2021/06/30 by P. Virtanen, F. S. Bergeret, I. V. Tokatly · 1 citation
Physics and Astronomy · #cond-mat.supr-con
paper · pdf · doi:10.1103/physrevb.104.064515
published as Phys. Rev. B 104, 064515 (2021) · 6 pages
arxiv created 2021/06/30 · arxiv updated 2021/09/02
We suggest a generalization of nonlinear σ-model for diffusive superconducting systems to account for magnetoelectric effects due to spin-orbit scattering. In the leading orders of spin-orbit strength and gradient expansion it includes two additional terms responsible for the spin-Hall effect and the spin-current swapping. First, assuming a delta-correlated disorder we derive the new terms from the Keldysh path integral representation of the generating functional. Then we argue phenomenologically that they exhaust all invariants allowed in the effective action to the leading order in the spin-orbit coupling (SOC). Finally, the results are confirmed by a direct derivation of the saddle-point (Usadel) equation from the quantum kinetic equations in the presence of randomly distributed impurities with SOC. At this point we correct a recent derivation of the Usadel equation that includes magneto-electric effects and does not resort to the Born approximation.