Superconducting quantum interference devices (SQUIDs) that incorporate two superconductor/insulator/superconductor (SIS) Josephson junctions in a closed loop form the core of some of the most sensitive detectors of magnetic and electric fields currently available. SQUIDs in these applications are typically operated with a finite voltage which generates microwave radiation through the ac Josephson effect. This radiation may impact the system being measured. We describe here a SQUID in which the Josephson junctions are formed from strips of normal metal (N) in good electrical contact with the superconductor (S). Such SNS SQUIDs can be operated under a finite voltage bias with performance comparable or potentially better than conventional SIS SQUIDs. However, they also permit a novel mode of operation that is based on the unusual interplay of quasiparticle currents and supercurrents in the normal metal of the Josephson junction. The new method allows measurements of the flux dependence of the critical current of the SNS SQUID without applying a finite voltage bias across the SNS junction, enabling sensitive flux detection without generating microwave radiation.
We study combined interference effects due to the Aharonov-Bohm (AB) and Aharonov-Casher (AC) phases in a Josephson supercurrent of local and nonlocal (split) Cooper pairs. We analyze a junction between two superconductors interconnected through a normal-state nanostructure with either (i) a ring, where single-electron interference is possible, or (ii) two parallel nanowires, where the single-electron interference can be absent, but the cross Andreeev reflection can occur. In the low-transmission regime in both geometries the AB and AC effects can be related to only local or nonlocal Cooper pa…
Motivated by recent experiments on nonlocal transport through multiterminal superconducting hybrid structures, we present self-consistent calculations based on quasiclassical Green's functions for the order parameter, currents and voltages in a system consisting of a diffusive superconductor connected to two normal and one superconducting electrodes. We investigate non-equilibrium effects for different biasing conditions corresponding to measurements of the nonlocal conductance and of the nonlocal resistance. It is shown that while the nonlocal conductance does not change its sign, this change…
Nonlocal entanglement is crucial for quantum information processes. While nonlocal entanglement has been realized for photons, it is much more difficult to demonstrate for electrons. One approach that has been proposed is to use hybrid superconducting/normal-metal devices, where a Cooper pair splits into spin-entangled electrons in two spatially separated normal-metal leads. This process of nonlocal Andreev reflection is predicted to lead to a negative nonlocal resistance and positive current-current correlation. By cross-correlation measurements as well as measurements of the local and nonloc…
Evanescent quasiparticles entering a superconductor and propagating over distances larger than the coherence length give rise to intermediate states induced by double Andreev scattering on disorder.The resulting effective attractive interaction between evanescent quasiparticles is retarded at the extremely slow frequency of the applied bias voltage. The non-BCS out-of-equilibrium mesoscopic condensate is compatible with a recent experiment [S. Russo et al., Phys. Rev. Lett. 95, 027002 (2005)]. Microscopic theory is discussed in the random phase approximation.
Nonlocality is a key feature discriminating quantum and classical physics. Quantum-interference phenomena, such as Young's double slit experiment, are one of the clearest manifestations of nonlocality, recently addressed as $dynamical$ to specify its origin in the quantum equations of motion. It is well known that loss of dynamical nonlocality can occur due to (partial) collapse of the wavefunction due to a measurement, such as which-path detection. However, alternative mechanisms affecting dynamical nonlocality have hardly been considered, although of crucial importance in many schemes for qu…
We examine nonlocal effects between normal-metal gold probes connected by superconducting aluminum. For highly transparent Au/Al interfaces, we find nonlocal voltages that obey a spatial and temperature evolution distinct from the nonequilibrium charge imbalance signals usually found in such systems. These voltages are consistent with the predicted effects of crossed Andreev reflection and elastic cotunneling, effects that involve coherent correlations between spatially separated electrons.
We study Andreev processes and nonlocal transport in a three-terminal graphene-superconductor hybrid system under a quantizing perpendicular magnetic field [G.-H. Lee et al., Nature Phys. 13, 693 (2017)]. We find that the amplitude of the crossed Andreev reflection (CAR) processes crucially depends on the orientation of the lattice. By employing Landauer-Büttiker scattering theory, we find that CAR is generally very small for a zigzag edge, while for an armchair edge it can be larger than the normal transmission, thereby resulting in a negative nonlocal resistance. In the case of an armchair e…
We have studied a Superconducting Quantum Interference SQUID device made from a single layer thin film of superconducting silicon. The superconducting layer is obtained by heavily doping a silicon wafer with boron atoms using the Gas Immersion Laser Doping (GILD) technique. The SQUID device is composed of two nano-bridges (Dayem bridges) in a loop and shows magnetic flux modulation at low temperature and low magnetic field. The overall behavior shows very good agreement with numerical simulations based on the Ginzburg-Landau equations.
We report a new nonlocal effect in vortex matter, where an electric current confined to a small region of a long and sufficiently narrow superconducting wire causes vortex flow at distances hundreds of inter-vortex separations away. The observed remote traffic of vortices is attributed to a very efficient transfer of a local strain through the one-dimensional vortex lattice, even in the presence of disorder. We also observe mesoscopic fluctuations in the nonlocal vortex flow, which arise due to "traffic jams" when vortex arrangements do not match a local geometry of a superconducting channel.
Josephson junctions defined in strong spin orbit semiconductors are highly interesting for the search for topological systems. However, next to topological edge states that emerge in a sufficient magnetic field, trivial edge states can also occur. We study the trivial edge states with superconducting quantum interference measurements on non-topological InAs Josephson junctions. We observe a SQUID pattern, an indication of superconducting edge transport. Also, a remarkable $h/e$ SQUID signal is observed that, as we find, stems from crossed Andreev states.
In this paper, we investigate thermal entanglement in a superconducting-quantum-interference-device qubit coupled to a cavity field. We show that the entanglement can be manipulated by varying temperature and an effective controlling parameter $B$ which depends on the external field and characteristic parameters of the system. We find that there exists a critical value of the controlling parameter $B_c$. Under a fixed temperature, increasing $B$ can increase entanglement in the regime of $B<B_c$, while the entanglement decreases with increasing $B$ in the regime of $B>B_c$.
We study superconducting quantum interference in a Josephson junction linked via edge states in two-dimensional (2D) insulators. We consider two scenarios in which the 2D insulator is either a topological or a trivial insulator supporting one-dimensional (1D) helical or nonhelical edge states, respectively. In equilibrium, we find that the qualitative dependence of critical supercurrent on the flux through the junction is insensitive to the helical nature of the mediating states and can, therefore, not be used to verify the topological features of the underlying insulator. However, upon applyi…
We study the magnetic and superconducting proximity effects in a semiconducting nanowire (NW) attached to superconducting leads and a ferromagnetic insulator (FI). We show that a sizable equilibrium spin polarization arises in the NW due to the interplay between the superconducting correlations and the exchange field in the FI. The resulting magnetization has a nonlocal contribution that spreads in the NW over the superconducting coherence length and is opposite in sign to the local spin polarization induced by the magnetic proximity effect in the normal state. For a Josephson-junction setup, …
We study the interband transport in a superconducting device composed of graphene with EuO-induced exchange interaction. We show that pure crossed Andreev reflection can be generated exclusively without the parasitic local Andreev reflection and elastic cotunnelling over a wide range of bias and Fermi levels in an EuO-graphene/superconductor/EuO-graphene device. The pure non-local conductance exhibits rapid on/off switching and oscillatory behavior when the Fermi levels in the normal and the superconducting leads are varied. The oscillation reflects the quasiparticle propagation in the superco…
Two majorana Fermions (MFs) localized at the two ends of the topological superconducting wire can interfere with each other and form the well known $4π$ Josephson current. We reveal that the density of states (Dos) for the electron part and the hole part also follow a parity correlated $4π$ period oscillation, while the Dos displays a $2π$ period oscillation when two trivial states interfere with each other. Thus, the period of Dos oscillation can be used to distinguish the MFs from the trivial localized states. Interestingly, such phenomena can be directly observed in a short superconducting …
Direct measurement of a $\sin(2φ)$ current phase relation in a graphene superconducting quantum interference device
Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel（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、内耳研究所）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（物质材料研究机构电子光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（物质材料研究机构材料纳米架构研究中心）
Recently, we have proposed the half-Josephson laser (HJL): a device that combines lasing with superconducting leads, providing a locking between the optical phase and the superconducting phase difference between the leads. In this work, we propose and investigate two setups derived from a superconducting quantum interference device (SQUID), where two conventional Josephson junctions are replaced by two HJLs. In the first setup, the HJLs share the same resonant mode, while in the second setup two separate resonant modes of the two lasers are coupled optically. We dub the setup `light-supercondu…
The mechanism of enhanced superconductivity in the one unit-cell (1UC) FeSe film on a SrTiO3 (STO) substrate has stimulated significant research interest but remains elusive. Using low-temperature, voltage-gated Raman spectroscopy and low-temperature valence electron energy loss spectroscopy (VEELS), we characterize the phonon behavior and interfacial charge transfer in single- and few-layer FeSe films on STO. Raman measurements reveal ambipolar softening of the FeSe vibrational modes, mimicking that of the underlying STO substrate. We attribute this behavior to an interfacial coupling effect …
Josephson current of spin-entangled electrons through the two branches of a SQUID-like structure with two quantum dots exhibits a magnetic-flux response different from the conventional Josephson current. Due to their interference, the period of maximum Josephson current changes from $h/2e$ to $h/e$, which can be used for detecting the Cooper-pair splitting efficiency. The nonlocal spin entanglement provides a quantum mechanical functionale for switching on and off this novel Josephson current, and explicitly a switch is formulated by including a pilot junction. It is shown that the device can …
The density of states of proximitized normal nanowires interrupting superconducting rings can be tuned by the magnetic flux piercing the loop. Using these as the contacts of a single-electron transistor allows to control the energetic mirror asymmetry of the conductor, this way introducing rectification properties. In particular, we show that the system works as a diode that rectifies both charge and heat currents and whose polarity can be reversed by the magnetic field and a gate voltage. We emphasize the role of dissipation at the island. The coupling to substrate phonons enhances the effect…
A cross-shaped diffusive system with two superconducting and two normal electrodes is considered. A voltage $eV < Δ$ is applied between the normal leads. Even in the absence of average current through the superconducting electrodes their presence increases the shot noise at the normal electrodes and doubles it in the case of a strong coupling to the superconductors. The nonequilibrium noise at the superconducting electrodes remains finite even in the case of a vanishingly small transport current due to the absence of energy transfer into the superconductors. This noise is suppressed by electro…
We show that in {\em ballistic} mesoscopic SNS junctions the period of critical current vs. magnetic flux dependence (magnetic interference pattern), $I_c(Φ)$, changes {\em continuously and non-monotonically} from $Φ_0$ to $2Φ_0$ as the length-to-width ratio of the junction grows, or temperature drops. In {\em diffusive} mesoscopic junctions the change is even more drastic, with the first zero of $I_c(Φ)$ appearing at $3Φ_0$. The effect is a manifestation of nonlocal relation between the supercurrent density and superfluid velocity in the normal part of the system, with the characteristic scal…
We model a superconducting p-n junction in which the n- and the p-sides are contacted through two optical quantum dots (QDs), each embedded into a photonic nanocavity. Whenever a Cooper pair is transferred from the n-side to the p-side, two photons are emitted. When the two electrons of a Cooper pair are transported through different QDs, polarization-entangled photons are created, provided that the Cooper pairs retain their spin singlet character while being spatially separated on the two QDs. We show that a CHSH Bell-type measurement is able to detect the entanglement of the photons over a b…
We report on an experimental and theoretical study of nonlocal transport in superconductor hybrid structures, where two normal-metal leads are attached to a central superconducting wire. As a function of voltage bias applied to both normal-metal electrodes, we find surprisingly large nonlocal conductance signals, almost of the same magnitude as the local conductance. We demonstrate that these signals are the result of strong heating of the superconducting wire, and that under symmetric bias conditions, heating mimics the effect of Cooper pair splitting.
We report on the fabrication and electrical transport properties of gate-tunable superconducting quantum interference devices (SQUIDs), made of semiconducting PbS nanowire contacted with PbIn superconducting electrodes. Applied with a magnetic field perpendicular to the plane of the nano-hybrid SQUID, periodic oscillations of the critical current due to the flux quantization in SQUID are observed up to T = 4.0 K. Nonsinusoidal current-phase relationship is obtained as a function of temperature and gate voltage, which is consistent with a short and diffusive junction model.
We investigate a superconducting quantum interference device (SQUID) based on carbon nanotubes in a fork geometry [J.-P. Cleuziou {\it et al.}, Nature Nanotechnology {\bf 1}, 53 (2006)], involving tunneling of evanescent quasiparticles through a superconductor over a distance comparable to the superconducting coherence length, with therefore ``non local'' processes generalizing non local Andreev reflection and elastic cotunneling. Non local processes induce a reduction of the critical current and modify the current-phase relation. We discuss arbitrary interface transparencies. Such devices in …
In this paper, we investigate the electronic transport properties of a quantum dot (QD) connected to two ferromagnetic leads and one superconductor lead in the Kondo regime by means of the finite-$U$ slave boson mean field approach and nonequilibrium Green function technique. In this three-terminal hybrid nano-device, we will focus our attention on the joint effects of the Konod correlation, superconducting proximity pairing, and spin polarization of leads. It is found that: the superconducting proximity effect will suppress the linear local conductance (LLC) stemming from the weakened Kondo p…
Starting from the reduced dynamical model of a two-junction quantum interference device, a quantum analog of the system has been exhibited, in order to extend the well known properties of this device to the quantum regime. By finding eigenvalues of the corresponding Hamiltonian operator, the persistent currents flowing in the ring have been obtained. The resulting quantum analog of the overdamped two-junction quantum interference device can be seen as a supercurrent qubit operating in the limit of negligible capacitance and finite inductance.
We report the fabrication and characterization of superconducting quantum interference devices (SQUIDs) made of Sb-doped Bi2Se3 topological insulator (TI) nanoribbon (NR) contacted with PbIn superconducting electrodes. When an external magnetic field was applied along the NR axis, the TI NR exhibited periodic magneto-conductance oscillations, the so-called Aharonov-Bohm oscillations, owing to one-dimensional subbands. Below the superconducting transition temperature of PbIn electrodes, we observed supercurrent flow through TI NR-based SQUID. The critical current periodically modulates with a m…
We discuss a quantum thermal machine that generates power from a thermally driven double quantum dot coupled to normal and superconducting reservoirs. Energy exchange between the dots is mediated by electron-electron interactions. We can distinguish three main mechanisms within the device operation modes. In the Andreev tunneling regime, energy flows in the presence of coherent superposition of zero- and two-particle states. Despite the intrinsic electron-hole symmetry of Andreev processes, we find that the heat engine efficiency increases with increasing coupling to the superconducting reserv…
We have measured the magnetoresistance of a dc superconducting quantum interference device in the form of an interrupted mesoscopic normal-metal loop in contact with two superconducting electrodes. Below the transition temperature of the superconducting electrodes, large $h/2e$ periodic magnetoresistance oscillations are observed. By adding a small dc bias to the ac measurement current, $h/4e$ oscillations can be produced. Lowering the temperature further leads to even larger oscillations, and eventually to sharp switching from the superconducting state to the normal state. This flux-dependent…
We analyze the quantum interference effects appearing in the charge current through the double quantum dots coupled in T-shape configuration to an isotropic superconductor and metallic lead. Owing to proximity effect the quantum dots inherit a pairing which has the profound influence on nonequilibrium charge transport, especially in the subgap regime |eV| < Delta. We discuss under what conditions the Fano-type lineshapes might appear in such Andreev conductance and consider a possible interplay with the strong correlation effects.
We present the realization and characterization of a novel-concept interferometer, the superconducting quantum interference proximity transistor (SQUIPT). Its operation relies on the modulation with the magnetic field of the density of states of a proximized metallic wire embedded in a superconducting ring. Flux sensitivities down to $\sim 10^{-5} Φ_0$Hz$^{-1/2}$ can be achieved even for a non-optimized design, with an intrinsic dissipation ($\sim 100$ fW) which is several orders of magnitude smaller than in conventional superconducting interferometers. Our results are in agreement with the th…
We report on the fabrication and electrical transport properties of superconducting quantum interference devices (SQUIDs) made from a (Bi_{1-x}Sb_x)_2Se_3 topological insulator (TI) nanoribbon (NR) connected with Pb0.5In0.5 superconducting electrodes. Below the transition temperature of the superconducting Pb0.5In0.5 electrodes, periodic oscillations of the critical current are observed in the TI NR SQUID under a magnetic field applied perpendicular to the plane owing to flux quantization. Also the output voltage modulates as a function of the external magnetic field. Moreover, the SQUID the S…
In this article we review the basic theoretical properties of a hybrid superconducting interferometer which exploits the phase dependence of the density of states of a metallic nanowire placed in good electric contact with a superconductor to achieve high sensitivity to magnetic flux. The operation of a prototype structure based on this principle, the superconducting quantum interference proximity transistor (SQUIPT), has been recently reported. Limited power dissipation joined with the opportunity to access single-spin detection make this interferometer attractive for the investigation of the…
Two-terminal conductance spectroscopy of superconducting devices is a common tool for probing Andreev and Majorana bound states. Here, we study theoretically a three-terminal setup, with two normal leads coupled to a grounded superconducting terminal. Using a single-electron scattering matrix, we derive the subgap conductance matrix for the normal leads and discuss its symmetries. In particular, we show that the local and the nonlocal elements of the conductance matrix have pairwise identical antisymmetric components. Moreover, we find that the nonlocal elements are directly related to the loc…
We present a method for fabricating Josephson junctions and superconducting quantum interference devices (SQUIDs) which is based on the local anodization of niobium strip lines 3 to 6.5 nm-thick under the voltage-biased tip of an Atomic Force Microscope. Microbridge junctions and SQUID loops are obtained either by partial or total oxidation of the niobium layer. Two types of weak link geometries are fabricated : lateral constriction (Dayem bridges) and variable thickness bridges. SQUIDs based on both geometries show a modulation of the maximum Josephson current with a magnetic flux periodic wi…
Crossed Andreev reflection in a lateral spin valve geometry device is an aspect of considerable recent interest, particularly with regards to Cooper pair splitting experiments to realize solid state quantum entanglement. In this work, devices are fabricated consisting of two ferromagnetic permalloy (Py) electrodes contacted by a overlaid perpendicular superconducting Ta electrode, of variable lateral in-plane offset within the expected BCS superconducting coherence length $ξ_0$. Experimental electrical transport measurements are presented of local and nonlocal conduction, showing characteristi…
We propose the concept of a quantized single-electron source based on the interplay between Coulomb blockade and magnetic flux-controllable superconducting proximity effect. We show that flux dependence of the induced energy gap in the density of states of a nanosized metallic wire can be exploited as an efficient tunable energy barrier which enables charge pumping configurations with enhanced functionalities. This control parameter strongly affects the charging landscape of a normal metal island with non-negligible Coulombic energy. Under a suitable evolution of a time-dependent magnetic flux…
We investigate phase-sensitive interference effects in a periodically $\sin(2πf_{\rm rf} t)$-driven, artificial two-state system connected to a microwave resonator at $f_{LC} \simeq 800$ MHz. We observe two kinds of multiphoton transitions in the two-state system, accompanied by: 1) Several quanta from the drive at $f_{\rm rf}$ and 2) one quantum at $f_{\rm rf}$ and several at $f_{LC}$. The former are described using phase-sensitive Landau-Zener transitions, while the latter are discussed in terms of vibronic transitions in diatomic molecules. Interference effects in the vibronic transitions g…
We propose and experimentally demonstrate detecting small single-cycle and few-cycle signals by using the symmetric double-well potential of a radio frequency superconducting quantum interference device (rf-SQUID). We show that the response of this bistable system to single- and few-cycle signals has a non-monotonic dependence on the noise strength. The response, measured by the probability of transition from initial potential well to the opposite one, becomes maximum when the noise-induced transition rate between the two stable states of the rf-SQUID is comparable to the signal frequency. Com…
We study impurity scattering in the normal and d-wave superconducting states of line nodal semimetals and show that, due to additional scattering phase space available for impurities on the surface, the quasiparticle interference pattern acquires an extended character instead of a discrete collection of delta function peaks. Moreover, using the T-matrix formalism, we demonstrate that the conventional behavior of a scalar impurity in a d-wave superconductor breaks down on the surface of a line nodal semimetal in the quasi flat band limit.
The thermoelectric performance of a topological Josephson nonlocal heat engine is thoroughly investigated. The nonlocal response is obtained by using a normal metal probe coupled with only one of the proximized helical edges in the middle of the junction. In this configuration, we investigate how the flux bias and the phase bias trigger the nonlocal thermoelectric effects under the application of a thermal difference between the superconducting terminals. Possible experimental nonidealities such as asymmetric proximized superconducting gaps are considered showing how the nonlocal response can …
Two-dimensional (2D) transition-metal dichalcogenide superconductors have unique and desirable properties for integration with conventional superconducting circuits. However, fully superconducting contact must be made between the 2D material and three-dimensional (3D) superconductors in order to employ the standard microwave drive and readout of qubits in such circuits. Here, we present a method for creating zero-resistance contacts between 2D NbSe$_2$ and 3D aluminum that behave as Josephson junctions (JJs) with large effective areas compared to 3D-3D JJs. We present a model for the supercurr…
Within the scattering approach, we develop a model for adiabatic quantum pumping in hybrid normal/superconductor systems where several superconducting leads are present. This is exploited to study Andreev-interference effects on adiabatically pumped charge in a 3-arm beam splitter attached to one normal and two superconducting leads with different phases of the order parameters. We derive expressions for the pumped charge through the normal lead for different parameters for the scattering region, and elucidate the effects due to Andreev interference. In contrast to what happens for voltage-dri…
A theory describing the operation of a superconducting nanowire quantum interference device (NQUID) is presented. The device consists of a pair of thin-film superconducting leads connected by a pair of topologically parallel ultra-narrow superconducting wires. It exhibits intrinsic electrical resistance, due to thermally-activated dissipative fluctuations of the superconducting order parameter. Attention is given to the dependence of this resistance on the strength of an externally applied magnetic field aligned perpendicular to the leads, for lead dimensions such that there is essentially com…
We study the critical Josephson current flowing through a double quantum dot weakly coupled to two superconducting leads. We use analytical as well as numerical methods to investigate this setup in the limit of small and large bandwidth leads in all possible charging states, where we account for on-site interactions exactly. Our results provide clear signatures of nonlocal spin-entangled pairs, which support interpretations of recent experiments [Deacon, R. S. et al., Nat. Commun. 6, 7446 (2015)]. In addition, we find that the ground state with one electron on each quantum dot can undergo a tu…
The design for an inductive superconducting quantum interference proximity transistor with enhanced performance, the L-SQUIPT, is presented and analyzed. The interferometer is based on a double-loop structure, where each ring comprises a superconductor-normal metal-superconductor mesoscopic Josephson weak-link and the read-out electrode is implemented in the form of a superconducting tunnel probe. Our design allows both to improve the coupling of the transistor to the external magnetic field and to increase the characteristic magnetic flux transfer functions, thereby leading to an improved ult…
