Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1103/PhysRevB.85.195127 http://hdl.handle.net/11449/226833 |
Resumo: | Generalized Wannier functions of a couple of bands in a one-dimensional crystal are investigated. A lower bound for the global minimum of the total spread is obtained. Assumption of such a value being the minimum leads to a first-order differential equation for the transformation matrix. Simple analytical solutions leading to real generalized Wannier functions are presented for consecutive bands in a crystal with inversion symmetry. Results are displayed for a particle in a diatomic Kronig-Penney potential. For the lowest couple of bands, calculated single-band Wannier functions resemble orbitals of a diatomic molecule, whereas generalized Wannier functions seem like orthogonalized atomic orbitals. The latter functions are neither symmetric nor antisymmetric and display increased exponential decay. For the next two pairs of bands, Wannier functions retain their centers and symmetries, and exponential decay does not increase. Results are also shown to be in agreement with solutions of the eigenvalue problem of the band-projected position operator. © 2012 American Physical Society. |
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Repositório Institucional da UNESP |
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Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimensionGeneralized Wannier functions of a couple of bands in a one-dimensional crystal are investigated. A lower bound for the global minimum of the total spread is obtained. Assumption of such a value being the minimum leads to a first-order differential equation for the transformation matrix. Simple analytical solutions leading to real generalized Wannier functions are presented for consecutive bands in a crystal with inversion symmetry. Results are displayed for a particle in a diatomic Kronig-Penney potential. For the lowest couple of bands, calculated single-band Wannier functions resemble orbitals of a diatomic molecule, whereas generalized Wannier functions seem like orthogonalized atomic orbitals. The latter functions are neither symmetric nor antisymmetric and display increased exponential decay. For the next two pairs of bands, Wannier functions retain their centers and symmetries, and exponential decay does not increase. Results are also shown to be in agreement with solutions of the eigenvalue problem of the band-projected position operator. © 2012 American Physical Society.Programa de Pós-Graduação em Ciência e Tecnologia de Materiais Unesp, 17033-360 Bauru, São PauloDepartamento de Matemática Faculdade de Ciências Unesp, 17033-360 Bauru, São PauloPrograma de Pós-Graduação em Ciência e Tecnologia de Materiais Unesp, 17033-360 Bauru, São PauloDepartamento de Matemática Faculdade de Ciências Unesp, 17033-360 Bauru, São PauloUniversidade Estadual Paulista (UNESP)Nacbar, Denis R. [UNESP]Bruno-Alfonso, Alexys [UNESP]2022-04-29T02:57:15Z2022-04-29T02:57:15Z2012-05-14info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevB.85.195127Physical Review B - Condensed Matter and Materials Physics, v. 85, n. 19, 2012.1098-01211550-235Xhttp://hdl.handle.net/11449/22683310.1103/PhysRevB.85.1951272-s2.0-84861710001Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPhysical Review B - Condensed Matter and Materials Physicsinfo:eu-repo/semantics/openAccess2024-04-29T14:59:42Zoai:repositorio.unesp.br:11449/226833Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:21:30.032898Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension |
title |
Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension |
spellingShingle |
Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension Nacbar, Denis R. [UNESP] |
title_short |
Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension |
title_full |
Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension |
title_fullStr |
Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension |
title_full_unstemmed |
Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension |
title_sort |
Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension |
author |
Nacbar, Denis R. [UNESP] |
author_facet |
Nacbar, Denis R. [UNESP] Bruno-Alfonso, Alexys [UNESP] |
author_role |
author |
author2 |
Bruno-Alfonso, Alexys [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) |
dc.contributor.author.fl_str_mv |
Nacbar, Denis R. [UNESP] Bruno-Alfonso, Alexys [UNESP] |
description |
Generalized Wannier functions of a couple of bands in a one-dimensional crystal are investigated. A lower bound for the global minimum of the total spread is obtained. Assumption of such a value being the minimum leads to a first-order differential equation for the transformation matrix. Simple analytical solutions leading to real generalized Wannier functions are presented for consecutive bands in a crystal with inversion symmetry. Results are displayed for a particle in a diatomic Kronig-Penney potential. For the lowest couple of bands, calculated single-band Wannier functions resemble orbitals of a diatomic molecule, whereas generalized Wannier functions seem like orthogonalized atomic orbitals. The latter functions are neither symmetric nor antisymmetric and display increased exponential decay. For the next two pairs of bands, Wannier functions retain their centers and symmetries, and exponential decay does not increase. Results are also shown to be in agreement with solutions of the eigenvalue problem of the band-projected position operator. © 2012 American Physical Society. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-05-14 2022-04-29T02:57:15Z 2022-04-29T02:57:15Z |
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://dx.doi.org/10.1103/PhysRevB.85.195127 Physical Review B - Condensed Matter and Materials Physics, v. 85, n. 19, 2012. 1098-0121 1550-235X http://hdl.handle.net/11449/226833 10.1103/PhysRevB.85.195127 2-s2.0-84861710001 |
url |
http://dx.doi.org/10.1103/PhysRevB.85.195127 http://hdl.handle.net/11449/226833 |
identifier_str_mv |
Physical Review B - Condensed Matter and Materials Physics, v. 85, n. 19, 2012. 1098-0121 1550-235X 10.1103/PhysRevB.85.195127 2-s2.0-84861710001 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Physical Review B - Condensed Matter and Materials Physics |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129057257160704 |