Universal Phenomenology of Charge-Spin Interconversion and Dynamics in Diffusive Systems with Spin-Orbit Coupling

We present 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 nonlinear σ model (NLSM), which at the saddle point yields the quantum kinetic Usadel-type equation, the equation that describes the main transport features of a system. 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 the corresponding 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 derive transport equations in 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.