Magnetoelectric effects in superconductors due to spin-orbit scattering : Nonlinear σ-model description
Virtanen, P., Bergeret, F. S., & Tokatly, I. V. (2021). Magnetoelectric effects in superconductors due to spin-orbit scattering : Nonlinear σ-model description. Physical Review B, 104(6), Article 064515. https://doi.org/10.1103/PhysRevB.104.064515
Published inPhysical Review B
DisciplineNanoscience CenterNanoscience Center
© 2021 American Physical Society
We suggest a generalization of the 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 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 magnetoelectric effects and does not resort to the Born approximation.
PublisherAmerican Physical Society (APS)
ISSN Search the Publication Forum2469-9950
Publication in research information system
MetadataShow full item record
Related funder(s)European Commission; Academy of Finland
Funding program(s)Academy Project, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingP.V. and F.S.B. acknowledge funding from EU's Horizon 2020 research and innovation program under Grant Agreement No. 800923 (SUPERTED). P.V. acknowledges funding from Academy of Finland Project 317118. I.V.T. acknowledges support by Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT1249-19). F.S.B. acknowledges funding by the Spanish Ministerio de Ciencia, Innovacion y Universidades (MICINN) (Project No. FIS2017-82804-P). ...
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