Unified description of spin transport, weak antilocalization, and triplet superconductivity in systems with spin-orbit coupling

The Eilenberger equation is a standard tool in the description of superconductors with an arbitrary degree of disorder. It can be generalized to systems with linear-in-momentum spin-orbit coupling (SOC), by exploiting the analogy of SOC with a non-Abelian background field. Such a field mixes singlet...

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Autores: Ilić, Stefan, Tokatly, Ilya, Bergeret, F. Sebastian
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/235607
Acceso en línea:http://hdl.handle.net/10261/235607
Access Level:acceso abierto
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spelling Unified description of spin transport, weak antilocalization, and triplet superconductivity in systems with spin-orbit couplingIlić, StefanTokatly, IlyaBergeret, F. SebastianThe Eilenberger equation is a standard tool in the description of superconductors with an arbitrary degree of disorder. It can be generalized to systems with linear-in-momentum spin-orbit coupling (SOC), by exploiting the analogy of SOC with a non-Abelian background field. Such a field mixes singlet and triplet components and yields the rich physics of magnetoelectric phenomena. In this work we show that the application of this equation extends further, beyond superconductivity. In the normal state, the linearized Eilenberger equation describes the coupled spin-charge dynamics. Moreover, its resolvent corresponds to the so-called Cooperons, and can be used to calculate the weak-localization corrections. Specifically, we show how to solve this equation for any source term and provide a closed-form solution for the case of Rashba SOC. We use this solution to address several problems of interest for spintronics and superconductivity. First, we study spin injection from ferromagnetic electrodes in the normal state, and describe the spatial evolution of spin density in the sample, and the complete crossover from the diffusive to the ballistic limit. Second, we address the so-called superconducting Edelstein effect, and generalize the previously known results to arbitrary disorder. Third, we study weak-localization correction beyond the diffusive limit, which can be a valuable tool in experimental characterization of materials with very strong SOC. We also address the so-called pure gauge case where the persistent spin helices form. Our work establishes the linearized Eilenberger equation as a powerful and a very versatile method for the study of materials with spin-orbit coupling, which often provides a simpler and more intuitive picture compared to alternative methods.We acknowledge funding from Spanish Ministerio de Ciencia, Innovación y Universidades (MICINN) (Projects No. FIS2016-79464-P and No. FIS2017-82804- P). I.V.T. acknowledges support by Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT1249-19). S.I. and F.S.B acknowledge funding from EUs Horizon 2020 research and innovation program under Grant Agreement No. 800923 (SUPERTED).Peer reviewedAmerican Physical SocietyMinisterio de Economía y Competitividad (España)Agencia Estatal de Investigación (España)Ministerio de Ciencia, Innovación y Universidades (España)Universidad del País VascoEusko JaurlaritzaEuropean Research CouncilEuropean CommissionConsejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202120212020info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10261/235607reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/FIS2016-79464-Pinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/FIS2017-82804-PFIS2017-82804-P/AEI/10.13039/501100011033info:eu-repo/grantAgreement/EC/H2020/800923https://doi.org/10.1103/PhysRevB.102.235430Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/2356072026-05-22T06:33:51Z
dc.title.none.fl_str_mv Unified description of spin transport, weak antilocalization, and triplet superconductivity in systems with spin-orbit coupling
title Unified description of spin transport, weak antilocalization, and triplet superconductivity in systems with spin-orbit coupling
spellingShingle Unified description of spin transport, weak antilocalization, and triplet superconductivity in systems with spin-orbit coupling
Ilić, Stefan
title_short Unified description of spin transport, weak antilocalization, and triplet superconductivity in systems with spin-orbit coupling
title_full Unified description of spin transport, weak antilocalization, and triplet superconductivity in systems with spin-orbit coupling
title_fullStr Unified description of spin transport, weak antilocalization, and triplet superconductivity in systems with spin-orbit coupling
title_full_unstemmed Unified description of spin transport, weak antilocalization, and triplet superconductivity in systems with spin-orbit coupling
title_sort Unified description of spin transport, weak antilocalization, and triplet superconductivity in systems with spin-orbit coupling
dc.creator.none.fl_str_mv Ilić, Stefan
Tokatly, Ilya
Bergeret, F. Sebastian
author Ilić, Stefan
author_facet Ilić, Stefan
Tokatly, Ilya
Bergeret, F. Sebastian
author_role author
author2 Tokatly, Ilya
Bergeret, F. Sebastian
author2_role author
author
dc.contributor.none.fl_str_mv Ministerio de Economía y Competitividad (España)
Agencia Estatal de Investigación (España)
Ministerio de Ciencia, Innovación y Universidades (España)
Universidad del País Vasco
Eusko Jaurlaritza
European Research Council
European Commission
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
description The Eilenberger equation is a standard tool in the description of superconductors with an arbitrary degree of disorder. It can be generalized to systems with linear-in-momentum spin-orbit coupling (SOC), by exploiting the analogy of SOC with a non-Abelian background field. Such a field mixes singlet and triplet components and yields the rich physics of magnetoelectric phenomena. In this work we show that the application of this equation extends further, beyond superconductivity. In the normal state, the linearized Eilenberger equation describes the coupled spin-charge dynamics. Moreover, its resolvent corresponds to the so-called Cooperons, and can be used to calculate the weak-localization corrections. Specifically, we show how to solve this equation for any source term and provide a closed-form solution for the case of Rashba SOC. We use this solution to address several problems of interest for spintronics and superconductivity. First, we study spin injection from ferromagnetic electrodes in the normal state, and describe the spatial evolution of spin density in the sample, and the complete crossover from the diffusive to the ballistic limit. Second, we address the so-called superconducting Edelstein effect, and generalize the previously known results to arbitrary disorder. Third, we study weak-localization correction beyond the diffusive limit, which can be a valuable tool in experimental characterization of materials with very strong SOC. We also address the so-called pure gauge case where the persistent spin helices form. Our work establishes the linearized Eilenberger equation as a powerful and a very versatile method for the study of materials with spin-orbit coupling, which often provides a simpler and more intuitive picture compared to alternative methods.
publishDate 2020
dc.date.none.fl_str_mv 2020
2021
2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Publisher's version
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/235607
url http://hdl.handle.net/10261/235607
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
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info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/FIS2016-79464-P
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/FIS2017-82804-P
FIS2017-82804-P/AEI/10.13039/501100011033
info:eu-repo/grantAgreement/EC/H2020/800923
https://doi.org/10.1103/PhysRevB.102.235430
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
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