Hierarchy of Floquet gaps and edge states for driven honeycomb lattices

Autores
Pérez Piskunow, Pablo Matías; Foa Torres, Luis Eduardo Francisco; Usaj, Gonzalo
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Electromagnetic driving in a honeycomb lattice can induce gaps and topological edge states with a structure of increasing complexity as the frequency of the driving lowers. While the high frequency case is the most simple to analyze we focus on the multiple photon processes allowed in the low frequency regime to unveil the hierarchy of Floquet edge-states. In the case of low intensities an analytical approach allows us to derive effective Hamiltonians and address the topological character of each gap in a constructive manner. At high intensities we obtain the net number of edge states, given by the winding number, with a numerical calculation of the Chern numbers of each Floquet band. Using these methods, we find a hierarchy that resembles that of a Russian nesting doll. This hierarchy classifies the gaps and the associated edge states in different orders according to the electron-photon coupling strength. For large driving intensities, we rely on the numerical calculation of the winding number, illustrated in a map of topological phase transitions. The hierarchy unveiled with the low energy effective Hamiltonians, alongside with the map of topological phase transitions discloses the complexity of the Floquet band structure in the low frequency regime. The proposed method for obtaining the effective Hamiltonian can be easily adapted to other Dirac Hamiltonians of two dimensional materials and even the surface of a 3D topological insulator.
Fil: Pérez Piskunow, Pablo Matías. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Foa Torres, Luis Eduardo Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Usaj, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina
Materia
Driven Quantum Systems
Floquet Topological Insulators
Graphene
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/44226
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/44226
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network_name_str CONICET Digital (CONICET)
spelling Hierarchy of Floquet gaps and edge states for driven honeycomb latticesPérez Piskunow, Pablo MatíasFoa Torres, Luis Eduardo FranciscoUsaj, GonzaloDriven Quantum SystemsFloquet Topological InsulatorsGraphenehttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Electromagnetic driving in a honeycomb lattice can induce gaps and topological edge states with a structure of increasing complexity as the frequency of the driving lowers. While the high frequency case is the most simple to analyze we focus on the multiple photon processes allowed in the low frequency regime to unveil the hierarchy of Floquet edge-states. In the case of low intensities an analytical approach allows us to derive effective Hamiltonians and address the topological character of each gap in a constructive manner. At high intensities we obtain the net number of edge states, given by the winding number, with a numerical calculation of the Chern numbers of each Floquet band. Using these methods, we find a hierarchy that resembles that of a Russian nesting doll. This hierarchy classifies the gaps and the associated edge states in different orders according to the electron-photon coupling strength. For large driving intensities, we rely on the numerical calculation of the winding number, illustrated in a map of topological phase transitions. The hierarchy unveiled with the low energy effective Hamiltonians, alongside with the map of topological phase transitions discloses the complexity of the Floquet band structure in the low frequency regime. The proposed method for obtaining the effective Hamiltonian can be easily adapted to other Dirac Hamiltonians of two dimensional materials and even the surface of a 3D topological insulator.Fil: Pérez Piskunow, Pablo Matías. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Foa Torres, Luis Eduardo Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Usaj, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; ArgentinaAmerican Physical Society2015-04-20info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/44226Pérez Piskunow, Pablo Matías; Foa Torres, Luis Eduardo Francisco; Usaj, Gonzalo; Hierarchy of Floquet gaps and edge states for driven honeycomb lattices; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 91; 4; 20-4-2015; 43625-1 / 43625-101050-2947CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.91.043625info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.043625info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:43:28Zoai:ri.conicet.gov.ar:11336/44226instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:43:28.583CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Hierarchy of Floquet gaps and edge states for driven honeycomb lattices
title Hierarchy of Floquet gaps and edge states for driven honeycomb lattices
spellingShingle Hierarchy of Floquet gaps and edge states for driven honeycomb lattices
Pérez Piskunow, Pablo Matías
Driven Quantum Systems
Floquet Topological Insulators
Graphene
title_short Hierarchy of Floquet gaps and edge states for driven honeycomb lattices
title_full Hierarchy of Floquet gaps and edge states for driven honeycomb lattices
title_fullStr Hierarchy of Floquet gaps and edge states for driven honeycomb lattices
title_full_unstemmed Hierarchy of Floquet gaps and edge states for driven honeycomb lattices
title_sort Hierarchy of Floquet gaps and edge states for driven honeycomb lattices
dc.creator.none.fl_str_mv Pérez Piskunow, Pablo Matías
Foa Torres, Luis Eduardo Francisco
Usaj, Gonzalo
author Pérez Piskunow, Pablo Matías
author_facet Pérez Piskunow, Pablo Matías
Foa Torres, Luis Eduardo Francisco
Usaj, Gonzalo
author_role author
author2 Foa Torres, Luis Eduardo Francisco
Usaj, Gonzalo
author2_role author
author
dc.subject.none.fl_str_mv Driven Quantum Systems
Floquet Topological Insulators
Graphene
topic Driven Quantum Systems
Floquet Topological Insulators
Graphene
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Electromagnetic driving in a honeycomb lattice can induce gaps and topological edge states with a structure of increasing complexity as the frequency of the driving lowers. While the high frequency case is the most simple to analyze we focus on the multiple photon processes allowed in the low frequency regime to unveil the hierarchy of Floquet edge-states. In the case of low intensities an analytical approach allows us to derive effective Hamiltonians and address the topological character of each gap in a constructive manner. At high intensities we obtain the net number of edge states, given by the winding number, with a numerical calculation of the Chern numbers of each Floquet band. Using these methods, we find a hierarchy that resembles that of a Russian nesting doll. This hierarchy classifies the gaps and the associated edge states in different orders according to the electron-photon coupling strength. For large driving intensities, we rely on the numerical calculation of the winding number, illustrated in a map of topological phase transitions. The hierarchy unveiled with the low energy effective Hamiltonians, alongside with the map of topological phase transitions discloses the complexity of the Floquet band structure in the low frequency regime. The proposed method for obtaining the effective Hamiltonian can be easily adapted to other Dirac Hamiltonians of two dimensional materials and even the surface of a 3D topological insulator.
Fil: Pérez Piskunow, Pablo Matías. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Foa Torres, Luis Eduardo Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Usaj, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina
description Electromagnetic driving in a honeycomb lattice can induce gaps and topological edge states with a structure of increasing complexity as the frequency of the driving lowers. While the high frequency case is the most simple to analyze we focus on the multiple photon processes allowed in the low frequency regime to unveil the hierarchy of Floquet edge-states. In the case of low intensities an analytical approach allows us to derive effective Hamiltonians and address the topological character of each gap in a constructive manner. At high intensities we obtain the net number of edge states, given by the winding number, with a numerical calculation of the Chern numbers of each Floquet band. Using these methods, we find a hierarchy that resembles that of a Russian nesting doll. This hierarchy classifies the gaps and the associated edge states in different orders according to the electron-photon coupling strength. For large driving intensities, we rely on the numerical calculation of the winding number, illustrated in a map of topological phase transitions. The hierarchy unveiled with the low energy effective Hamiltonians, alongside with the map of topological phase transitions discloses the complexity of the Floquet band structure in the low frequency regime. The proposed method for obtaining the effective Hamiltonian can be easily adapted to other Dirac Hamiltonians of two dimensional materials and even the surface of a 3D topological insulator.
publishDate 2015
dc.date.none.fl_str_mv 2015-04-20
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/44226
Pérez Piskunow, Pablo Matías; Foa Torres, Luis Eduardo Francisco; Usaj, Gonzalo; Hierarchy of Floquet gaps and edge states for driven honeycomb lattices; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 91; 4; 20-4-2015; 43625-1 / 43625-10
1050-2947
CONICET Digital
CONICET
url http://hdl.handle.net/11336/44226
identifier_str_mv Pérez Piskunow, Pablo Matías; Foa Torres, Luis Eduardo Francisco; Usaj, Gonzalo; Hierarchy of Floquet gaps and edge states for driven honeycomb lattices; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 91; 4; 20-4-2015; 43625-1 / 43625-10
1050-2947
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.91.043625
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.043625
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
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:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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