A novel time-reversal symmetry breaking state is found theoretically in the Josephson junction between the two-gap superconductor and the conventional s-wave superconductor. This occurs due to the frustration between the three order parameters analogous to the two antiferromagnetically coupled XY-spins put under a magnetic field. This leads to the interface states with the energies inside the superconducting gap. Possible experimental observations of this state with broken time-reversal symmetry are discussed.
We study magnetization reversal in a $φ_0$ Josephson junction with direct coupling between magnetic moment and Josephson current. Our simulations of magnetic moment dynamics show that by applying an electric current pulse, we can realize the full magnetization reversal. We propose different protocols of full magnetization reversal based on the variation of the Josephson junction and pulse parameters, particularly, electric current pulse amplitude, damping of magnetization and spin-orbit interaction. We discuss experiments which can probe the magnetization reversal in $φ_0$-junctions.
The magnetization reversal in ${φ_0}$-Josephson junction with direct coupling between magnetic moment and Josephson current has been studied. By adding pulse signal, the dynamics of magnetic moment components have been simulated and the full magnetization reversal at different parameters of the junction has been demonstrated. We obtain a detailed pictures representing the intervals of the damping parameter $α$, Josephson to magnetic energy relation $G$ and spin-orbit coupling parameter $r$ with full magnetization reversal. A periodicity in the appearance of magnetization reversal intervals wit…
Topological superconductors are gapped superconductors with protected Majorana surface/edge states on the boundary. In this paper, we study the Josephson coupling between time-reversal invariant topological superconductors and s-wave superconductors. The Majorana edge/surface states of time-reversal invariant topological superconductors in all physical dimensions 1, 2, 3 have a generic topological property which we named as time-reversal anomaly. Due to the time-reversal anomaly, the Josephson coupling prefers a nonzero phase difference between topological and trivial superconductors. The nont…
In order to examine the influences of the spatial dependence of the pair potential, the d.c. Josephson current in d-wave superconductors is calculated using self-consistently determined pair potentials. The results show that the suppression of the d-wave pair potential near the insulator does not have serious effect on the properties of the Josephson current. On the other hand, drastic changes are obtained due to the inducement of a subdominant s-wave component, which spontaneously breaks time reversal symmetry. Especially, a rapid enhancement of the Josephson current at low temperature predic…
The $φ_0$ Josephson junctions formed by ordinary superconductors and a magnetic non-centrosymmetric interlayer are studied. We derive an analytical solution for the magnetization dynamics induced by an arbitrary current pulse and formulate the criteria for magnetization reversal. Using the obtained results, the form and duration of the current pulse are optimized. The agreement between analytical and numerical investigations is reached in the case of a large product of the ratio Josephson to magnetic energy, strength of spin-orbit interaction and a minimal value of the current pulse. The obtai…
In superconductors with three or more bands, time-reversal symmetry (TRS) may be broken in the presence of repulsive interband couplings, resulting in a pair of degenerate states characterized by opposite chiralities. We consider a Josephson junction between a three-band superconductor with broken TRS and a single-band superconductor. Phenomena such as asymmetric critical currents, subharmonic Shapiro steps and symmetric Fraunhhofer patterns are revealed theoretically. Existing experimental results are discussed in terms of the present work.
We study a magnetization reversal by an electric current pulse in a superconductor/insulating ferromagnet/superconductor Josephson junction placed on top of a 3D topological insulator. It is demonstrated that such a system is perspective for low-dissipative spintronics because of the strong spin-momentum locking in the TI surface states. This property provides an ideally strong coupling between the orbital and spin degrees of freedom thus giving a possibility of efficient reversal of the magnetic moment by current pulse with amplitude lower than the critical current, that results in strongly r…
Usually, the superconducting quantum interference device (SQUID) consists of two Josephson junctions and the interference therein is modulated by a magnetic flux. In this work, we propose an electrically modulated SQUID consisting of single Josephson junction coupled by a time-reversal breaking Weyl semimetal thin film. For a low Fermi energy, the Josephson current is only mediated by Fermi arc surface states, and has an arbitrary ground-state phase difference \phi0 which is directly proportional to the product of the transverse electric field and the cross section area of the junction.For a s…
Sr$_{2}$RuO$_{4}$ is one of the most promising candidates of a topological superconductor with broken time-reversal symmetry, because a number of experiments have revealed evidences for a spin-triplet chiral $p$-wave superconductivity. In order to clarify the time-reversal symmetry of Sr$_{2}$RuO$_{4}$, we introduce a novel test that examines the invariance of the Josephson critical current under the inversion of both the current and magnetic fields, in contrast to the detection of a spontaneous magnetic field employed in past experiments. Analyses of the transport properties of the planar and…
Exotic superconductors, such as high T$_C$, topological, and heavy-fermion superconductors, require phase sensitive measurements to determine the underlying pairing. Here we investigate the proximity-induced superconductivity in nanowires of SnTe, where an $s\pm is^{\prime}$ superconducting state is produced that lacks the time-reversal and valley-exchange symmetry of the parent SnTe. This effect, in conjunction with a ferroelectric distortion of the lattice at low temperatures, results in a marked alteration of the properties of Josephson junctions fabricated using SnTe nanowires. This work e…
A detailed numerical study on the directed motion of ac-driven vortices and antivortices in 2D Josephson junction arrays (JJA) with an asymmetric periodic pinning potential is reported. Dc-voltage rectification shows a strong dependence on vortex density as well as an inversion of the vortex flow direction with ac amplitude for a wide range of vortex density around $f$=1/2 ($f$=$Ha^2 / Φ_0$), in good agreement with recent experiments by Shalóm and Pastoriza [Phys. Rev. Lett. {\bf 94}, 177001 (2005)]. The study of vortex structures, spatial and temporal correlations, and vortex-antivortex pairs…
We consider a simple model of a multidomain superconductor-ferromagnet-superconductor (SFS) Josephson junction. Sign-alternating magnetization $M$ in domains leads to a spatial modulation of the phase difference $ϕ(x)$. Due to this modulation the Josephson critical current $I_{c}$ may have a different sign depending on the ratio of the magnetic flux in a domain, 4$πMa(2d_{F}),$ to the magnetic flux quantum. This phase modulation, but not a nonmonotonic dependence of the local critical current density $j_{c}$, may be the reason for oscillations of the current $I_{c}$ {\bf \}as a function of the…
We report the first experimental observation of the two-node thickness dependence of the critical current in Josephson junctions with a ferromagnetic interlayer. Vanishings of the critical current correspond to transitions into pi-state and back into conventional 0-state. The experimental data allow to extract the superconducting order parameter oscillation period and the pair decay length in the ferromagnet. We develope a theoretical approach based on Usadel equations, which takes into account the spin-flip scattering. Results of numerical calculations are in good agreement with the experimen…
We present an experimental and theoretical study of row switching in two-dimensional Josephson junction arrays. We have observed novel dynamic states with peculiar percolative patterns of the voltage drop inside the arrays. These states were directly visualized using laser scanning microscopy and manifested by fine branching in the current-voltage characteristics of the arrays. Numerical simulations show that such percolative patterns have an intrinsic origin and occur independently of positional disorder. We argue that the appearance of these dynamic states is due to the presence of various m…
We consider a Rashba spin-orbit coupled nanowire with anisotropic spin-singlet superconducting pairing and time-reversal-invariant symmetry. We explore the evolution of the topological superconducting phases of this system due to geometric deformations for the representative case of a wire bent in a semielliptical shape. We find that when the system is in its topological superconducting phase, strong inhomogeneities in the profile curvature can produce a pair of localized eigenmodes, which can be attributed to a nonuniform topological phase. The curved geometric profile also allows to tune the…
A Josephson junction consisting of an Anderson impurity weakly coupled with two-band and single-band superconductors exposes a time reversal breaking ground state when the coupling between the two bands exceeds a certain threshold. The critical regime occurs around local moment formation. This indicates a fundamental and distinct role of strong correlations: Driving a system into a time reversal breaking ground state. One of the observable consequences is that the impurity magnetization in this phase is reduced.
Josephson current between two superconductors provides a phase sensitive tool for probing their pairing symmetries. Here we fabricate and study experimentally high-quality Josephson junctions between a conventional s-wave superconductor Nb and a multi-band iron-pnictide Ba$_{1-x}$Na$_x$Fe$_2$As$_2$. Junctions exhibit a large enough critical current density to preclude the d-wave symmetry of the order parameter in the pnictide. However, the $I_cR_n$ product is very small $\simeq 3~μ$V, which is not consistent with the sign-preserving $s_{++}$ symmetry either. We argue that the small $I_cR_n$ va…
We discuss the problem of broken time reversal symmetry near grain boundaries in a d-wave superconductor based on a Ginzburg-Landau theory. It is shown that such a state can lead to fractional vortices on the grain boundary. Both analytical and numerical results show the structure of this type of state.
We study spontaneous time-reversal symmetry breaking at Josephson tunnel junctions of d-wave superconductors in the absence of subdominant components of the order parameter. For tunnel junctions, when the orientation is close to 0/45 (for which a gap lobe points towards the junction on one side and a gap node on the other), the mechanism of the symmetry breaking is the splitting of midgap states (MGS) by spontaneous establishment of a phase difference $ϕ=\pm π/2$ across the junction. This occurs for transparencies $D\ggξ_0/λ$ and temperatures $k_BT\ll DΔ_0$, where $ξ_0$ is the coherence length…
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 show that under certain conditions multiband superconductors with broken time-reversal symmetry have a new vortex viscosity-generating mechanism which is different from that in conventional superconductors. It appears due to the existence of mixed superfluid phase-density mode inside vortex core. This new contribution is dominant near the time reversal symmetry breaking phase transition. The results could be relevant for three band superconductor $Ba_{1-x}K_{x}Fe_2As_2$.
Spatial distributions of spontaneous magnetic fields near a surface of cuprate high-$T_C$ superconductor YBCO with broken time-reversal symmetry are calculated using the Ginzburg-Landau theory derived from the $t-J$ model. It is found that the magnetic field exists in a narrow region inside the superconductor, and it decays quickly outside the surface. Experimental approaches possible to detect such spontaneous magnetic fields are discussed.
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 cal…
We present experimental observation of broken-symmetry states in a superconducting loop with three Josephson junctions. These states are generic for discrete breathers in Josephson ladders. The existence region of the breather-like states is found to be in good accordance with the theoretical expectations. We observed three different resonant states in the current-voltage characteristics of the broken-symmetry state, as predicted by theory. The experimental dependence of the resonances on the external magnetic field is studied in detail.
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…
Comment on "High Resolution Polar Effect Measurements of Sr2RuO4: Evidence for Broken Time-Reversal Symmetry in the Superconducting State" by J. Xia et al., Phys. Rev. Lett. 97, 167002 (2006).
Polar Kerr effect in the spin-triplet superconductor Sr2RuO4 was measured with high precision using a Sagnac interferometer with a zero-area Sagnac loop. We observed non-zero Kerr rotations as big as 65 nanorad appearing below Tc in large domains. Our results imply a broken time reversal symmetry state in the superconducting state of Sr2RuO4, similar to He3-A.
Time-reversal-invariant topological superconductor (TRITOPS) wires host Majorana Kramers pairs that have been predicted to mediate a fractional Josephson effect with $4π$ periodicity in the superconducting phase difference. We explore the TRITOPS fractional Josephson effect in the presence of time-dependent `local mixing' perturbations that instantaneously preserve time-reversal symmetry. Specifically, we show that just as such couplings render braiding of Majorana Kramers pairs non-universal, the Josephson current becomes either aperiodic or $2π$-periodic (depending on conditions that we quan…
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…
Conventional superconductors are strong diamagnets that through the Meissner effect expel magnetic fields. It would therefore be surprising if a superconducting ground state would support spontaneous magnetics fields. Such time-reversal symmetry broken states have been proposed for the high-temperature superconductors, but their identification remains experimentally controversial. Here we show a route to a low-temperature superconducting state with broken time-reversal symmetry that may accommodate currently conflicting experiments. This state is characterised by an unusual vortex pattern in t…
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 …
Broken time reversal symmetry (BTRS) in d wave superconductors is studied and is shown to yield current carrying surface states. The corresponding spontaneous magnetization is temperature independent near the critical temperature Tc for weak BTRS, in accord with recent data. For strong BTRS and thin films we expect a temperature dependent spontaneous magnetization with a paramagnetic anomaly near Tc. The Hall conductance is found to vanish at zero wavevector q and finite frequency w, however at finite q,w it has an unusual structure.
Broken time reversal symmetry (BTRS) in d+id' as well as in d+is superconductors is studied and is shown to yield current carrying surface states. We evaluate the temperature and thickness dependence of the resulting spontaneous magnetization and show a marked difference between weak and strong BTRS. We also derive the Hall conductance which vanishes at zero wavevector q and finite frequency w, however at finite q,w it has an unusual structure. The chirality of the surface states leads to quantum Hall effects for spin and heat transport in d+id' superconductors.
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…
Bulk TiSe$_2$ is an intrinsically layered transition metal dichalcogenide (TMD) hosting both superconducting and charge density wave (CDW) ordering. Motivated by the recent progress in preparing two-dimensional TMDs, we study these frustrated orderings in {\it single} trilayer of TiSe$_2$ within a renormalization group approach. We establish that a novel state with time-reversal symmetry broken chiral superconductivity can emerge from the strong competition between CDW formation and superconductivity. Its stability depends on the precise strength and screening of the electron-electron interact…
We demonstrate that films of unconventional (d-wave) superconductor at temperatures $T\lesssim 0.43 T_c$ can exhibit unusual superconducting phases. The new ground states beside the broken gauge and the point group symmetries can spontaneously break (i) continuous translational symmetry and form periodic order parameter structures in the plane of the film, or (ii) time-reversal symmetry and develop supercurrent flowing along the film. These states are result of the strong transverse inhomogeniety present in films with thickness of several coherence lengths. We show a natural similarity between…
In three-band BCS superconductors with repulsive interband interactions, frustration between the bands can lead to an inherently complex gap function, arising out of a phase difference between the bands in the range 0 and π. Since the complex conjugate of this state is also a solution, the ground state is degenerate, and there appears a time-reversal-symmetry-broken state. In this paper we investigate the existence of this state as a function of interband coupling strength and show how a new phase transition appears between the TRSB and conventional BCS states.
Motivated by recent progress in the superconductivity nonreciprocal phenomena, we study the general theory of Josephson diodes. The central ingredient for Josephson diodes is the asymmetric proximity process inside the tunneling barrier. From the symmetry breaking point of view, there are two types of Josephson diodes, inversion breaking and time-reversal breaking. For the inversion breaking case, applying voltage bias could effectively tune the proximity process like the voltage-dependent Rashba coupling or electric polarization giving rise to $I_c(V)\neq I_c(-V)$ and $I_{r+}\neq I_{r-}$. For…
A detailed analysis of the symmetric tetracrystal geometry used in phase-sensitive pairing symmetry experiments on high Tc superconductors is carried out for both bulk and surface time-reversal symmetry-breaking states, such as the d+id' and d+is states. The results depend critically on the substrate geometry. In the general case, for the bulk d+id' (or d+is) state, the measured flux quantization should in general not be too different from that obtained in the pure d-wave case, provided |d'| << |d| (or |s| << |d|). However, in one particular high symmetry geometry, the d+id' state gives result…
Using Monte Carlo simulations, we explore the phase diagram and the phase transitions in $\groupUZ$ $n$-band superconductors with spontaneously broken time-reversal symmetry (also termed $s+is$ superconductors), focusing on the three-band case. In the limit of infinite penetration length, the system under consideration can, for a certain parameter regime, have a single first order phase transition from a $\groupUZ$ broken state to a normal state due to a nontrivial interplay between $\groupU$ vortices and $\groupZ$ domain walls. This regime may also apply to multicomponent superfluids. For oth…
Type II Lifshitz invariant and optically active Higgs mode in time-reversal symmetry broken superconductors
Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院凝聚态理论研究所）；Department of Physics, University of Tokyo（东京大学物理学系）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Trans-Scale Quantum Science Institute, University of Tokyo（东京大学跨尺度量子科学研究所）
We report point contact Andreev Reflection (PCAR) measurements on a high-quality single crystal of the non-centrosymmetric superconductor Re6Zr. We observe that the PCAR spectra can be fitted by taking two isotropic superconducting gaps with Delta_1 ~ 0.79 meV and Delta_2 ~ 0.22 meV respectively, suggesting that there are at least two bands which contribute to superconductivity. Combined with the observation of time reversal symmetry breaking at the superconducting transition from muon spin relaxation measurements (Phys. Rev. Lett. 112, 107002 (2014)), our results imply an unconventional super…
Over the last years a lot of theoretical and experimental efforts have been made to find states with broken time reversal symmetry (BTRS) in multi-band superconductors. In particular, it was theoretically proposed that in the Ba$_{1-x}$K$_{x}$Fe$_2$As$_2$ system either an $s+is$ or an $s+id$ BTRS state may exist at high doping levels in a narrow region of the phase diagram. Here we report the observation of an enhanced zero field muon spin relaxation rate below the superconducting transition temperature for a high quality crystalline sample with $x \approx$ 0.73. This indicates that indeed the…
Electric Control of Polarity in Spin-Orbit Josephson Diode
Pohang University of Science and Technology (POSTECH)（浦项科技大学）；Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；Center for Theoretical Physics of Complex Systems, Institute of Basic Science (IBS)（基础科学研究院复杂系统理论物理中心）；University of Tennessee（田纳西大学）；Quantum Technology Institute, Korea Research Institute of Standards and Science (KRISS)（韩国标准科学研究所量子技术研究所）
The symmetry properties of the order parameter characterize different phases of unconventional superconductors. In the case of the heavy-fermion superconductor UPt$_3$, a key question is whether its multiple superconducting phases preserve or break time-reversal symmetry (TRS). We tested for asymmetry in the phase shift between left and right circularly polarized light reflected from a single crystal of UPt$_3$ at normal incidence, finding that this so-called polar Kerr effect appears only below the lower of the two zero-field superconducting transition temperatures. Our results provide eviden…
We report the results of a search for spontaneous magnetism due to a time reversal symmetry breaking phase in the superconducting state of (110)-oriented YBCO films, expected near the surface in this geometry. Zero field and weak transverse field measurements performed using the low-energy muon spin rotation technique with muons implanted few nm inside optimally-doped YBCO-(110) films show no appearance of spontaneous magnetic fields below the superconducting temperature down to 2.9 K. Our results give an upper limit of ~0.02 mT for putative spontaneous internal fields.
Due to the absence of a center of inversion in some superconducting compounds, a p-wave admixture to the dominant d-wave order parameter must exist. If time-reversal is also violated, an allowed invariant is the product of the d-wave, p-wave and an appropriately directed current. We show that this leads to an anomalous Josephson current for tunneling along the direction parallel to the axis of the p-wave component, where the current is the Meissner current and the Josephson loop current along the surface of the tunnel barrier. These ideas are applied to the superconducting state of the cuprate…
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.…
The cryptoferromagnetic state (the state with intrinsic domain structure) in superconducting ferromagnets subjected to external magnetic field is studied theoretically. Ferromagnetism originates either from electron spin or the intrinsic angular momentum of Cooper pairs (chiral p-wave superconductors like $\mathrm{Sr_2 Ru O_4}$). The phase transitions towards the Meissner and the mixed states are investigated, and the magnetic phase diagrams are obtained. Cryptoferromagnetism, as a form coexistence of superconductivity and ferromagnetism, can be detected by observation of magnetization curves …
