Usadel equation in the presence of intrinsic spin-orbit coupling: A unified theory of magnetoelectric effects in normal and superconducting systems
AbstractThe Usadel equation is the standard theoretical tool for the description of superconducting structures in the diffusive limit. Here, I derive the Usadel equation for gyrotropic materials with a generic linear in momentum spin-orbit coupling. It accounts for the spin-charge/singlet-triplet coupling and in the normal state reduces to the system of spin-charge diffusion equations describing various magnetoelectric effects, such as the spin Hall effect (SHE), the spin-galvanic effect (SGE), and their inverses. Therefore the derived Usadel equation establishes a direct connection of these effects to their superconducting counterparts. The working power of the present formalism is illustrated on the example of the bulk SGE.