Camadas de heteroestruturas hexagonais planas modeladas por grafos quânticos
Autor(a) principal: | |
---|---|
Data de Publicação: | 2022 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/16601 |
Resumo: | We started this work by reviewing an application of periodic quantum graph theory to model monolayer hexagonal materials with δ_a and δ_b parameters associated with the different types of atoms located in their vertices. We verified that materials of this nature have gaps in their spectral bands and express the size of this opening according to these parameters. In the Chapters 2 and 3, extend this modeling to equal bilayers, stacked in type AA and AA′, and in the Chapters 4, we studied heterostructures with two mixed layers and the “sandwich” hexagonal boron graphene-nitride: a single graphene sheet between two layers of hBN, and a single hBN sheet between two layers of graphene. In each of these configurations, we use the Schrödinger operator with its respective boundary conditions and we introduced a weak t_0 interaction parameter between the connections of different layers. We analyzed initially the dispersion relationship obtained in these models regarding the existence of conical or parabolic touches and confirmed, in rigorous models, known results in the physical literature, namely: hBN bilayers do not have Dirac cones, but, in AA stacking we identified the presence of parabolic touches. In the case of mixed bilayers, our study allows us to conclude that the inclusion of an hBN layer over a graphene layer can induce a gap in the graphene sheet and we express the width of this gap according to the parameters t_0 e δ_a. In the study of “sandwiches”, hBN-graphene-hBN and graphene-hBN-graphene, for certain particular values of the parameters, we found that the inclusion of a single graphene sheet between two sheets of hBN does not eliminate the gap of the hBN, but induces a reduction in the width of the spectral gap in an order of magnitude; by on the other hand, in the case graphene-hBN-graphene, the graphene cone at the origin prevails in this sandwich, but it also caused gaps in the other Dirac cones of the graphene. Such results can be justified by the fact that, in these heterostructures, carbon atoms have interacted with other inequivalent hBN, nitrogen, and boron atoms, causing a reduction or increase of the gaps. Finally, in the last chapter, we consider hexagonal quantum graphs and we adapt our proposal to include a magnetic field in the hBN sheet. We demonstrate that if the magnetic flux is constant in the hexagonal network and is a rational multiple of 2π, then there will be values of thisflux such that, for certain boundary conditions at the vertices (modeling the hBN), the conical touches in the operator scattering relation will cease to exist and we guarantee the existence of gaps. |
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Souza, Osmar do NascimentoOliveira, César Rogério dehttp://lattes.cnpq.br/5485204156806697http://lattes.cnpq.br/983964973357063254026b8c-6671-4098-9086-5154c35876272022-09-12T11:44:15Z2022-09-12T11:44:15Z2022-08-24SOUZA, Osmar do Nascimento. Camadas de heteroestruturas hexagonais planas modeladas por grafos quânticos. 2022. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/16601.https://repositorio.ufscar.br/handle/ufscar/16601We started this work by reviewing an application of periodic quantum graph theory to model monolayer hexagonal materials with δ_a and δ_b parameters associated with the different types of atoms located in their vertices. We verified that materials of this nature have gaps in their spectral bands and express the size of this opening according to these parameters. In the Chapters 2 and 3, extend this modeling to equal bilayers, stacked in type AA and AA′, and in the Chapters 4, we studied heterostructures with two mixed layers and the “sandwich” hexagonal boron graphene-nitride: a single graphene sheet between two layers of hBN, and a single hBN sheet between two layers of graphene. In each of these configurations, we use the Schrödinger operator with its respective boundary conditions and we introduced a weak t_0 interaction parameter between the connections of different layers. We analyzed initially the dispersion relationship obtained in these models regarding the existence of conical or parabolic touches and confirmed, in rigorous models, known results in the physical literature, namely: hBN bilayers do not have Dirac cones, but, in AA stacking we identified the presence of parabolic touches. In the case of mixed bilayers, our study allows us to conclude that the inclusion of an hBN layer over a graphene layer can induce a gap in the graphene sheet and we express the width of this gap according to the parameters t_0 e δ_a. In the study of “sandwiches”, hBN-graphene-hBN and graphene-hBN-graphene, for certain particular values of the parameters, we found that the inclusion of a single graphene sheet between two sheets of hBN does not eliminate the gap of the hBN, but induces a reduction in the width of the spectral gap in an order of magnitude; by on the other hand, in the case graphene-hBN-graphene, the graphene cone at the origin prevails in this sandwich, but it also caused gaps in the other Dirac cones of the graphene. Such results can be justified by the fact that, in these heterostructures, carbon atoms have interacted with other inequivalent hBN, nitrogen, and boron atoms, causing a reduction or increase of the gaps. Finally, in the last chapter, we consider hexagonal quantum graphs and we adapt our proposal to include a magnetic field in the hBN sheet. We demonstrate that if the magnetic flux is constant in the hexagonal network and is a rational multiple of 2π, then there will be values of thisflux such that, for certain boundary conditions at the vertices (modeling the hBN), the conical touches in the operator scattering relation will cease to exist and we guarantee the existence of gaps.Iniciamos este trabalho revisando uma aplicação da teoria de grafos quânticos periódicos para modelar monocamada de materiais hexagonais com parâmetros δ_a e δ_b associados aos tipos de átomos distintos situados em seus vértices. Verificamos que materiais dessa natureza possuem lacunas em suas bandas espectrais e expressamos o tamanho dessa abertura em função desses parâmetros. Nos Capítulos 2 e 3, estendemos essa modelagem para bicamadas iguais, empilhadas no tipo AA e AA′, e no Capítulo 4, estudamos heteroestruturas com duas camadas mistas e os “sanduíche” grafeno-nitreto de boro hexagonal: folha de grafeno entre hBN, e hBN entre grafenos. Em cada uma dessas configurações, usamos o operador de Schrödinger com suas respectivas condições de contorno e introduzimos um parâmetro de interação fraca t_0 entre as conexões de diferentes camadas. Analisamos analiticamente a relação de dispersão obtida nesses modelos quanto à existência de toques cônicos ou parabólicos e confirmamos, em modelos rigorosos, resultados conhecidos na literatura física, a saber: bicamadas de hBN não possuem cones de Dirac, porém no empilhamento AA identificamos a presença de toques parabólicos. No caso de bicamadas mistas, nosso estudo permite concluir que a inclusão de uma camada de hBN sobre uma de grafeno pode induzir um gap na folha de grafeno e expressamos a largura desse gap em função dos parâmetros t_0, δ_a. No estudo dos “sanduíches”, hBN-grafeno-hBN e grafeno-hBN-grafeno, para certos valores particulares dos parâmetros, verificamos que a inclusão de uma folha de grafeno entre duas de hBN não elimina o gap do hBN, mas induz uma redução na largura da lacuna espectral em uma ordem de grandeza; por outro lado, no caso grafeno-hBN-grafeno, o cone do grafeno na origem prevalece neste sanduíche, porém também provocou lacunas nos outros cones de Dirac do grafeno. Tais resultados podem ser justificados pelo fato de que, nessas heteroestruturas, os átomos de carbono terem interagido com outros átomos inequivalentes de hBN, nitrogênio e boro, provocando redução ou aumento das lacunas. Por fim, no último capítulo, consideramos grafos quânticos hexagonais e adaptamos nossa proposta para incluir um campo magnético na folha de hBN. Demonstramos que se o fluxo magnético for constante na rede hexagonal e for múltiplo racional de 2π, então existirão valores desse fluxo de forma que, para certas condições de contorno nos vértices (modelando o hBN), os toques cônicos na relação de dispersão do operador deixarão de existir e garantimos a existência de lacunas.Não recebi financiamentoporUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Pós-Graduação em Matemática - PPGMUFSCarAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessGrafos quânticosHeteroestruturasGrafeno - Nitreto de BoroOperador de SchrodingerCampo magnéticoCones de DiracQuantum graphsGraphene - Boron nitrideHeterostructuresSchrodinger operatorMagnetic fieldDirac conesCIENCIAS EXATAS E DA TERRA::MATEMATICACamadas de heteroestruturas hexagonais planas modeladas por grafos quânticosLayers of planar hexagonal heterostructures modeled by quantum graphsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis600600bcffdcda-5ce8-4296-ae3a-1650ea990cfdreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufscar.br/bitstream/ufscar/16601/6/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD56ORIGINALTese_com_folha_aprovacao.pdfTese_com_folha_aprovacao.pdfTese - Versão finalapplication/pdf5202242https://repositorio.ufscar.br/bitstream/ufscar/16601/4/Tese_com_folha_aprovacao.pdf113d865d21da2cb714af9daef3d64399MD54Carta_comprovante.pdfCarta_comprovante.pdfCarta comprovanteapplication/pdf285517https://repositorio.ufscar.br/bitstream/ufscar/16601/5/Carta_comprovante.pdf5fca385e0d9b69c0f60db004d09184a7MD55TEXTTese_com_folha_aprovacao.pdf.txtTese_com_folha_aprovacao.pdf.txtExtracted texttext/plain141838https://repositorio.ufscar.br/bitstream/ufscar/16601/7/Tese_com_folha_aprovacao.pdf.txt5f2de556a2163d1cff5a1cb94999aff4MD57Carta_comprovante.pdf.txtCarta_comprovante.pdf.txtExtracted texttext/plain1https://repositorio.ufscar.br/bitstream/ufscar/16601/9/Carta_comprovante.pdf.txt68b329da9893e34099c7d8ad5cb9c940MD59THUMBNAILTese_com_folha_aprovacao.pdf.jpgTese_com_folha_aprovacao.pdf.jpgIM Thumbnailimage/jpeg7570https://repositorio.ufscar.br/bitstream/ufscar/16601/8/Tese_com_folha_aprovacao.pdf.jpg1fdb02179df59dfdb9c1e6297f53a344MD58Carta_comprovante.pdf.jpgCarta_comprovante.pdf.jpgIM Thumbnailimage/jpeg11186https://repositorio.ufscar.br/bitstream/ufscar/16601/10/Carta_comprovante.pdf.jpg79c02107cc63b8cbffc709daecc17e66MD510ufscar/166012023-09-18 18:32:19.354oai:repositorio.ufscar.br:ufscar/16601Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:32:19Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.por.fl_str_mv |
Camadas de heteroestruturas hexagonais planas modeladas por grafos quânticos |
dc.title.alternative.eng.fl_str_mv |
Layers of planar hexagonal heterostructures modeled by quantum graphs |
title |
Camadas de heteroestruturas hexagonais planas modeladas por grafos quânticos |
spellingShingle |
Camadas de heteroestruturas hexagonais planas modeladas por grafos quânticos Souza, Osmar do Nascimento Grafos quânticos Heteroestruturas Grafeno - Nitreto de Boro Operador de Schrodinger Campo magnético Cones de Dirac Quantum graphs Graphene - Boron nitride Heterostructures Schrodinger operator Magnetic field Dirac cones CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Camadas de heteroestruturas hexagonais planas modeladas por grafos quânticos |
title_full |
Camadas de heteroestruturas hexagonais planas modeladas por grafos quânticos |
title_fullStr |
Camadas de heteroestruturas hexagonais planas modeladas por grafos quânticos |
title_full_unstemmed |
Camadas de heteroestruturas hexagonais planas modeladas por grafos quânticos |
title_sort |
Camadas de heteroestruturas hexagonais planas modeladas por grafos quânticos |
author |
Souza, Osmar do Nascimento |
author_facet |
Souza, Osmar do Nascimento |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/9839649733570632 |
dc.contributor.author.fl_str_mv |
Souza, Osmar do Nascimento |
dc.contributor.advisor1.fl_str_mv |
Oliveira, César Rogério de |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/5485204156806697 |
dc.contributor.authorID.fl_str_mv |
54026b8c-6671-4098-9086-5154c3587627 |
contributor_str_mv |
Oliveira, César Rogério de |
dc.subject.por.fl_str_mv |
Grafos quânticos Heteroestruturas Grafeno - Nitreto de Boro Operador de Schrodinger Campo magnético Cones de Dirac |
topic |
Grafos quânticos Heteroestruturas Grafeno - Nitreto de Boro Operador de Schrodinger Campo magnético Cones de Dirac Quantum graphs Graphene - Boron nitride Heterostructures Schrodinger operator Magnetic field Dirac cones CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Quantum graphs Graphene - Boron nitride Heterostructures Schrodinger operator Magnetic field Dirac cones |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
We started this work by reviewing an application of periodic quantum graph theory to model monolayer hexagonal materials with δ_a and δ_b parameters associated with the different types of atoms located in their vertices. We verified that materials of this nature have gaps in their spectral bands and express the size of this opening according to these parameters. In the Chapters 2 and 3, extend this modeling to equal bilayers, stacked in type AA and AA′, and in the Chapters 4, we studied heterostructures with two mixed layers and the “sandwich” hexagonal boron graphene-nitride: a single graphene sheet between two layers of hBN, and a single hBN sheet between two layers of graphene. In each of these configurations, we use the Schrödinger operator with its respective boundary conditions and we introduced a weak t_0 interaction parameter between the connections of different layers. We analyzed initially the dispersion relationship obtained in these models regarding the existence of conical or parabolic touches and confirmed, in rigorous models, known results in the physical literature, namely: hBN bilayers do not have Dirac cones, but, in AA stacking we identified the presence of parabolic touches. In the case of mixed bilayers, our study allows us to conclude that the inclusion of an hBN layer over a graphene layer can induce a gap in the graphene sheet and we express the width of this gap according to the parameters t_0 e δ_a. In the study of “sandwiches”, hBN-graphene-hBN and graphene-hBN-graphene, for certain particular values of the parameters, we found that the inclusion of a single graphene sheet between two sheets of hBN does not eliminate the gap of the hBN, but induces a reduction in the width of the spectral gap in an order of magnitude; by on the other hand, in the case graphene-hBN-graphene, the graphene cone at the origin prevails in this sandwich, but it also caused gaps in the other Dirac cones of the graphene. Such results can be justified by the fact that, in these heterostructures, carbon atoms have interacted with other inequivalent hBN, nitrogen, and boron atoms, causing a reduction or increase of the gaps. Finally, in the last chapter, we consider hexagonal quantum graphs and we adapt our proposal to include a magnetic field in the hBN sheet. We demonstrate that if the magnetic flux is constant in the hexagonal network and is a rational multiple of 2π, then there will be values of thisflux such that, for certain boundary conditions at the vertices (modeling the hBN), the conical touches in the operator scattering relation will cease to exist and we guarantee the existence of gaps. |
publishDate |
2022 |
dc.date.accessioned.fl_str_mv |
2022-09-12T11:44:15Z |
dc.date.available.fl_str_mv |
2022-09-12T11:44:15Z |
dc.date.issued.fl_str_mv |
2022-08-24 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
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doctoralThesis |
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publishedVersion |
dc.identifier.citation.fl_str_mv |
SOUZA, Osmar do Nascimento. Camadas de heteroestruturas hexagonais planas modeladas por grafos quânticos. 2022. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/16601. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/16601 |
identifier_str_mv |
SOUZA, Osmar do Nascimento. Camadas de heteroestruturas hexagonais planas modeladas por grafos quânticos. 2022. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/16601. |
url |
https://repositorio.ufscar.br/handle/ufscar/16601 |
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por |
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por |
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600 600 |
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Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
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openAccess |
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Universidade Federal de São Carlos Câmpus São Carlos |
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Programa de Pós-Graduação em Matemática - PPGM |
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UFSCar |
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Universidade Federal de São Carlos Câmpus São Carlos |
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