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dc.contributor.authorVirtanen, P.
dc.contributor.authorBergeret, F. S.
dc.contributor.authorTokatly, I. V.
dc.date.accessioned2021-10-15T07:18:04Z
dc.date.available2021-10-15T07:18:04Z
dc.date.issued2021
dc.identifier.citationVirtanen, P., Bergeret, F. S., & Tokatly, I. V. (2021). Magnetoelectric effects in superconductors due to spin-orbit scattering : Nonlinear σ-model description. <i>Physical Review B</i>, <i>104</i>(6), Article 064515. <a href="https://doi.org/10.1103/PhysRevB.104.064515" target="_blank">https://doi.org/10.1103/PhysRevB.104.064515</a>
dc.identifier.otherCONVID_101465509
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/78223
dc.description.abstractWe 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.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherAmerican Physical Society (APS)
dc.relation.ispartofseriesPhysical Review B
dc.rightsIn Copyright
dc.titleMagnetoelectric effects in superconductors due to spin-orbit scattering : Nonlinear σ-model description
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202110155255
dc.contributor.laitosFysiikan laitosfi
dc.contributor.laitosDepartment of Physicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.description.reviewstatuspeerReviewed
dc.relation.issn2469-9950
dc.relation.numberinseries6
dc.relation.volume104
dc.type.versionpublishedVersion
dc.rights.copyright© 2021 American Physical Society
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber800923
dc.relation.grantnumber800923
dc.relation.grantnumber317118
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/800923/EU//SUPERTED
dc.subject.ysospin (kvanttimekaniikka)
dc.subject.ysosuprajohteet
dc.subject.ysomagneettiset ominaisuudet
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p38874
jyx.subject.urihttp://www.yso.fi/onto/yso/p9946
jyx.subject.urihttp://www.yso.fi/onto/yso/p597
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.1103/PhysRevB.104.064515
dc.relation.funderEuroopan komissiofi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderEuropean Commissionen
dc.relation.funderAcademy of Finlanden
jyx.fundingprogramFET Future and Emerging Technologies, H2020fi
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundingprogramFET Future and Emerging Technologies, H2020en
jyx.fundingprogramAcademy Project, AoFen
jyx.fundinginformationP.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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