The nanowires are suspended 15\,nm above a local gate electrode. The charge density in the nanowires can be controlled by a small change in the gate voltage. For large negative gate voltages, the number of conducting channels is reduced gradually and we observe a stepwise decrease of both conductance and critical current before the conductance vanishes completely.
We determine the quasi-particle excitation spectrum in the normal region of a narrow ballistic superconductor--normal-metal--superconductor (SNS) Josephson contact. Increasing the effective chemical potential in the contact converts the electronic levels into Andreev-levels carrying supercurrent. The opening of these superchannels leads to a supercurrent quantization which exhibits a non-universal behavior in general and we discuss its dependence on the junction parameters.
In this paper I study the energy resolved supercurrent of a junction consisting of a dirty normal metal between two superconductors. I also consider a cross geometry with two additional arms connecting the above mentioned junction with two normal reservoirs at equal and opposite voltages. The dependence of the supercurrent between the two superconductors on the applied voltages is studied.
We numerically analyze the effect of finite length of the superconducting regions on the low-energy spectrum, current-phase curves, and critical currents in junctions between trivial and topological superconductors. Such junctions are assumed to arise in nanowires with strong spin-orbit coupling under external magnetic fields and proximity-induced superconductivity. We show that all these quantities exhibit a strong dependence on the length of the topological sector in the topological phase and serve as indicators of the topological phase and thus the emergence of Majorana bound states at the …
We investigate transverse charge and spin dc supercurrents in a ferromagnet coupled to a superconductor where the ferromagnet has inhomogeneous magnetic structure. These transverse supercurrents arise from non-trivial structure of the magnetization. The magnetic structure manifested in the transverse charge supercurrent is essentially different from that discussed in the context of anomalous Hall effect, reflecting the disspationless nature of supercurrent. Possible candidates of magnetic structure to verify our prediction are also discussed.
We show that, for a quantum point contact between two superconductors of different gap magnitudes, Andreev bound states do not exist for certain phase differences and gap ratios. Continuum states may dominate the transport, and the supercurrent noise is qualitatively different from the case of equal gaps.
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.
Edge supercurrents in superconductors have long been an elusive target. Interest in them has reappeared in the context of topological superconductivity. We report the observation of a robust edge supercurrent in the Weyl superconductor MoTe2. In a magnetic field B, fluxoid quantization generates a periodic modulation of the edge condensate observable as a "fast-mode" oscillation of the critical current Ic versus B. Remarkably, the fast-mode frequency is distinct from the conventional Fraunhofer oscillation displayed by the bulk supercurrent. We confirm that the fast mode frequency increases wi…
We have measured the tunneling density of states (DOS) in a superconductor carrying a supercurrent or exposed to an external magnetic field. The pair correlations are weakened by the supercurrent, leading to a modification of the DOS and to a reduction of the gap. As predicted by the theory of superconductivity in diffusive metals, we find that this effect is similar to that of an external magnetic field.
We report on an experimental investigation of the combined effect of nonequilibrium quasiparticle injection and supercurrent in superconducting aluminum wires. At low temperature, we observe the supercurrent-induced coupling of energy and charge imbalance with spectral resolution. At high magnetic fields, in the presence of a Zeeman splitting of the density of states, we find evidence for an additional spin-dependent coupling which has been recently predicted theoretically.
We report on the observation of gate-tunable proximity-induced superconductivity and multiple Andreev reflections (MAR) in a bulk-insulating BiSbTeSe$_2$ topological insulator nanoribbon (TINR) Josephson junction (JJ) with superconducting Nb contacts. We observe a gate-tunable critical current ($I_C$) for gate voltages ($V_g$) above the charge neutrality point ($V_{CNP}$), with $I_C$ as large as 430 nA. We also observe MAR peaks in the differential conductance ($dI/dV$) versus DC voltage ($V_{dc}$) across the junction corresponding to sub-harmonic peaks (at $V_{dc} = V_n = 2Δ_{Nb}/en$, where $…
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 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.
We introduce the general formalism to describe spin torques induced by the supercurrents injected from the adjacent superconducting electrodes into the spin-textured ferromagnets. By considering the adiabatic limit for the equal-spin superconducting correlations in the ferromagnet we show that the supercurrent can generate both the field-like spin transfer torque and the spin-orbital torque. These dissipationless spin torques are expressed through the current-induced corrections to the effective field derived from the system energy. The general formalism is applied to show that the supercurren…
Quasiclassical Green's functions of a short superconductor/normal metal/superconductor (SNS) junction are calculated for multi-mode junction with arbitrary electron transmission properties. They provide the basis for description of all of the junction transport characteristics, and are used to calculate the equilibrium spectral density of supercurrent fluctuations.
The local nonequilibrium quasiparticle distribution function in a normal-metal wire depends on the applied voltage over the wire and the type and strength of different scattering mechanisms. We show that in a setup with superconducting reservoirs, in which the supercurrent and the dissipative current flow (anti)parallel, the distribution function can also be tuned by applying a supercurrent between the contacts. Unlike the usual control by voltage or temperature, this leads to a Peltier-like effect: the supercurrent converts an externally applied voltage into a difference in the effective temp…
A junction with two superconductors coupled by a normal metal hosts Andreev bound states whose energy spectrum is phase-dependent and exhibits a minigap, resulting in a periodic supercurrent. Phase-dependent dissipation also appears at finite frequency due to relaxation of Andreev bound states. While dissipation and supercurrent versus phase have previously been measured near thermal equilibrium, their behavior in nonequilibrium is still elusive. By measuring the ac susceptibility of a graphene-superconductor junction under microwave irradiation, we find supercurrent response deviates from adi…
A chiral quantum Hall (QH) edge state placed in proximity to an s-wave superconductor experiences induced superconducting correlations. Recent experiments have observed the effect of proximity-coupling in QH edge states through signatures of the mediating process of Andreev reflection. We present the microscopic theory behind this effect by modeling the system with a many-body Hamiltonian, consisting of an s-wave superconductor, subject to spin-orbit coupling and a magnetic field, which is coupled by electron tunneling to a QH edge state. By integrating out the superconductor we obtain an effe…
Cooper pairs in superconductors are normally spin singlet. Nevertheless, recent studies suggest that spin-triplet Cooper pairs can be created at carefully engineered superconductor-ferromagnet interfaces. If Cooper pairs are spin-polarized they would transport not only charge but also a net spin component, but without dissipation, and therefore minimize the heating effects associated with spintronic devices. Although it is now established that triplet supercurrents exist, their most interesting property - spin - is only inferred indirectly from transport measurements. In conventional spintroni…
Gate-controlled supercurrent (GCS) in superconductor nanobridges has recently attracted attention as a means to create superconducting field effect transistors. Despite the clear advantage for applications with low power consumption and high switching speeds, the microscopic mechanism of the field effect is still under debate. In this work, we realize GCS for the first time in an epitaxial superconductor, which is created as a shell on an InAs nanowire. We show that the supercurrent in the epitaxial Al layer can be switched to the normal state by applying $\simeq\pm$ 23$\,$V on a bottom gate i…
The spin-galvanic (inverse Edelstein) and inverse spin-Hall effects are calculated for a hybrid system that combines thin superconductor and Rashba-metal layers. These effects are produced by a nonequilibrium spin polarization which is injected into the normal metal layer. This polarization gives rise to an electric potential that relaxes within some characteristic length, which is determined by Andreev reflection. Within this length the dissipative electric current of quasiparticles in the normal layer converts into the supercurrent. This process involves only subgap states and at low tempera…
We have generalized a quasiclassical model for Weyl semimetals with a tilted band in the presence of an externally applied magnetic field. This model is applicable to ballistic, moderately disordered, and samples containing a high density of nonmagnetic impurities. We employ this formalism and show that a self-biased supercurrent, creating a ϕ0-junction, can flow through a triplet channel in Weyl semimetals. Furthermore, our results demonstrate that multiple supercurrent reversals are accessible through varying junction thickness and parameters characterizing Weyl semimetals. We discuss the in…
Hybrid superconductor-semiconductor nanowires with Rashba spin-orbit coupling are arguably becoming the leading platform for the search of Majorana bound states (MBSs) in engineered topological superconductors. We perform a systematic numerical study of the low-energy Andreev spectrum and supercurrents in short and long superconductor-normal-superconductor junctions made of nanowires with strong Rashba spin-orbit coupling, where an external Zeeman field is applied perpendicular to the spin-orbit axis. In particular, we investigate the detailed evolution of the Andreev bound states from the tri…
We study the quantization of the supercurrent and conductance of a superconducting quantum point contact (SQPC) in a superconductor-two dimensional electrongas-superconductor (S-2DEG-S) Josephson junction with a split gate. The supercurrent and the conductance values change stepwise as a function of the gate voltage. We observe the onset of the first transport mode contributing both to the supercurrent and the conductance of the SQPC. Furthermore the steps in the supercurrent and the conductance appear at the same gate voltage values. This shows, that each transport mode in the SQPC contribute…
We have studied superconductor/normal metal/superconductor (SNS) junctions consisting of short Au or Cu wires between Nb or Al banks. The Nb based junctions display inherent electron heating effects induced by the high thermal resistance of the NS boundaries. The Al based junctions show in addition subharmonic gap structures in the differential conductance dI/dV and a pronounced peak in the excess noise at very low voltages V. We suggest that the noise peak is caused by fluctuations of the supercurrent at the onset of Josephson coupling between the superconducting banks. At intermediate temper…
The multi-terminal Josephson effect allows DC supercurrent to flow at finite commensurate voltages. Existing proposals to realize this effect rely on nonlocal Andreev processes in superconductor-normal-superconductor junctions. However, this approach requires precise control over microscopic states and is obscured by dissipative current. We show that standard tunnel Josephson circuits also support multiplet supercurrent mediated only by local tunneling processes. Furtheremore, we observe that the supercurrents persist even in the high charging energy regime in which only sequential Cooper tran…
At the interface between a ferromagnetic insulator and a superconductor there is a coupling between the spins of the two materials. We show that when a supercurrent carried by triplet Cooper pairs flows through the superconductor, the coupling induces a magnon spin current in the adjacent ferromagnetic insulator. The effect is dominated by Cooper pairs polarized in the same direction as the ferromagnetic insulator, so that charge and spin supercurrents produce similar results. Our findings demonstrate a way of converting Cooper pair supercurrents to magnon spin currents.
We theoretically study coherent multiple Andreev reflections in a biased three-terminal Josephson junction. We demonstrate that the direct current flowing through the junction consists of supercurrent components when the bias voltages are commensurate. This dissipationless current depends on the phase in the superconducting leads and stems from the Cooper pair transfer processes induced by non-local Andreev reflections of the quasiparticles originating from the superconducting leads. We identify supercurrent-enhanced lines in the current and conductance maps of the recent measurement [Y. Cohen…
A weak parallel Zeeman field combined with the spin-orbit coupling can induce the supercurrent in an s-wave two-dimensional superconductor. At the same time, the thermodynamically equilibrium state of such a system is characterized by the helix phase where the order parameter varies in space as $\exp(i\mathbf{Qr})$. In this state the electric current that is induced by the Zeeman interaction is exactly counterbalanced by the current produced by the gradient of the order-parameter. We studied the interplay of the helix state and magnetoelectric current in the case of a varying in space Zeeman f…
We investigate anomalous Hall effect in a magnet coupled to a triplet superconductor under phase gradient. It is found that the anomalous Hall supercurrent arises from non-trivial structure of the magnetization. The magnetic structure manifested in the Hall supercurrent is characterized by even order terms of the exchange coupling, essentially different from that discussed in the context of anomalous Hall effect, reflecting the disspationless nature of supercurrent. We also discuss a possible candidate for magnetic structure to verify our prediction.
Supercurrent Diode Effect in Josephson Interferometers with Multiband Superconductors
CNR-SPIN（意大利国家研究委员会自旋物理学研究所）；Institute for Theoretical Solid State Physics, Leibniz-Institut für Festkörper- und Werkstoffforschung IFW-Dresden（德累斯顿勒布尼兹固体与材料研究所凝聚态物理理论研究所）；Istituto Lombardo “Accademia di Scienze e Lettere”（伦巴第科学院）；NEST Istituto Nanoscienze-CNR and Scuola Normale Superiore（意大利国家研究委员会纳米科学研究所与比萨高等师范学院）；Universitá di Salerno（萨莱诺大学）
Superconductor-graphene-superconductor (SGS) junction provides a unique platform to study relativistic electrodynamics of Dirac fermions combined with proximity-induced superconductivity. We report observation of the Josephson effect in proximity-coupled superconducting junctions of graphene in contact with Pb1-xInx (x=0.07) electrodes for temperatures as high as T = 4.8K, with a large IcRn (~ 255 microV). This demonstrates that Pb1-xInx SGS junction would facilitate the development of the superconducting quantum information devices and superconductor-enhanced phase-coherent transport of graph…
Using tunneling spectroscopy, we have measured the local electron energy distribution function in the normal part of a superconductor-normal metal-superconductor (SNS) Josephson junction containing an extra lead to a normal reservoir. In the presence of simultaneous supercurrent and injected quasiparticle current, the distribution function exhibits a sharp feature at very low energy. The feature is odd in energy, and odd under reversal of either the supercurrent or the quasiparticle current direction. The feature represents an effective temperature gradient across the SNS Josephson junction th…
We propose a mechanism whereby spin supercurrents can be manipulated in superconductor/ferromagnet proximity systems via nonequilibrium spin injection. We find that if a spin supercurrent exists in equilibrium, a nonequilibrium spin accumulation will exert a torque on the spins transported by this current. This interaction causes a new spin supercurrent contribution to manifest out of equilibrium, which is proportional to and polarized perpendicularly to both the injected spins and equilibrium spin current. This is interesting for several reasons: as a fundamental physical effect; due to possi…
We report the emergence of zero-energy states in the trivial phase of a short nanowire junction with strong spin-orbit coupling and magnetic field, formed by strong coupling between the nanowire and two superconductors. The zero-energy states appear in the junction when the superconductors induce a large energy shift in the nanowire, such that the junction naturally forms a quantum dot, a process that is highly tunable by the superconductor width. Most importantly, we demonstrate that the zero-energy states produce a $π$-shift in the phase-biased supercurrent, which can be used as a simple too…
We study the transport properties of a Josephson junction consisting of two identical $s$-wave superconductors separated by an even-layer ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ (MBT). Using recursive Green's function method, we calculate the supercurrent in the presence of a perpendicular magnetic field and find that its quantum interference exhibits distinct patterns when the MBT is in different magnetic states. In the antiferromagnetic state, the MBT is an axion insulator supporting an extended "hinge" supercurrent, which leads to a sinusoidal interference pattern decaying with the field str…
When superconductivity couples with noncollinear spin textures, rich physics arises; for instance, singlet Cooper pairs can be converted to triplet pairs, and topological superconductors can be realized. For their applications, the controllability of noncollinear magnetism is a crucial issue. Here, we propose that a supercurrent can induce and control noncollinear magnetic orders in a correlated metal on top of a singlet superconductor. We show that the magnetic instability in the correlated metal is enhanced by the proximity effect of supercurrents, which leads to phase transitions from a par…
We show that finite current in superconductors can induce topological phase transitions, as a result of the deformation of the quasiparticle spectrum by a finite center-of-mass (COM) momentum of the Cooper pairs. To show the wide applicability of this mechanism, we examine the topological properties of three prototypical systems, the Kitaev chain, $s$-wave superconductors, and $d$-wave superconductors. We introduce a finite COM momentum as an external field corresponding to supercurrent and show that all the models exhibit current-induced topological phase transitions. We also discuss the poss…
We present a theoretical study of the Josephson coupling of two s-wave superconductors which are connected through a diffusive contact consisting of noncollinear ferromagnetic domains. First, we consider a contact with two domains with magnetization vectors misoriented by an angle $θ$. Using the quantum circuit theory, we find that in addition to the charge supercurrent, a spin supercurrent, which is even in $ϕ$ and odd in $θ$, with a spin polarization normal to the magnetization vectors flows between the domains. Furthermore, with asymmetric insulating barriers at the interfaces of the juncti…
We show that injecting nonequilibrium spins into the superconducting leads strongly enhances the stationary Josephson current through a superconductor-ferromagnet-superconductor junction. The resulting long-range super-current through a ferromagnet is carried by triplet Cooper pairs that are formed in s-wave superconductors by the combined effects of spin injection and exchange interaction. We quantify the exchange interaction in terms of Landau Fermi-liquid factors. The magnitude and direction of the long-range Josephson current can be manipulated by varying the angles of the injected polariz…
Local spins coupled to superconductors give rise to several emerging phenomena directly linked to the competition between Cooper pair formation and magnetic exchange. These effects are generally scrutinized using a spectroscopic approach which relies on detecting the in-gap bound modes arising from Cooper pair breaking, the so-called Yu-Shiba-Rusinov (YSR) states. However, the impact of local magnetic impurities on the superconducting order parameter remains largely unexplored. Here, we use scanning Josephson spectroscopy to directly visualize the effect of magnetic perturbations on Cooper pai…
We report that spin supercurrents in magnetic superconductors and superconductor/ferromagnetic insulator bilayers can induce the Dzyaloshinskii-Moriya interaction which strength is proportional to the superconducting order parameter amplitude. This effect leads to the existence of inhomogeneous parity-breaking ground states combining the chiral magnetic helix and the pair density wave orders. The formation of such states takes place via the penetration of chiral domain walls at the threshold temperature below the superconducting transition. We find regimes with both the single and the re-entra…
