A1 Journal article (refereed)
Magnetoelectric effects in superconductors due to spin-orbit scattering : Nonlinear σ-model description (2021)

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

JYU authors or editors

Publication details

All authors or editors: Virtanen, P.; Bergeret, F. S.; Tokatly, I. V.

Journal or series: Physical Review B

ISSN: 2469-9950

eISSN: 2469-9969

Publication year: 2021

Publication date: 30/08/2021

Volume: 104

Issue number: 6

Article number: 064515

Publisher: American Physical Society (APS)

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1103/PhysRevB.104.064515

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/78223

Publication is parallel published: https://arxiv.org/abs/2106.15859


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.

Keywords: superconductors; magnetic properties; spin (quantum mechanics)

Contributing organizations

Related projects

Ministry reporting: Yes

Reporting Year: 2021

JUFO rating: 2

Last updated on 2022-20-09 at 14:16