Theory of the spin-galvanic effect and the anomalous phase-shift ${\phi }_0$ in superconductors and Josephson junctions with intrinsic spin-orbit coupling

Abstract

Due to the spin-orbit coupling (SOC) an electric current flowing in a normal metal or semiconductor can induce a bulk magnetic moment. This effect is known as the Edelstein (EE) or magneto-electric effect. Similarly, in a bulk superconductor a phase gradient may create a finite spin density. The inverse effect, also known as the spin-galvanic effect, corresponds to the creation of a supercurrent by an equilibrium spin polarization. Here, by exploiting the analogy between a linear-in-momentum SOC and a background SU(2) gauge field, we develop a quasiclassical transport theory to deal with magneto-electric effects in superconducting structures. For bulk superconductors this approach allows us to easily reproduce and generalize a number of previously known results. For Josephson junctions we establish a direct connection between the inverse EE and the appearance of an anomalous phase-shift ${\phi }_0$ in the current-phase relation. In particular we show that ${\phi }_0$ is proportional to the equilibrium spin-current in the weak link. We also argue that our results are valid generically, beyond the particular case of linear-in-momentum SOC. The magneto-electric effects discussed in this study may find applications in the emerging field of coherent spintronics with superconductors.

v1: article version of the preprints arXiv:1408.4533 and arXiv:1409.4563 in letter format, with far more results and details. v2: some typos and mistakes corrected, new presentation of the derivation at all temperature in the ballistic regime (section VI), including a new fig.2 to illustrate this section. v3: accepted version, with extra references

References in corpus (86)

• Spin Hall effect
• Proximity effects in superconductor-ferromagnet heterostructures
• Odd Triplet Superconductivity and Related Phenomena in Superconductor-Ferromagnet Structures
• Direct electronic measurement of the spin Hall effect
• Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system
• Spin Seebeck insulator
• Coupling of two superconductors through a ferromagnet : evidence for a pi-junction
• Superconducting Spintronics
• Room Temperature Reversible Spin Hall Effect
• Superconducting 2D system with lifted spin degeneracy: Mixed singlet-triplet state
• Observation of spin-triplet superconductivity in Co-based Josephson Junctions
• Manipulation of Majorana fermion, Andreev reflection and Josephson current on topological insulators
• Spin current and polarization in impure 2D electron systems with spin-orbit coupling
• Current induced electron spin polarization in strained semiconductors
• Direct coupling between magnetism and superconducting current in Josephson Phi junction
• Indication of intrinsic spin Hall effect in 4d and 5d transition metals
• Inverse Edelstein Effect
• Temperature dependence of spin diffusion length and spin Hall angle in Au and Pt
• Anomalous Josephson effect induced by spin-orbit interaction and Zeeman effect in semiconductor nanowires
• Enhancement of the Josephson current by an exchange field in superconductor-ferromagnet structures
• Fully developed triplet proximity effect
• Josephson current in superconductor-ferromagnet structures with a nonhomogeneous magnetization
• Spin-orbit coupling as a source of long-range triplet proximity effect in superconductor-ferromagnet hybrid structures
• Evidence for Triplet Superconductivity in a Superconductor-Ferromagnet Spin Valve
• Anomalous Josephson Current in Junctions with Spin-Polarizing Quantum Point Contacts
• Symmetries of Pairing Correlations in Superconductor-Ferromagnet Nanostructures
• 2D superconductivity with strong spin-orbit interaction
• Anomalous Josephson current through a spin-orbit coupled quantum dot
• Huge thermoelectric effects in ferromagnet-superconductor junctions in the presence of a spin-splitting field
• Josephson junctions with negative second harmonic in the current-phase relation: properties of novel varphi-junctions
• Singlet-triplet conversion and the long-range proximity effect in superconductor-ferromagnet structures with generic spin dependent fields
• Periodic alternating $0,\pi$-junction structures as realization of $\varphi$-Josephson junctions
• Topological Josephson ${\varphi }_0$-junctions
• Magnetic moment manipulation by a Josephson current
• Experimental evidence of a ϕ Josephson junction
• Enhancement of the superconducting transition temperature in Nb/Permalloy bilayers by controlling the domain state of the ferromagnet
• Optimization of spin-triplet supercurrent in ferromagnetic Josephson junctions
• Equilibrium spin currents: Non-Abelian gauge invariance and color diamagnetism in condensed matter
• Spin-dependent Cooper Pair Phase and Pure Spin Supercurrents in Strongly Polarized Ferromagnets
• Spontaneous supercurrent induced by ferromagnetic pi-junctions
• Inverse spin switch effects in Ferromagnet / Superconductor hybrids with strong ferromagnets
• Non-sinusoidal current-phase relationship in Josephson junctions from the 3D topological insulator HgTe
• Josephson current in s-wave superconductor / Sr_2RuO_4 junctions
• Anomalous Josephson current, incipient time-reversal symmetry breaking, and Majorana bound states in interacting multi-level dots
• Reversible control of spin-polarised supercurrents in ferromagnetic Josephson junctions
• Quasiclassical approach to the spin-Hall effect in the two-dimensional electron gas
• Spin-orbit interaction in a two-dimensional electron gas: a SU(2) formulation
• Long range spin supercurrents in ferromagnetic CrO${}_2$ using a multilayer contact structure
• Josephson junction with magnetic-field tunable ground state
• Non-Abelian gauge fields in the gradient expansion: generalized Boltzmann and Eilenberger equations
• Spin Orbit coupling and Anomalous Josephson effect in Nanowires
• Spin-orbit induced chirality of Andreev states in Josephson junctions
• Anomalous Josephson current through a ferromagnetic trilayer junction
• Spin relaxation in a generic two-dimensional spin-orbit coupled system
• Pure 2nd harmonic current phase relation in Spin filter Josephson junctions
• Scanning tunneling spectroscopy study of the proximity effect in a disordered two-dimensional metal
• Magnonic Charge Pumping via Spin-Orbit Coupling
• Spin Supercurrent, Magnetization Dynamics, and Phi-State in Spin-Textured Josephson Junctions
• Angular dependence of superconductivity in superconductor / spin valve heterostructures
• Influence of the Rashba effect on the Josephson current through a superconductor/Luttinger liquid/superconductor tunnel junction
• Macroscopic quantum tunneling in spin filter ferromagnetic Josephson junctions
• Spin-Hall effect on edge magnetization and electric conductance of a 2D semiconductor strip
• Zero Energy Peak and Triplet Correlations in Nanoscale SFF Spin-Valves
• Electronic transport through ferromagnetic and superconducting junctions with spin-filter tunneling barriers
• Peculiar properties of the Josephson junction at the transition from 0 to Pi state
• Josephson Current through Semiconductor Nanowire with Spin-Orbit Interaction in Magnetic Field
• Proposal for a phase-coherent thermoelectric transistor
• Spontaneous Edge Accumulation of Spin Currents in Finite-Size Two-Dimensional Diffusive Spin-Orbit Coupled SFS Heterostructures
• Interplay of ferromagnetism and triplet superconductivity in a Josephson junction
• Nonuniform states in noncentrosymmetric superconductors
• Very large thermophase in ferromagnetic Josephson junctions
• Josephson interferometer in a ring topology as a symmetry prove of Sr_2RuO_4
• Spin Triplet Supercurrent in Co/Ni Multilayer Josephson Junctions with Perpendicular Anisotropy
• Double path interference and magnetic oscillations in Cooper pair transport through a single nanowire
• Anomalous double peak structure in Nb/Ni superconductor/ferromagnet tunneling DOS
• Spectroscopy and critical temperature of diffusive superconducting/ferromagnetic hybrid structures with spin-active interfaces
• Supra-oscillatory critical temperature dependence of Nb-Ho bilayers
• Spin-polarized Josephson and quasiparticle currents in superconducting spin-filter tunnel junctions
• Transport equations for superconductors in the presence of spin interaction
• Spin-Hall effects in a Josephson contact
• Proximity-induced density-of-states oscillations in a superconductor/strong-ferromagnet system
• Dynamic spin-Hall effect and driven spin helix for linear spin-orbit interactions
• Classical Yang-Mills theory in condensed matter physics
• Phase-dependent heat transport through magnetic Josephson tunnel junctions
• Magnetic anisotropy of critical current in nanowire Josephson junction with spin-orbit interaction
• Manifestation of a spin-splitting field in a thermally-biased Josephson junction

Cited by in corpus (110)

• A Josephson junction supercurrent diode
• Josephson ${\phi }_0$-junction in nanowire quantum dots
• Theory of the supercurrent diode effect in Rashba superconductors with arbitrary disorder
• Colloquium: Nonequilibrium effects in superconductors with a spin-splitting field
• Spin-Orbit induced phase-shift in Bi${}_2$Se${}_3$ Josephson junctions
• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Gate Controlled Anomalous Phase Shift in Al/InAs Josephson Junctions
• Microwave spectroscopy of spinful Andreev bound states in ballistic semiconductor Josephson junctions
• Thermal, electric and spin transport in superconductor/ferromagnetic-insulator structures
• Magnetoelectrics in Disordered Topological Insulator Josephson Junctions
• Effect of Rashba and Dresselhaus spin-orbit coupling on supercurrent rectification and magnetochiral anisotropy of ballistic Josephson junctions
• Anomalous current in diffusive ferromagnetic Josephson junctions
• Hybrid helical state and superconducting diode effect in S/F/TI heterostructures
• Proximity-induced triplet superconductivity in Rashba materials
• Microscopic study of the Josephson supercurrent diode effect in Josephson junctions based on two-dimensional electron gas
• Geometry controlled superconducting diode and anomalous Josephson effect triggered by the topological phase transition in curved proximitized nanowires
• Triplet proximity effect in superconducting heterostructures with a half-metallic layer
• Field-free anomalous junction and superconducting diode effect in spin split superconductor/topological insulator junctions
• Tunable Anomalous Andreev Reflection and Triplet Pairings in Spin Orbit Coupled Graphene
• A cryogenic memory element based on an anomalous Josephson junction
• Sign reversal of the AC and DC supercurrent diode effect and 0-$\pi$-like transitions in ballistic Josephson junctions
• Generation of a superconducting vortex via Néel skyrmions
• Quasiclassical theory of magnetoelectric effects in superconducting heterostructures in the presence of the spin-orbit coupling
• Ferromagnetic Materials for Josephson π Junctions
• Ferromagnetic resonance and magnetic precessions in ${\phi }_0$ junction
• Manifestation of extrinsic spin Hall effect in superconducting structures: Non-dissipative magnetoelectric effects
• Creation of spin-triplet Cooper pairs in the absence of magnetic ordering
• Generalized quasiclassical theory of the long-range proximity effect and spontaneous currents in superconducting heterostructures with strong ferromagnets
• Colossal orbital-Edelstein effect in non-centrosymmetric superconductors
• Magnetoelectric effects in Josephson junctions
• Resistive state of SFS Josephson junctions in the presence of moving domain walls
• Zeeman and spin-orbit effects in the Andreev spectra of nanowire junctions
• Quasiclassical theory of superconducting spin-splitter effects and spin-filtering via altermagnets
• Usadel equation in the presence of intrinsic spin-orbit coupling: A unified theory of magneto-electric effects in normal and superconducting systems
• Thermal noise effects on the magnetization switching of a ferromagnetic anomalous Josephson junction
• Magnetoelectric Andreev effect due to proximity-induced non-unitary triplet superconductivity in helical metals
• Mechanism of generation of a Josephson phase shift by an Abrikosov vortex
• Anomalous phase shift in a Josephson junction via an antiferromagnetic interlayer
• Electrical control of magnetization in S/F/S junctions on a 3D topological insulator
• Analytical criteria for magnetization reversal in ${\phi }_0$ Josephson junction
• Influence of the impurity scattering on charge transport in unconventional superconductor junctions
• ${\phi }_0$-Josephson junction in twisted bilayer graphene induced by a valley-polarized state
• Microwave spectroscopy of interacting Andreev spins
• Spin supercurrent in two-dimensional superconductors with Rashba spin-orbit interaction
• Quantum Tunneling of the Magnetic Moment in the S/F/S Josephson ${\mathbf{\phi }}_0$-Junction
• Magnetization reversal in S/F/S Josephson junctions on a 3D topological insulator
• Charge transport through spin-polarized tunnel junction between two spin-split superconductors
• Odd triplet superconductivity induced by the moving condensate
• Ballistic Josephson junctions in the presence of generic spin dependent fields
• rf-SQUID measurements of anomalous Josephson effect
• Superconducting diode effect in diffusive superconductors and Josephson junctions with Rashba spin-orbit coupling
• Nonlinear $\sigma$-model for disordered systems with intrinsic spin-orbit coupling
• Chirality selective spin interactions mediated by the superconducting current
• Spin-orbit-enhanced robustness of supercurrent in graphene/WS${}_2$ Josephson junctions
• Locking of magnetization and Josephson oscillations at ferromagnetic resonance in ${\phi }_0$ junction under external radiation
• Switchable Josephson current in junctions with spin-orbit coupling
• Supercurrent generation by spin injection in an s-wave superconductor-Rashba metal bilayer
• Supercurrent Induced Charge-Spin Conversion in Spin-Split Superconductors
• Zeeman and Orbital Driven Phase Transitions in Planar Josephson Junctions
• Geometry -- dependent effects in Majorana nanowires
• Semiclassical quantization of spinning quasiparticles in ballistic Josephson junctions
• Anisotropic vortex squeezing in synthetic Rashba superconductors: a manifestation of Lifshitz invariants
• Nonreciprocal superconducting transport and the spin Hall effect in gyrotropic structures
• Switching current distributions in ferromagnetic anomalous Josephson junctions
• Anomalous Josephson effect in planar noncentrosymmetric superconducting devices
• Tunable superconducting critical temperature in ballistic hybrid structures with strong spin-orbit coupling
• Magnetization Reversal by Tuning Rashba Spin-Orbit Interaction and Josephson Phase in a Ferromagnetic Josephson Junction
• Controlling spin supercurrents via nonequilibrium spin injection
• Theory of magnetic response in finite two-dimensional superconductors
• Long-range interaction of magnetic moments in a coupled system of S/F/S Josephson junctions with anomalous ground-state phase shift
• Dissipationless Nonlinearity in Quantum Material Josephson Diodes
• Manipulating Magnetic Moments by Superconducting Currents
• Proximity effect in a ferromagnetic semiconductor with spin-orbit interactions
• Anomalous supercurrent modulated by interfacial magnetizations in Josephson junctions with ferromagnetic bilayers
• Nonreciprocal Josephson linear response
• Giant spin splitting and $0-\pi$ Josephson transitions from the Edelstein effect in quantum spin-Hall insulators
• Supercurrent Vortex Pinball via a Triplet Cooper Pair Inverse Edelstein Effect
• Anomalous Josephson Effect in Topological Insulator-Based Josephson Trijunction
• Direct and inverse superspin Hall effect in two-dimensional systems: Electrical detection of spin supercurrents
• Magnetoelectric effects in superconductor/ferromagnet bilayers
• Unconventional Josephson supercurrent diode effect induced by chiral spin-orbit coupling
• Anomalous Josephson diode effect in superconducting multilayers
• Controllable magnetic states in chains of coupled phi-0 Josephson junctions with ferromagnetic weak links
• Generation of polarized spin-triplet Cooper pairings by magnetic barriers in superconducting junctions
• Nonlocal magnetolectric effects in diffusive conductors with spatially inhomogeneous spin-orbit coupling
• Manifestations of spin-orbit coupling in a cuprate superconductor
• A Unified Description of Spin Transport, Weak Antilocalization and Triplet Superconductivity in Systems with Spin-Orbit Coupling
• Spontaneous generation of vortices by a nonuniform Zeeman field in a two-dimensional Rashba coupled superconductor
• Supercurrent vortices and Majorana zero modes induced by an inplane Zeeman field on the surface of a three-dimensional topological insulator
• Long-range effect of a Zeeman field on the electric current through the helical metal-superconductor interface in Andreev interferometer
• Interplay between superconductivity and spin-dependent fields in nanowire-based systems
• Magnetic eigenmodes in chains of coupled phi0-Josephson junctions with ferromagnetic weak links
• Magnetoelectric effects in diffusive two-dimensional superconductors studied by the nonlinear $\sigma$ model
• Proximity Effect in Superconducting Heterostructures with Strong Spin-Orbit Coupling and Spin Splitting
• Spin and orbital Edelstein effect in spin-orbit coupled noncentrosymmetric superconductor
• Probing the magnetoelectric effect in noncentrosymmetric superconductors by equal-spin Andreev tunneling
• Fraunhofer oscillations of the critical current at a varying Zeeman field in a spin-orbit coupled Josephson junction
• Correspondence between bulk equilibrium spin-currents and edge spin accumulation in wires with spin-orbit coupling
• Dynamical Hall responses of disordered superconductors
• Anisotropic differential conductance of a mixed parity superconductor/ferromagnet structure
• Signatures of Long-Range Spin-Triplet Component in Andreev Interferometer
• Anomalous Andreev interferometer: Study of an anomalous Josephson junction coupled to a normal wire
• Asymmetric Fraunhofer pattern in Josephson junctions from heterodimensional superlattice V${}_5$S${}_8$
• Interfacial spin-orbit coupling in superconducting hybrid systems
• Non uniform superconductivity in wires with strong spin-orbit coupling
• Inverse spin galvanic effect in proximitized superconductor/paramagnet systems
• Perspectives on Magnetic/Superconductor Hybrid Systems: Long-range Electromagnetic Phenomena Induced by Proximity Effect and Interfacial Spin-orbit Coupling
• Anomalous phase shift and superconducting diode effect in Josephson junctions via thin films of rare-earth intermetallic magnets
• Gradient expansion of the non-Abelian gauge-covariant Moyal star-product
• Originality of resonance and locking phenomena in SFS ${\phi }_0$ Josephson junction