A universal phenomenology of charge-spin interconversion and dynamics in diffusive systems with spin-orbit coupling

TL;DR

This paper develops a unified effective field theory describing charge-spin interconversion and transport phenomena in diffusive metals with spin-orbit coupling, applicable to both normal and superconducting states.

Contribution

It introduces a symmetry-based phenomenological framework that captures all SOC effects in diffusive systems, extending to superconductors and hybrid interfaces.

Findings

Derivation of a quantum kinetic Usadel-type equation incorporating SOC effects.

Identification of symmetry constraints that fix the form of the effective action.

Application to phenomena like spin Hall, spin current swapping, and spin-galvanic effects.

Abstract

We present an effective field theory for a unified description of transport in normal and superconducting metals in the presence of generic spin-orbit coupling (SOC). The structure of the quantum kinetic theory in the diffusive regime is determined by a set of fundamental constraints -- charge conjugation symmetry, the causality principle, and the crystal symmetry of a material. These symmetries uniquely fix the action of the Keldysh non-linear $\sigma$ model (NLSM), which at the saddle point yields the quantum kinetic Usadel-type equation. Our phenomenological approach is reminiscent of the Ginzburg-Landau theory, but is valid for superconductors in the whole temperature range, describes the diffusive transport in the normal state, and naturally captures the effects of superconducting fluctuations. As an application, we derive the NLSM and quantum transport equations which include all effects of spin-orbit coupling, allowed by the crystal symmetry, for example, the spin Hall, spin current swapping or spin-galvanic effects. Our approach can be extended to systems with broken time reversal symmetry, as well as to the description of hybrid interfaces, where the spin-charge interconversion can be enhanced due to strong interfacial SOC.