The ac Josephson effect in a ferromagnetic Josephson junction, which is composed of two superconductors separated by a ferromagnetic metal (FM), is studied by a tunneling Hamiltonian and Green's function method. We obtain two types of superconducting phase dependent current, i.e., Josephson current and quasiparticle-pair-interference current (QPIC). These currents change their signs with thickness of the FM layer due to the 0-$π$ transition characteristic to the ferromagnetic Josephson junction. As a function of applied voltage, the Josephson critical current shows a logarithmic divergence called the Riedel peak at the gap voltage, while the QPIC shows a discontinuous jump. The Riedel peak reverses due to the 0-$π$ transition and disappears near the 0-$π$ transition point. The discontinuous jump in the QPIC also represents similar behaviors to the Riedel peak. These results are in contrast to the conventional ones.
We study the Josephson current through a ferromagnetic trilayer, both in the diffusive and clean limits. For colinear (parallel or antiparallel) magnetizations in the layers, the Josephson current is small due to short range proximity effect in superconductor/ferromagnet structures. For non colinear magnetizations, we determine the conditions for the Josephson current to be dominated by another contribution originating from long range triplet proximity effect.
A linear Josephson junction mediated by the surface states of a time-reversal-invariant Weyl or Dirac semimetal localizes Majorana flat bands protected by the time-reversal symmetry. We show that as a result, the Josephson current exhibits a discontinuous jump at $π$ phase difference which can serve as an experimental signature of the Majorana bands. The magnitude of the jump scales proportionally to the junction width and the momentum space distance between the Weyl nodes. It also exhibits a characteristic dependence on the junction orientation. We demonstrate that the jump is robust against …
We theoretically investigate the magnetization inside a normal metal containing the Rashba spin-orbit interaction (RSOI) induced by the proximity effect in an s-wave superconductor/normal metal/ferromagnetic metal/s-wave superconductor (S/N/F/S) Josephson junction. By solving the linearized Usadel equation taking account of the RSOI,we find that the direction of the magnetization induced by the proximity effect in N can be reversed by tuning the RSOI.Moreover, we also find that the direction of the magnetization inside N can be reversed by changing the superconducting phase difference, i.e., J…
We investigate transverse Josephson current in superconductor/normal metal/superconductor junctions where the normal metal has Rashba type spin-orbit coupling. It is shown that trans- verse current arises from the spin-orbit coupling in the normal metal. This effect is specific to superconducting current and the transverse current vanishes in the normal state. In addition, this transverse Josephson effect is purely stationary and applied magnetic field is unnecessary to realize this effect, in contrast to the Hall effect in the normal state. We also discuss physical interpretation of this effe…
For Josephson junctions based on s-wave superconductors, time-reversal symmetry is known to allow for powerful relations between the normal-state junction properties, the excitation spectrum, and the Josephson current. Here we provide analogous relations for Josephson junctions involving one-dimensional time-reversal-invariant topological superconductors supporting Majorana-Kramers pairs, considering both topological-topological and s-wave-topological junctions. Working in the regime where the junction is much shorter than the superconducting coherence length, we obtain a number of analytical …
The Josephson current in a diffusive superconductor/ferromagnet/superconductor junction with precessing magnetization is calculated within the quasiclassical theory of superconductivity. When the junction is phase-biased, a stationary current (without a.c. component) can flow through it despite the non-equilibrium condition. A large critical current is predicted due to a dynamically induced long range triplet proximity effect. Such effect could be observed in a conventional hybrid device close to the ferromagnetic resonance.
We theoretically propose a principle for precise measurement of oscillatory domain wall (DW) by a ferromagnetic Josephson junction, which is composed of a ferromagnetic wire with DW and two superconducting electrodes. The current-voltage curve exhibits stepwise structures, only when DW oscillates in the ferromagnetic wire. The voltage step appears at V = n(\hbar/2e)ω_DW with the fundamental constant \hbar/e, integer number n, and the DW frequency ω_DW. Since V can be determined in the order of 10^9 accuracy, the oscillatory DW will be measured more precisely than present status by conventional…
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…
Coupling of Josephson-phase and spin-waves is theoretically studied in a superconductor/ferromagnetic insulator/superconductor (S/FI/S) junction. Electromagnetic (EM) field inside the junction and the Josephson current coupled with spin-waves in FI are calculated by combining Maxwell and Landau-Lifshitz-Gilbert equations. In the S/FI/S junction, it is found that the current-voltage (I-V) characteristic shows two resonant peaks. Voltages at the resonant peaks are obtained as a function of the normal modes of EM field, which indicates a composite excitation of the EM field and spin-waves in the …
AC Josephson current density in a Josephson junction with DC bias is spatially modulated by an external magnetic field, and induces an electromagnetic (EM) field inside the junction. The current-voltage ($I$-$V$) curve exhibits peaks due to the resonance between the EM field and the spatially modulated AC Josephson current density. This is called {\it Fiske resonance}. Such a spatially modulated Josephson current density can be also induced by a non-uniform insulating barrier and the Fiske resonance appears without external magnetic field. This is called zero-field Fiske resonance (ZFFR). In t…
We study the Josephson junction mediated by the quantum spin Hall edge states and show that electron-electron interactions lead to a dissipationless fractional Josephson effect in the presence of time-reversal symmetry. Surprisingly, the periodicity is $8π$, corresponding to a Josephson frequency $eV/2\hbar$. We estimate the magnitude of interaction induced many-body level splitting responsible for this effect and argue that it can be measured using tunneling spectroscopy. For strong interactions we show that the Josephson effect is associated with the weak tunneling of charge $e/2$ quasiparti…
We show experimentally and theoretically that there is a coupling via the Aharonov-Bohm phase between the order parameter of a ferromagnet and a singlet, s-wave, Josephson supercurrent. We have investigated the possibility of measuring the dispersion of such spin waves by varying the magnetic field applied in the plane of the junction and demonstrated the electromagnetic nature of the coupling by the observation of magnetic resonance side-bands to microwave induced Shapiro steps.
We investigate the interplay between ferromagnetic and superconducting order at the edge of a quantum spin Hall insulator. Using complementary analytical and self-consistent numerical approaches, we study a ferromagnetic Josephson junction and show how the direct coupling between magnetism and the superconducting U(1) phase gives rise to several unusual phenomena which distinguishes the present system from its non-topological equivalent. In particular, we demonstrate how the anomalous current-phase relation triggers supercurrent-induced magnetization dynamics and also study the spatial localiz…
We report the observation of a current-phase relation dominated by the second Josephson harmonic in superconductor-ferromagnet-superconductor junctions. The exotic current-phase relation is realized in the vicinity of a temperature-controlled 0-to-$π$ junction transition, at which the first Josephson harmonic vanishes. Direct current-phase relation measurements, as well as Josephson interferometry, non-vanishing supercurrent and half-integer Shapiro steps at the 0-$π$ transition self-consistently point to an intrinsic second harmonic term, making it possible to rule out common alternative orig…
We determine the current-phase relation (CPR) of two-terminal configurations of Josephson junctions containing two-dimensional (2D) time-reversal invariant topological superconductors (TRITOPS), including TRITOPS-TRITOPS, as well as junctions between topological and non-topological superconductors (TRITOPS-S). We focus on long junctions for which several channels intervene in the tunneling coupling through the junction. We present a description of the topological edge modes for different TRITOPS models including $p$-wave pairing and the combination of $s$-wave pairing with spin-orbit coupling.…
Solid-state qubits have the potential for the large-scale integration and for the flexibility of layout for quantum computing. However, their short decoherence time due to the coupling to the environment remains an important problem to be overcome. We propose a new superconducting qubit which incorporates a spin-electronic device: the qubit consists of a superconducting ring with a ferromagnetic pi junction which has a metallic contact and a normal Josephson junction with an insulating barrier. Thus, a quantum coherent two-level state is formed without an external magnetic field. This feature …
We investigate the Josephson transport through a ferromagnetic oxide film, e.g., La$_2$BaCuO$_5$, theoretically. Using the recursive Green's function technique, we found the formation of a pi-junction in such systems. Moreover the 0-pi phase transition is induced by increasing the temperature. Such ferromagnetic-oxide based Josephson junctions may become an element in the architecture of future quantum computers.
We discuss the effects of thermal noise on the magnetic response of a lateral ferromagnetic Josephson junction with spin-orbit coupling and out-of-plane magnetization. The direction of the magnetic moment in the ferromagnetic layer can be inverted by using controlled current pulses. This phenomenon is due to the magnetoelectric effect that couples the flowing charge current and the magnetization of the ferromagnet. We investigate the magnetization reversal effect versus intrinsic parameters of the ferromagnet, such as the Gilbert damping and strength of the spin-orbit coupling. We estimate the…
We show that the time reversal symmetry inevitably breaks in a superconducting Josephson junction formed by two superconductors with different pairing symmetries dubbed as i-Josephson junction. While the leading conventional Josephson coupling vanishes in such an i-Josephson junction, the second order coupling from tunneling always generates chiral superconductivity orders with broken time reversal symmetry. Josephson frequency in the i-junction is doubled, namely $ω= 4eV /h$. The result provides a way to engineer topological superconductivity such as the d + id' -wave superconducting state ch…
We study dynamics of tunnel Josephson junctions with a thin ferromagnetic layer F [superconductor-insulator-ferromagnet-superconductor (SIFS) junctions]. On the basis of derived equations relating the superconducting phase and magnetic moment to each other we analyze collective excitations in the system and find a new mode which is a hybrid of plasmalike and spin waves. The latter are coupled together in a broad range of parameters characterizing the system. Using the solution describing the collective modes we demonstrate that besides the Fiske steps new peaks appear on the I-V characteristic…
We present a quantitative study of the current-voltage characteristics (CVC) of SFIFS Josephson junctions (S denotes bulk superconductor, F - metallic ferromagnet, I - insulating barrier) with weak ferromagnetic interlayers in the diffusive limit. The problem is solved in the framework of the nonlinear Usadel equations. We consider the case of a strong tunnel barrier such that the left SF and the right FS bilayers are decoupled. We calculate the density of states (DOS) in SF bilayers using a self-consistent numerical method. Then we obtain the CVC of corresponding SFIFS junctions, and discuss …
We propose a heat valve based on the interplay between thermal transport and proximity-induced exchange splitting in Josephson tunnel junctions. We demonstrate that the junction heat conductance strongly depends on the relative alignment of the exchange fields induced in the superconductors. Colossal magneto-heat resistance ratios as large as 10^7% are predicted to occur under proper temperature and phase conditions, as well as suitable ferromagnet-superconductor combinations. Moreover, the quantum phase tailoring, intrinsic to the Josephson coupling, offers an additional degree of freedom for…
We study the Josephson effect in graphene-based ballistic superconductor-ferromagnet-superconductor (SFS) junctions. We find an oscillatory Josephson coupling $I_c R_N$ of F graphene whose amplitude is nonvanishing for a half-metallic graphene, increases for the exchange fields $h$ above the Fermi energy $E_{F}$ and shows only a slow damping at strong exchange fields $h\gg E_{F}$. We interpret this long range Josephson coupling as the result of the exchange mediated Andreev-Klein process at FS interfaces which enhances the induced antiparallel-spin superconducting correlations in F graphene by…
We investigate the current-phase relation of S/F/S junctions near the crossover between the 0 and the pi ground states. We use Nb/CuNi/Nb junctions where this crossover is driven both by thickness and temperature. For a certain thickness a non-zero minimum of critical current is observed at the crossover temperature. We analyze this residual supercurrent by applying a high frequency excitation and observe the formation of half-integer Shapiro steps. We attribute these fractional steps to a doubling of the Josephson frequency due to a sin(2*phi) current-phase relation. This phase dependence is …
Via a direct coupling between the magnetic order parameter and the singlet Josephson supercurrent, we detect spin-wave resonances, and their dispersion, in ferromagnetic Josephson junctions in which the usual insulating or metallic barrier is replaced with a weak ferromagnet. The coupling arises within the Fraunhofer interferential description of the Josephson effect, because the magnetic layer acts as a time dependent phase plate. A spin-wave resonance at a frequency ws implies a dissipation that is reflected as a depression in the current-voltage curve of the Josephson junction when hbar ws …
We study the combined effects of spin-orbit interaction, magnetic field, and Coulomb charging on the Josephson current-phase relation, I(φ), for a multi-level quantum dot tunnel-contacted by two conventional s-wave superconductors with phase difference φ. A general model is formulated and analyzed in the cotunneling regime (weak tunnel coupling) and in the deep subgap limit, fully taking into account interaction effects. We determine the conditions for observing a finite anomalous supercurrent I_a=I(φ=0). For a two-level dot with spin-orbit coupling and arbitrarily weak Zeeman field B, we find…
In 2010, several experimental groups obtained compelling evidence for spin-triplet supercurrent in Josephson junctions containing strong ferromagnetic materials. Our own best results were obtained from large-area junctions containing a thick central Co/Ru/Co "synthetic antiferromagnet" and two thin outer layers made of Ni or PdNi alloy. Because the ferromagnetic layers in our samples are multi-domain, one would expect the sign of the local current-phase relation inside the junctions to vary randomly as a function of lateral position. Here we report measurements of the area dependence of the cr…
We study the effect of the interfacial transparency on the Josephson current in a diffusive ferromagnetic contact between two superconductors. In contrast to the cases of the fully transparent and the low-transparency interfaces, the current-phase relation is shown to be nonsinusoidal for a finite transparency. It is demonstrated that even for the nearly fully transparent interfaces the small corrections due to weak interfacial disorders contribute a small second-harmonic component in the current-phase relation. For a certain thicknesses of the ferromagnetic contact and the exchange field this…
The electrical and structural properties of Co40Fe40B20 (CoFeB) alloy are tunable with thermal annealing. This is key in the optimization of CoFeB-based spintronic devices, where the advantageously low magnetic coercivity, high spin polarization, and controllable magnetocrystalline anisotropy are utilised. So far, there has been no report on superconducting devices based on CoFeB. Here, we report Nb/CoFeB/Nb Josephson devices and demonstrate an enhancement of the critical current by up to 700% following thermal annealing due to increased structural ordering of the CoFeB. The results demonstrat…
Josephson junctions containing multiple ferromagnetic layers can carry spin-triplet supercurrent under certain conditions. Large-area junctions containing multiple domains are expected to have a random distribution of 0 or pi coupling across the junction surface, whereas magnetized samples should have uniquely pi coupling everywhere. We have measured the area dependence of the critical current in such junctions, and confirm that the critical current scales linearly with area in magnetized junctions. For as-grown (multi-domain) samples, the results are mixed. Samples grown on a thick Nb base ex…
Superconductor-ferromagnet (S-F) interfaces in two-dimensional (2D) heterostructures present a unique opportunity to study the interplay between superconductivity and ferromagnetism. The realization of such nanoscale heterostructures in van der Waals (vdW) crystals remains largely unexplored due to the challenge of making an atomically-sharp interface from their layered structures. Here, we build a vdW ferromagnetic Josephson junction (JJ) by inserting a few-layer ferromagnetic insulator Cr2Ge2Te6 into two layers of superconductor NbSe2. Owing to the remanent magnetic moment of the barrier, th…
We study all the possible different two terminal configurations of Josephson junctions containing wires of time-reversal invariant topological superconductors (TRITOPS) and ordinary superconductors, including combinations with an interacting quantum dot between both wires in the junction. We introduce simple effective Hamiltonians which explain the different qualitative behaviors obtained. We analyze a wide range of phenomena, including occurrence and quenching of the so called $0-π$ transition, anomalous periodicity and jumps of the Josephson current as a function of the phase difference, and…
We study the Josephson transport in a high-Tc superconductor/ferromagnetic-insulator(FI)/high-Tc superconductor numerically. We found the formation of a pi-junction in such systems. More remarkably the ground state of such junction alternates between 0- and pi-states when thickness of FI is increasing by a single atomic layer. We propose an experimental setup for observing the atomic-scale 0-pi transition. Such FI-based pi-junctions can be used to implement highly-coherent quantum bits.
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…
Time reversal invariant topological superconducting (TRITOPS) wires are known to host a fractional spin hbar/4 at their ends. We investigate how this fractional spin affects the Josephson current in a TRITOPS-quantum dot-TRITOPS Josephson junction, describing the wire in a model which can be tuned between a topological and a nontopological phase. We compute the equilibrium Josephson current of the full model by continuous-time Monte Carlo simulations and interpret the results within an effective low-energy theory. We show that in the topological phase, the 0-to-pi transition is quenched via fo…
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…
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…
We report on the fabrication of Nb/AlO_x/Pd_{0.82}Ni_{0.18}/Nb superconductor/insulator/ferromagnetic metal/superconductor (SIFS) Josephson junctions with high critical current densities, large normal resistance times area products, high quality factors, and very good spatial uniformity. For these junctions a transition from 0- to π-coupling is observed for a thickness d_F ~ 6 nm of the ferromagnetic Pd_{0.82}Ni_{0.18} interlayer. The magnetic field dependence of the π-coupled junctions demonstrates good spatial homogeneity of the tunneling barrier and ferromagnetic interlayer. Magnetic charac…
We consider a Josephson bijunction consisting of a thin $SIS$ $π$-Josephson junction sandwiched between two-dimensional semiconducting layers with strong Rashba spin-orbit interaction. Each of these layers forms an $SNS$ junction due to proximity-induced superconductivity. The $SIS$ junction is assumed to be thin enough such that the two Rashba layers are tunnel-coupled. We show that, by tuning external gates, this system can be controllably brought into a time-reversal invariant topological superconducting phase with a Kramers pair of Majorana bound states being localized at the end of the no…
The concept of thermophase refers to the appearance of a phase gradient inside a superconductor originating from the presence of an applied temperature bias across it. The resulting supercurrent flow may, in suitable conditions, fully counterbalance the temperature-bias-induced quasiparticle current therefore preventing the formation of any voltage drop, i.e., a thermovoltage, across the superconductor. Yet, the appearance of a thermophase is expected to occur in Josephson-coupled superconductors as well. Here we theoretically investigate the thermoelectric response of a thermally-biased Josep…
We theoretically study the magnetism induced by the proximity effect in the normal metal of ferromagnetic Josephson junction composed of two $s$-wave superconductors separated by ferromagnetic metal/normal metal/ferromagnetic metal junction (${S}/{F}/{N}/{F}/{S}$ junction). We calculate the magnetization in the $N$ by solving the Eilenberger equation. We show that the magnetization arises in the ${N}$ when the product of anomalous Green's functions of the spin-triplet even-frequency odd-parity Cooper pair and spin-singlet odd-frequency odd-parity Cooper pair in the ${N}$ has a finite value. Th…
Signatures of time-reversal-symmetry breaking in multiband 2H-TaS2 revealed by zero-field Josephson nonreciprocity
CIC nanoGUNE BRTA（纳米科学中心）；Centro de Física de Materiales – Materials Physics Center (CFM-MPC) CSIC-EHU（材料物理中心）；Istituto di Struttura della Materia, Consiglio Nazionale delle Ricerche（意大利国家研究理事会材料结构研究所）
We present a quantitative study of the current-voltage characteristics (CVC) of diffusive superconductor/ insulator/ ferromagnet/ superconductor (SIFS) tunnel Josephson junctions. In order to obtain the CVC we calculate the density of states (DOS) in the F/S bilayer for arbitrary length of the ferromagnetic layer, using quasiclassical theory. For a ferromagnetic layer thickness larger than the characteristic penetration depth of the superconducting condensate into the F layer, we find an analytical expression which agrees with the DOS obtained from a self-consistent numerical method. We discus…
Josephson-Phase Reversal of Non-Bloch Andreev Propagation
College of Physics and Materials Science, Tianjin Normal University（天津师范大学物理与材料科学学院）；Interdisciplinary Center, Tianjin Normal University（天津师范大学交叉研究中心）；Center for Joint Quantum Studies & Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系量子联合研究中心及天津市低维材料物理与制备技术重点实验室）
We investigate Josephson junctions on the surface of a three-dimensional topological insulator in planar, step, and edge geometries. The elliptical nature of the Dirac cone representing the side surface states of the topological insulator results in a scaling factor in the Josephson current in a step junction as compared to the planar junction. In edge junctions, the contribution of the Andreev bound states to the Josephson current vanishes due to spin-momentum locking of the surface states. Furthermore, we consider a junction with a ferromagnetic insulator between the superconducting regions.…
The Josephson current flowing through weak links containing ferromagnetic elements is studied theoretically under the condition that the quasiparticle distribution over energy states in the interlayer is spin-dependent. It is shown that the interplay between the spin-dependent quasiparticle distribution and the triplet superconducting correlations induced by the proximity effect between the superconducting leads and ferromagnetic elements of the interlayer, leads to the appearence of an additional contribution to the Josephson current. This additional contribution $j_t$ can be extracted from t…
The breaking of time-reversal symmetry in a triplet superconductor Josephson junction is shown to cause a magnetic instability of the tunneling barrier. Using a Ginzburg-Landau analysis of the free energy, we predict that this novel functional behaviour reflects the formation of an exotic Josephson state, distinguished by the existence of fractional flux quanta at the barrier. The crucial role of the orbital pairing state is demonstrated by studying complementary microscopic models of the junction. Signatures of the magnetic instability are found in the critical current of the junction.
We have measured a long-range supercurrent in Josephson junctions containing Co (a strong ferromagnetic material) when we insert thin layers of either PdNi or CuNi weakly-ferromagnetic alloys between the Co and the two superconducting Nb electrodes. The critical current in such junctions hardly decays for Co thicknesses in the range of 12-28 nm, whereas it decays very steeply in similar junctions without the alloy layers. The long-range supercurrent is controllable by the thickness of the alloy layer, reaching a maximum for a thickness of a few nm. These experimental observations provide stron…
We study a diffusive superconductor--ferromagnet--superconductor (SFS) junction with in-plane ferromagnetic domains. Close to the superconducting transition temperature, we describe the proximity effect in the junction with the linearized Usadel equations. We find that properties of such a junction depend on the size of the domains relative to the magnetic coherence length. In the case of large domains, the junction exhibits transitions to the $π$ state, similarly to a single-domain SFS junction. In the case of small domains, the magnetization effectively averages out, and the junction is alwa…
We predict anomalous atomic-scale 0-pi transitions in a Josephson junction with a ferromagnetic-insulator (FI) barrier. The ground state of such junction alternates between 0- and pi-states when thickness of FI is increasing by a single atomic layer. We find that the mechanism of the 0-pi transition can be attributed to thickness-dependent phase-shifts between the wave numbers of electrons and holes in FI. Based on these results, we show that stable pi-state can be realized in junctions based on high-Tc superconductors with La$_2$BaCuO$_5$ barrier.
