Nonlinear $\sigma$-model for disordered systems with intrinsic spin-orbit coupling

Abstract

We derive the nonlinear $\sigma$-model to describe diffusive transport in normal metals and superconductors with intrinsic spin-orbit coupling (SOC). The SOC is described via an SU(2) gauge field, and we expand the model to the fourth order in gradients to find the leading non-Abelian field-strength contribution. This contribution generates the spin-charge coupling that is responsible for the spin-Hall effect. We discuss how its symmetry differs from the leading quasiclassical higher-order gradient terms. We also derive the corresponding Usadel equation describing the diffusive spin-charge dynamics in superconducting systems. As an example, we apply the obtained equations to describe the anomalous supercurrent in dirty Rashba superconductors at arbitrary temperatures.

13 pages + supplementary material

References in corpus (15)

• Anderson Transitions
• An Exact SU(2) Symmetry and Persistent Spin Helix in a Spin-Orbit Coupled System
• A Josephson junction supercurrent diode
• Direct coupling between magnetism and superconducting current in Josephson Phi junction
• Intrinsic Superconducting Diode Effect
• A phenomenological theory of superconductor diodes
• Universal Josephson diode effect
• Theory of the supercurrent diode effect in Rashba superconductors with arbitrary disorder
• Observation of Inverse Edelstein Effect in Rashba-Split 2DEG between SrTiO3 and LaAlO3 at Room Temperature
• Non-Abelian gauge fields in the gradient expansion: generalized Boltzmann and Eilenberger equations
• Effective field theory of the disordered Weyl semimetal
• Theory of coupled spin-charge transport due to spin-orbit interaction in inhomogeneous two-dimensional electron liquids
• Strong interfacial exchange field in a heavy metal/ferromagnetic insulator system determined by spin Hall magnetoresistance
• Multifractally-enhanced superconductivity in thin films
• Non-linear sigma model with particle-hole asymmetry for the disordered two-dimensional electron gas

Cited by in corpus (11)

• Superconducting diode effect in diffusive superconductors and Josephson junctions with Rashba spin-orbit coupling
• Quantum transport theory for unconventional magnets: Interplay of altermagnetism and p-wave magnetism with superconductivity
• Nonreciprocal superconducting transport and the spin Hall effect in gyrotropic structures
• Magnetoelectric effects in diffusive two-dimensional superconductors studied by the nonlinear $\sigma$ model
• Dynamical Hall responses of disordered superconductors
• Spin-split superconductivity in spin-orbit coupled hybrid nanowires with ferromagnetic barriers
• Interfacial spin-orbit coupling in superconducting hybrid systems
• Interplay between Superconductivity and Altermagnetism in Disordered Materials and Heterostructures
• Superconducting Diode Effect in Weak Localization Regime
• Quantum Altermagnetic Instability in Disordered Metals
• Josephson anomalous vortices