Graphene and non-Abelian quantization

Autores
Falomir, Horacio Alberto; Gamboa, J; Loewe, M; Nieto, Mariela Natalia
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we employ a simple nonrelativistic model to describe the low energy excitation of graphene. The model is based on a deformation of the Heisenberg algebra which makes the commutator of momenta proportional to the pseudo-spin. We solve the Landau problem for the resulting Hamiltonian, which reduces in the large mass limit while keeping the Fermi velocity fixed,to the usual linear one employed to describe these excitations as massless Dirac fermions. This model, extended to negative mass, allows us to reproduce the leading terms in the low energy expansion of the dispersion relation for both nearest and next-to-nearest-neighbor interactions. Taking into account the contributions of both Dirac points, the resulting Hall conductivity, evaluated with a ζ -function approach, is consistent with the anomalous integer quantum Hall effect found in graphene. Moreover, when considered in first order perturbation theory, it is shown that the next-to-leading term in the interaction between nearest neighbor produces no modifications in the spectrum of the model while an electric field perpendicular to the magnetic field produces just a rigid shift of this spectrum.
Fil: Falomir, Horacio Alberto. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Gamboa, J. Pontificia Universidad Católica de Chile. Facultad de Física; Chile
Fil: Loewe, M. Pontificia Universidad Católica de Chile. Facultad de Física; Chile
Fil: Nieto, Mariela Natalia. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Materia
Graphene
Anomalous Integer Quantum Hall Effect
Non-Abelian Quantization
Non-commutative Quantum Mechanics
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:11336/271214
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Graphene and non-Abelian quantizationFalomir, Horacio AlbertoGamboa, JLoewe, MNieto, Mariela NataliaGrapheneAnomalous Integer Quantum Hall EffectNon-Abelian QuantizationNon-commutative Quantum Mechanicshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In this paper, we employ a simple nonrelativistic model to describe the low energy excitation of graphene. The model is based on a deformation of the Heisenberg algebra which makes the commutator of momenta proportional to the pseudo-spin. We solve the Landau problem for the resulting Hamiltonian, which reduces in the large mass limit while keeping the Fermi velocity fixed,to the usual linear one employed to describe these excitations as massless Dirac fermions. This model, extended to negative mass, allows us to reproduce the leading terms in the low energy expansion of the dispersion relation for both nearest and next-to-nearest-neighbor interactions. Taking into account the contributions of both Dirac points, the resulting Hall conductivity, evaluated with a ζ -function approach, is consistent with the anomalous integer quantum Hall effect found in graphene. Moreover, when considered in first order perturbation theory, it is shown that the next-to-leading term in the interaction between nearest neighbor produces no modifications in the spectrum of the model while an electric field perpendicular to the magnetic field produces just a rigid shift of this spectrum.Fil: Falomir, Horacio Alberto. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Gamboa, J. Pontificia Universidad Católica de Chile. Facultad de Física; ChileFil: Loewe, M. Pontificia Universidad Católica de Chile. Facultad de Física; ChileFil: Nieto, Mariela Natalia. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaIOP Publishing2012-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/271214Falomir, Horacio Alberto; Gamboa, J; Loewe, M; Nieto, Mariela Natalia; Graphene and non-Abelian quantization; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 45; 13; 4-2012; 1-211751-8113CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/1751-8121/45/13/135308info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/45/13/135308info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:52:12Zoai:ri.conicet.gov.ar:11336/271214instacron: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:34982025-09-29 09:52:13.062CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Graphene and non-Abelian quantization
title Graphene and non-Abelian quantization
spellingShingle Graphene and non-Abelian quantization
Falomir, Horacio Alberto
Graphene
Anomalous Integer Quantum Hall Effect
Non-Abelian Quantization
Non-commutative Quantum Mechanics
title_short Graphene and non-Abelian quantization
title_full Graphene and non-Abelian quantization
title_fullStr Graphene and non-Abelian quantization
title_full_unstemmed Graphene and non-Abelian quantization
title_sort Graphene and non-Abelian quantization
dc.creator.none.fl_str_mv Falomir, Horacio Alberto
Gamboa, J
Loewe, M
Nieto, Mariela Natalia
author Falomir, Horacio Alberto
author_facet Falomir, Horacio Alberto
Gamboa, J
Loewe, M
Nieto, Mariela Natalia
author_role author
author2 Gamboa, J
Loewe, M
Nieto, Mariela Natalia
author2_role author
author
author
dc.subject.none.fl_str_mv Graphene
Anomalous Integer Quantum Hall Effect
Non-Abelian Quantization
Non-commutative Quantum Mechanics
topic Graphene
Anomalous Integer Quantum Hall Effect
Non-Abelian Quantization
Non-commutative Quantum Mechanics
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we employ a simple nonrelativistic model to describe the low energy excitation of graphene. The model is based on a deformation of the Heisenberg algebra which makes the commutator of momenta proportional to the pseudo-spin. We solve the Landau problem for the resulting Hamiltonian, which reduces in the large mass limit while keeping the Fermi velocity fixed,to the usual linear one employed to describe these excitations as massless Dirac fermions. This model, extended to negative mass, allows us to reproduce the leading terms in the low energy expansion of the dispersion relation for both nearest and next-to-nearest-neighbor interactions. Taking into account the contributions of both Dirac points, the resulting Hall conductivity, evaluated with a ζ -function approach, is consistent with the anomalous integer quantum Hall effect found in graphene. Moreover, when considered in first order perturbation theory, it is shown that the next-to-leading term in the interaction between nearest neighbor produces no modifications in the spectrum of the model while an electric field perpendicular to the magnetic field produces just a rigid shift of this spectrum.
Fil: Falomir, Horacio Alberto. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
Fil: Gamboa, J. Pontificia Universidad Católica de Chile. Facultad de Física; Chile
Fil: Loewe, M. Pontificia Universidad Católica de Chile. Facultad de Física; Chile
Fil: Nieto, Mariela Natalia. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina
description In this paper, we employ a simple nonrelativistic model to describe the low energy excitation of graphene. The model is based on a deformation of the Heisenberg algebra which makes the commutator of momenta proportional to the pseudo-spin. We solve the Landau problem for the resulting Hamiltonian, which reduces in the large mass limit while keeping the Fermi velocity fixed,to the usual linear one employed to describe these excitations as massless Dirac fermions. This model, extended to negative mass, allows us to reproduce the leading terms in the low energy expansion of the dispersion relation for both nearest and next-to-nearest-neighbor interactions. Taking into account the contributions of both Dirac points, the resulting Hall conductivity, evaluated with a ζ -function approach, is consistent with the anomalous integer quantum Hall effect found in graphene. Moreover, when considered in first order perturbation theory, it is shown that the next-to-leading term in the interaction between nearest neighbor produces no modifications in the spectrum of the model while an electric field perpendicular to the magnetic field produces just a rigid shift of this spectrum.
publishDate 2012
dc.date.none.fl_str_mv 2012-04
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/11336/271214
Falomir, Horacio Alberto; Gamboa, J; Loewe, M; Nieto, Mariela Natalia; Graphene and non-Abelian quantization; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 45; 13; 4-2012; 1-21
1751-8113
CONICET Digital
CONICET
url http://hdl.handle.net/11336/271214
identifier_str_mv Falomir, Horacio Alberto; Gamboa, J; Loewe, M; Nieto, Mariela Natalia; Graphene and non-Abelian quantization; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 45; 13; 4-2012; 1-21
1751-8113
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/1751-8121/45/13/135308
info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/45/13/135308
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
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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
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
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 13.070432

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