A Unified Description of Spin Transport, Weak Antilocalization and Triplet Superconductivity in Systems with Spin-Orbit Coupling

Abstract

The Eilenberger equation is a standard tool in the description of superconductors with an arbitrary degree of disorder. It can be generalized to systems with linear-in-momentum spin-orbit coupling (SOC), by exploiting the analogy of SOC with a non-abelian background field. Such field mixes singlet and triplet components and yields the rich physics of magnetoelectric phenomena. In this work we show that the application of this equation extends further, beyond superconductivity. In the normal state, the linearized Eilenberger equation describes the coupled spin-charge dynamics. Moreover, its resolvent corresponds to the so called Cooperons, and can be used to calculate the weak localization corrections. Specifically, we show how to solve this equation for any source term and provide a closed-form solution for the case of Rashba SOC. We use this solution to address several problems of interest for spintronics and superconductivity. Firstly, we study spin injection from ferromagnetic electrodes in the normal state, and describe the spatial evolution of spin density in the sample, and the complete crossover from the diffusive to the ballistic limit. Secondly, we address the so-called superconducting Edelstein effect, and generalize the previously known results to arbitrary disorder. Thirdly, we study weak localization correction beyond the diffusive limit, which can be a valuable tool in experimental characterization of materials with very strong SOC. We also address the so-called pure gauge case where the persistent spin helices form. Our work establishes the linearized Eilenberger equation as a powerful and a very versatile method for the study of materials with spin-orbit coupling, which often provides a simpler and more intuitive picture compared to alternative methods.

arXiv comment14 pages, 8 figures

References in corpus (55)

• Spintronics: Fundamentals and applications
• Van der Waals heterostructures
• New Perspectives for Rashba Spin-Orbit Coupling
• Graphene Spintronics
• Odd Triplet Superconductivity and Related Phenomena in Superconductor-Ferromagnet Structures
• Superconducting Spintronics
• Superconducting 2D system with lifted spin degeneracy: Mixed singlet-triplet state
• Non-ballistic spin field-effect transistor
• An Exact SU(2) Symmetry and Persistent Spin Helix in a Spin-Orbit Coupled System
• Emergence of the persistent spin helix in semiconductor quantum wells
• Superconductivity and spin-orbit coupling in non-centrosymmetric materials: a review
• Quasiclassical Green's function approach to mesoscopic superconductivity
• Spin current and polarization in impure 2D electron systems with spin-orbit coupling
• Gate-Controlled Spin-Orbit Quantum Interference Effects in Lateral Transport
• Weak Antilocalization and Spin Precession in Quantum Wells
• Direct coupling between magnetism and superconducting current in Josephson Phi junction
• Josephson ${\phi }_0$-junction in nanowire quantum dots
• Room temperature spin Hall effect in graphene/MoS${}_2$ van der Waals heterostructures
• Theory of Spin-Charge Coupled Transport in a Two-Dimensional Electron Gas with Rashba Spin-Orbit Interactions
• Direct mapping of the formation of a persistent spin helix: Supplementary information
• Odd-frequency superconductivity
• Spin-orbit coupling as a source of long-range triplet proximity effect in superconductor-ferromagnet hybrid structures
• Symmetries of Pairing Correlations in Superconductor-Ferromagnet Nanostructures
• Theoretical aspects of Andreev spectroscopy and tunneling spectroscopy in non-centrosymmetric superconductors: a topical review
• 2D superconductivity with strong spin-orbit interaction
• Tunable room-temperature spin galvanic and spin Hall effects in van der Waals heterostructures
• Theory of 2D superconductor with broken inversion symmetry
• Spin-Orbit induced phase-shift in Bi${}_2$Se${}_3$ Josephson junctions
• Theory of the spin-galvanic effect and the anomalous phase-shift ${\phi }_0$ in superconductors and Josephson junctions with intrinsic spin-orbit coupling
• A Josephson phase battery
• Gate Controlled Anomalous Phase Shift in Al/InAs Josephson Junctions
• Equilibrium spin currents: Non-Abelian gauge invariance and color diamagnetism in condensed matter
• z/-z Symmetry of spin-orbit coupling and weak localization in graphene
• Gate-tunable Spin-Galvanic Effect in Graphene Topological insulator van der Waals Heterostructures at Room Temperature
• Spin-orbit interaction in a two-dimensional electron gas: a SU(2) formulation
• Non-Abelian gauge fields in the gradient expansion: generalized Boltzmann and Eilenberger equations
• Stretchable persistent spin helices in GaAs quantum wells
• Spin relaxation in a generic two-dimensional spin-orbit coupled system
• Diffusive and precessional spin dynamics in a two-dimensional electron gas with disorder: a gauge theory view
• Gate-Tunable Reversible Rashba-Edelstein Effect in a Few-Layer Graphene/2H-TaS2 Heterostructure at Room Temperature
• Phase diagram of a surface superconductor in parallel magnetic field
• Spin-Hall effect on edge magnetization and electric conductance of a 2D semiconductor strip
• Theory of coupled spin-charge transport due to spin-orbit interaction in inhomogeneous two-dimensional electron liquids
• Dimensional Dependence of Weak Localization Corrections and Spin Relaxation in Quantum Wires with Rashba Spin-Orbit Coupling
• Duality of the spin and density dynamics for two-dimensional electrons with a spin-orbit coupling
• Usadel equation in the presence of intrinsic spin-orbit coupling: A unified theory of magneto-electric effects in normal and superconducting systems
• Spin Hall Effect in Bilayer Graphene Combined with an Insulator up to Room Temperature
• Dynamic spin-Hall effect and driven spin helix for linear spin-orbit interactions
• Symmetry Breaking of the Persistent Spin Helix in Quantum Transport
• Ballistic Josephson junctions in the presence of generic spin dependent fields
• Weak Localization, Spin Relaxation, and Spin-Diffusion: The Crossover Between Weak and Strong Rashba Coupling Limits
• Semiclassical quantization of spinning quasiparticles in ballistic Josephson junctions
• Nonlocal magnetolectric effects in diffusive conductors with spatially inhomogeneous spin-orbit coupling
• Interplay between superconductivity and spin-dependent fields in nanowire-based systems
• Spin polarization induced by an electric field in the presence of weak localization effects

Cited by in corpus (4)

• Magnetoelectric effects in Josephson junctions
• Spin supercurrent in superconductor/ferromagnet van-der-Waals heterostructures
• Spin and orbital Edelstein effect in spin-orbit coupled noncentrosymmetric superconductor
• Weak localization at arbitrary disorder strength in systems with generic spin-dependent fields