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-reversal breaking by a magnetic flux. We also show that our diodes have a characteristic AC response, revealed by the Shapiro steps. Even the simplest realization of our Josephson diode paradigm that relies on only two junctions can achieve efficiencies of up to $\sim40\%$ and, interestingly, far greater efficiencies are achievable by concatenating multiple interferometer loops.
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…
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…
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…
We demonstrate that perfect conversion between charged supercurrents in superconductors and neutral supercurrents in electron-hole pair condensates is possible via a new Andreev-like scattering mechanism. As a result, when two superconducting circuits are coupled through a bilayer exciton condensate, the superflow in both layers is drastically modified. Depending on the phase biases the supercurrents can be completely blocked or exhibit perfect drag.
A Kapitza Pendulum Route to Supercurrent Tunnel Diodes
Istituto di Struttura della Materia of the National Research Council（国家研究委员会材料结构研究所）；Institute for Theoretical Solid State Physics, IFW Dresden（德累斯顿IFW理论固体质物理研究所）；CNR-SPIN；Istituto Lombardo “Accademia di Scienze e Lettere”（伦巴第科学院与文学院）；NEST Istituto Nanoscienze-CNR and Scuola Normale Superiore（CNR纳米科学研究所NEST与比萨高等师范学院）；Würzburg-Dresden Cluster of Excellence ct.qmat（维尔茨堡-德累斯顿卓越集群ct.qmat）；Universitá di Salerno（萨莱诺大学）
We propose a Josephson junction setup based on a topological insulator (TI) thin film to detect Majorana states, which exploits the unique helical and extended nature of the TI surface state. When the magnetic flux through the junction is close to an integer number of flux quanta, Majorana states, present on both surfaces of the film, give rise to a narrow peak-dip structure in the current- phase relation by hybridizing at the edge of the junction. Moreover, the maximal Majorana-state contribution to Josephson current takes a (nearly) universal value, approximately equal to the supercurrent ca…
A Josephson supercurrent has been induced into the three-dimensional topological insulator Bi1.5Sb0.5Te1.7Se1.3. We show that the transport in Bi1.5Sb0.5Te1.7Se1.3 exfoliated flakes is dominated by surface states and that the bulk conductivity can be neglected at the temperatures where we study the proximity induced superconductivity. We prepared Josephson junctions with widths in the order of 40 nm and lengths in the order of 50 to 80 nm on several Bi1.5Sb0.5Te1.7Se1.3 flakes and measured down to 30 mK. The Fraunhofer patterns unequivocally reveal that the supercurrent is a Josephson supercur…
Coupling the surface state of a topological insulator (TI) to an s-wave superconductor is predicted to produce the long-sought Majorana quasiparticle excitations. However, superconductivity has not been measured in surface states when the bulk charge carriers are fully depleted, i.e., in the true topological regime that is relevant for investigating Majorana modes. Here, we report measurements of DC Josephson effects in TI-superconductor junctions as the chemical potential is moved from the bulk bands into the band gap, or through the true topological regime characterized by the presence of on…
We theoretically investigate the mapping of the supercurrent distribution in a planar superconductor-normal-superconductor junction in the presence of a perpendicular magnetic field via the scanning gate microscopy technique. We find that the distribution of counter-propagating supercurrents aligned in Josephson vortices can be mapped by the change of the critical current induced by the tip of the scanning probe, if the flux in the junction is set close to maxima of the Fraunhofer pattern. Instead, when the magnetic field drives the junction to a supercurrent minimum in the Fraunhofer pattern,…
We study the Josephson effect for a topologically nontrivial superconducting (TS) wire with Majorana fermion end states and tunnel-coupled to s-wave BCS superconducting (S) electrodes. In an S-TS junction, no supercurrent flow is possible under fairly general conditions. For the S-TS-S junction, bulk TS quasiparticles must be accessible to have a Josephson effect. In the noninteracting case, we derive the exact current-phase relation (CPR) and find π-periodic behavior with negative critical current for weak tunnel couplings. Charging effects then cause the anomalous CPR $I(φ)=I_c \cosφ$, where…
The Josephson effect describes the generic appearance of a supercurrent in a weak link between two superconductors. Its exact physical nature however deeply influences the properties of the supercurrent. Detailed studies of Josephson junctions can reveal microscopic properties of the superconducting pairing (spin-triplet correlations, $d$-wave symmetry) or of the electronic transport (quantum dot, ballistic channels). In recent years, considerable efforts have focused on the coupling of superconductors to topological insulators, in which transport is mediated by topologically protected Dirac s…
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…
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…
It has been predicted theoretically that an unconventional odd-frequency spin-triplet component of superconducting order parameter can be induced in multilayered ferromagnetic structures with non-collinear magnetization. In this work we study experimentally nano-scale devices, in which a ferromagnetic spin valve is embedded into a Josephson junction. We demonstrate two ways of in-situ analysis of such Josephson spin valves: via magnetoresistance measurements and via in-situ magnetometry based on flux quantization in the junction. We observe that supercurrent through the device depends on the r…
Wires made of topological insulators (TI) are a promising platform for searching for Majorana bound states. These states can be probed by analyzing the fractional ac Josephson effect in Josephson junctions with the TI wire as a weak link. An axial magnetic field can be used to tune the system from trivial to topologically nontrivial. Here we investigate the oscillations of the supercurrent in such wire Josephson junctions as a function of the axial magnetic field strength and different contact transparencies. Although the current flows on average parallel to the magnetic field we observe $h/2e…
The Josephson junction of a strong spin-orbit material under a magnetic field is a promising Majorana fermion candidate. Supercurrent enhancement by a magnetic field has been observed in the InAs nanowire Josephson junctions and assigned to a topological transition. In this work we observe a similar phenomenon but discuss the non-topological origin by considering trapping of quasiparticles by vortices that penetrate the superconductor under a finite magnetic field. This assignment is supported by the observed hysteresis of the switching current when sweeping up and down the magnetic field. Our…
The Josephson effect is a kind of macroscopic quantum phenomenon that supercurrent flows through a Josephson junction without any voltage applied. We predict a novel vortex-state-mediated Josephson effect in an SNS Josephson junction supporting vortices. The vortex-state-mediated supercurrent is enhanced or reduced significantly in magnitude depending on the junction length, and exhibits several steps with the number of effective propagating channels in current-phase evolution at zero temperature. At finite temperatures, these supercurrent steps persist in the short junction limit, and develop…
We demonstrate enhanced robustness of the supercurrent through graphene-based Josephson junctions in which strong spin-orbit interactions (SOIs) are induced. We compare the persistence of a supercurrent at high magnetic fields between Josephson junctions with graphene on hexagonal boron-nitride and graphene on WS$_2$, where strong SOIs are induced via the proximity effect. We find that in the shortest junctions both systems display signatures of induced superconductivity, characterized by a suppressed differential resistance at a low current, in magnetic fields up to 1 T. In longer junctions h…
Superconductor-graphene-superconductor (SGS) junction provides a unique platform to study relativistic electrodynamics of Dirac fermions combined with proximity-induced superconductivity. We report observation of the Josephson effect in proximity-coupled superconducting junctions of graphene in contact with Pb1-xInx (x=0.07) electrodes for temperatures as high as T = 4.8K, with a large IcRn (~ 255 microV). This demonstrates that Pb1-xInx SGS junction would facilitate the development of the superconducting quantum information devices and superconductor-enhanced phase-coherent transport of graph…
Motivated by recent experiments revealing superconductivity in MoS$_2$, we investigate the Josephson effect in the monolayer MoS$_2$ at the presence of an exchange splitting. We show that the supercurrent reversal known as $0-π$ transition can occur by varying the doping via gate voltages. This is in contrast to common superconductor/ferromagnet/superconductor junctions in which successive $0-π$ transition take place with the variation of junction length or temperature. In fact for the case of MoS$_2$ we find that both the amplitude and the period of oscillations show a dependence on the dopin…
We present a study of a graphene-based Josephson junction with dedicated side gates carved from the same sheet of graphene as the junction itself. These side gates are highly efficient, and allow us to modulate carrier density along either edge of the junction in a wide range. In particular, in magnetic fields in the $1-2$ Tesla range, we are able to populate the next Landau level, resulting in Hall plateaus with conductance that differs from the bulk filling factor. When counter-propagating quantum Hall edge states are introduced along either edge, we observe supercurrent localized along that…
We propose a realization of the superconducting diode effect in flux biased superconducting circuits of Josephson junctions. So far the observation of the superconducting diode effect has been limited to rather exotic material platforms. In theoretical proposals, it relied on a non-sinusoidal form of the current phase relation of Josephson junctions. Here, we show how the diode effect can be engineered in superconducting circuits without any such requirements. The only necessary ingredients are standard sinusoidal Josephson junctions and flux bias lines that are readily available in scalable i…
We 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…
We study experimentally nanoscale Josephson junctions and Josephson spin-valves containing strong Ni ferromagnets. We observe that in contrast to junctions, spin valves with the same geometry exhibit anomalous Ic(H) patterns with two peaks separated by a dip. We develop several techniques for in-situ characterization of micromagnetic states in our nano-devices, including magnetoresistance, absolute Josephson fluxometry and First-Order-Reversal-Curves analysis. They reveal a clear correlation of the dip in supercurrent with the antiparallel state of a spin-valve and the peaks with two noncollin…
It is necessary to break both time-reversal and parity symmetries to realize a Josephson, or superconducting, diode exhibiting nonreciprocal critical direct-currents (DC). In fact, these conditions are still insufficient. The dependencies of the free energy on the phase difference across the junction and the magnetic field are classified, exhibiting the current-reversion (JR), field-reversion, and field-current reversion conditions, respectively. To exhibit the DC Josephson diode effect, all symmetries satisfying the JR condition need to be broken. The relations of critical currents with respe…
We investigate superconducting quantum interference devices consisting of two highly transmissive Josephson junctions coupled by a superconducting loop, all defined in an epitaxial InAs/Al heterostructure. A novel device design allows for independent measurements of the Andreev bound state spectrum within the normal region of a junction and the resulting current-phase relation. We show that knowledge of the Andreev bound state spectrum alone is enough to derive the independently measured phase dependent supercurrent. On the other hand, the opposite relation does not generally hold true as deta…
Non-reciprocal charge transport in supercurrent diodes (SDs) polarized growing interest in the last few years for its potential applications in superconducting electronics (SCE). So far, SD effects have been reported in complex hybrid superconductor/semiconductor structures or metallic systems subject to moderate magnetic fields, thus showing a limited potentiality for practical applications in SCE. Here, we report the design and the realization of a monolithic SD by exploiting a Dayem bridge-based superconducting quantum interference device (SQUID). Our structure allows reaching rectification…
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…
Non-reciprocal electronic transport in a spatially homogeneous system arises from the simultaneous breaking of inversion and time-reversal symmetries. Superconducting and Josephson diodes, a key ingredient for future non-dissipative quantum devices, have recently been realized. Only a few examples of a vertical superconducting diode effect have been reported and its mechanism, especially whether intrinsic or extrinsic, remains elusive. Here we demonstrate a substantial supercurrent non-reciprocity in a van der Waals vertical Josephson junction formed with a Td-WTe2 barrier and NbSe2 electrodes…
Superconducting diode effect, in analogy to the nonreciprocal resistive charge transport in semiconducting diode, is a nonreciprocity of dissipationless supercurrent. Such an exotic phenomenon originates from intertwining between symmetry-constrained supercurrent transport and intrinsic quantum functionalities of helical/chiral superconductors. In this article, research progress of superconducting diode effect including fundamental concepts, material aspects, device prospects, and theoretical/experimental development is reviewed. First, fundamental mechanisms to cause superconducting diode eff…
Josephson junctions made of closely-spaced conventional superconductors on the surface of 3D topological insulators have been proposed to host Andreev bound states (ABSs) which can include Majorana fermions. Here, we present an extensive study of the supercurrent carried by low energy ABSs in Nb/Bi$_2$Se$_3$/Nb Josephson junctions in various SQUIDs as we modulate the carrier density in the Bi$_2$Se$_3$ barriers through electrostatic top gates. As previously reported, we find a precipitous drop in the Josephson current at a critical value of the voltage applied to the top gate. This drop has be…
In the past year, several groups have observed evidence for long-range spin-triplet supercurrent in Josephson junctions containing ferromagnetic (F) materials. In our work, the spin-triplet pair correlations are created by non-collinear magnetizations between a central Co/Ru/Co "synthetic antiferromagnet" (SAF) and two outer thin F layers. Here we present data showing that the spin-triplet supercurrent is enhanced up to 20 times after our samples are subject to a large in-plane magnetizing field. This surprising result can be explained if the Co/Ru/Co SAF undergoes a "spin-flop" transition, wh…
