Gauge covariances and nonlinear optical responses
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/47444 |
Resumo: | The formalism of the reduced density matrix is pursued in both length and velocity gauges of the perturbation to the crystal Hamiltonian. The covariant derivative is introduced as a convenient representation of the position operator. This allow us to write compact expressions for the reduced density matrix in any order of the perturbation which simplifies the calculations of nonlinear optical responses; as an example, we compute the first and third order contributions of the monolayer graphene. Expressions obtained in both gauges share the same formal structure, allowing a comparison of the effects of truncation to a finite set of bands. This truncation breaks the equivalence between the two approaches: its proper implementation can be done directly in the expressions derived in the length gauge, but require a revision of the equations of motion of the reduced density matrix in the velocity gauge. |
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Gauge covariances and nonlinear optical responsesNonlinear OpticsGrapheneCiências Naturais::Ciências FísicasScience & TechnologyThe formalism of the reduced density matrix is pursued in both length and velocity gauges of the perturbation to the crystal Hamiltonian. The covariant derivative is introduced as a convenient representation of the position operator. This allow us to write compact expressions for the reduced density matrix in any order of the perturbation which simplifies the calculations of nonlinear optical responses; as an example, we compute the first and third order contributions of the monolayer graphene. Expressions obtained in both gauges share the same formal structure, allowing a comparison of the effects of truncation to a finite set of bands. This truncation breaks the equivalence between the two approaches: its proper implementation can be done directly in the expressions derived in the length gauge, but require a revision of the equations of motion of the reduced density matrix in the velocity gauge.The work of G.B.V. and D.J.P. is supported by Fundação para a Ciência e Tecnologia (FCT) under the Grants No. PD/BI/129220/2017 and No. PD/BD/135019/2017, respectively. N.M.R.P. acknowledges funding from the European Commission within the project "Graphene-Driven Revolutions in ICT and Beyond" (Ref. No. 696656) and the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing Grant No. UID/FIS/04650/2013.info:eu-repo/semantics/publishedVersionAmerican Physical SocietyUniversidade do MinhoVentura, G. B.Passos, D. J.Santos, J. M. B. Lopes dosLopes, J. M. Viana ParentePeres, N. M. R.2017-03-222017-03-22T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/47444eng2469-995010.1103/PhysRevB.96.035431info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:53:58Zoai:repositorium.sdum.uminho.pt:1822/47444Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:53:28.628130Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Gauge covariances and nonlinear optical responses |
title |
Gauge covariances and nonlinear optical responses |
spellingShingle |
Gauge covariances and nonlinear optical responses Ventura, G. B. Nonlinear Optics Graphene Ciências Naturais::Ciências Físicas Science & Technology |
title_short |
Gauge covariances and nonlinear optical responses |
title_full |
Gauge covariances and nonlinear optical responses |
title_fullStr |
Gauge covariances and nonlinear optical responses |
title_full_unstemmed |
Gauge covariances and nonlinear optical responses |
title_sort |
Gauge covariances and nonlinear optical responses |
author |
Ventura, G. B. |
author_facet |
Ventura, G. B. Passos, D. J. Santos, J. M. B. Lopes dos Lopes, J. M. Viana Parente Peres, N. M. R. |
author_role |
author |
author2 |
Passos, D. J. Santos, J. M. B. Lopes dos Lopes, J. M. Viana Parente Peres, N. M. R. |
author2_role |
author author author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Ventura, G. B. Passos, D. J. Santos, J. M. B. Lopes dos Lopes, J. M. Viana Parente Peres, N. M. R. |
dc.subject.por.fl_str_mv |
Nonlinear Optics Graphene Ciências Naturais::Ciências Físicas Science & Technology |
topic |
Nonlinear Optics Graphene Ciências Naturais::Ciências Físicas Science & Technology |
description |
The formalism of the reduced density matrix is pursued in both length and velocity gauges of the perturbation to the crystal Hamiltonian. The covariant derivative is introduced as a convenient representation of the position operator. This allow us to write compact expressions for the reduced density matrix in any order of the perturbation which simplifies the calculations of nonlinear optical responses; as an example, we compute the first and third order contributions of the monolayer graphene. Expressions obtained in both gauges share the same formal structure, allowing a comparison of the effects of truncation to a finite set of bands. This truncation breaks the equivalence between the two approaches: its proper implementation can be done directly in the expressions derived in the length gauge, but require a revision of the equations of motion of the reduced density matrix in the velocity gauge. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-03-22 2017-03-22T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/47444 |
url |
http://hdl.handle.net/1822/47444 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
2469-9950 10.1103/PhysRevB.96.035431 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
American Physical Society |
publisher.none.fl_str_mv |
American Physical Society |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799133130381066240 |