Anéis e pontos quânticos de fósforo negro investigadas por modelo contínuo

Detalhes bibliográficos
Ano de defesa: 2016
Autor(a) principal: Sousa, Gabriel Oliveira de
Orientador(a): Chaves, Andrey
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Não Informado pela instituição
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Link de acesso: http://www.repositorio.ufc.br/handle/riufc/20058
Resumo: The possibility of obtaining two-dimensional systems from layered materials has been attracting a lot of research on these materials, since their few layer properties are very different from their respective bulk ones, which opens up great possibilities in technological applications. Black phosphorus exhibit several interesting properties, among them, a direct energy gap, that enables the possibility of fabricating electronic devices (in contrast e.g. with the gapless semi-metallic graphene), and which can be tuned by the number of layers, varying from 0.3 eV for a bulk up to 2.0 eV for a monolayer, thus covering a relatively large range of the energy spectrum for optical devices. Besides, the fact that this is a very anisotropic material has brought even more attention to it, towards novel ways of exploring this anisotropy in new technologies. In this work, we have derived the effective mass approximation from the tight binding model and used the out coming approximate Hamiltonian to study nanostructures based on monolayer black phosphorus. In this model, the anisotropic features of black phosphorus are reflected in the difference between effective masses in different directions. Firstly, we compare the finite difference methods with the analytical solution for a circular quantum dot, which, due to its elliptical contour of energy bands, is given by Mathieu functions for solving the resulting Schrödinger equation. With this comparison, we verify the compatibility between these methods. Within the effective mass approximation, we investigate the effect of external electromagnetic fields on a black phosphorus quantum ring, thus analysing the effect of the interplay between these fields and the system anisotropy on its electronic states. Due to the anisotropy, under an applied magnetic field, this ring does not exhibit Aharonov-Bohm oscillations, which can be recovered by assuming an elliptic ring-like confinement. We also investigate the effect of an external electric field applied in x and y directions in a black phosphorus quantum ring on its energy levels. Our results show that, as a consequence of a wave function localization induced by mass anisotropy, energy levels decay quadratically (Stark effect) with the field if it is applied along the armchair direction, whereas an almost linear Stark effect, along with a series of crossing excited states, is observed for a field applied in the zigzag direction, leading to a behavior that is in close resemblance to a double quantum well under a perpendicular electric field.
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spelling Sousa, Gabriel Oliveira deCosta, Diego Rabelo daChaves, Andrey2016-10-07T15:49:06Z2016-10-07T15:49:06Z2016SOUSA, G. O. Anéis e pontos quânticos de fósforo negro investigadas por modelo contínuo. 2016. 73 f. Dissertação (Mestrado em Física) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2016.http://www.repositorio.ufc.br/handle/riufc/20058The possibility of obtaining two-dimensional systems from layered materials has been attracting a lot of research on these materials, since their few layer properties are very different from their respective bulk ones, which opens up great possibilities in technological applications. Black phosphorus exhibit several interesting properties, among them, a direct energy gap, that enables the possibility of fabricating electronic devices (in contrast e.g. with the gapless semi-metallic graphene), and which can be tuned by the number of layers, varying from 0.3 eV for a bulk up to 2.0 eV for a monolayer, thus covering a relatively large range of the energy spectrum for optical devices. Besides, the fact that this is a very anisotropic material has brought even more attention to it, towards novel ways of exploring this anisotropy in new technologies. In this work, we have derived the effective mass approximation from the tight binding model and used the out coming approximate Hamiltonian to study nanostructures based on monolayer black phosphorus. In this model, the anisotropic features of black phosphorus are reflected in the difference between effective masses in different directions. Firstly, we compare the finite difference methods with the analytical solution for a circular quantum dot, which, due to its elliptical contour of energy bands, is given by Mathieu functions for solving the resulting Schrödinger equation. With this comparison, we verify the compatibility between these methods. Within the effective mass approximation, we investigate the effect of external electromagnetic fields on a black phosphorus quantum ring, thus analysing the effect of the interplay between these fields and the system anisotropy on its electronic states. Due to the anisotropy, under an applied magnetic field, this ring does not exhibit Aharonov-Bohm oscillations, which can be recovered by assuming an elliptic ring-like confinement. We also investigate the effect of an external electric field applied in x and y directions in a black phosphorus quantum ring on its energy levels. Our results show that, as a consequence of a wave function localization induced by mass anisotropy, energy levels decay quadratically (Stark effect) with the field if it is applied along the armchair direction, whereas an almost linear Stark effect, along with a series of crossing excited states, is observed for a field applied in the zigzag direction, leading to a behavior that is in close resemblance to a double quantum well under a perpendicular electric field.A possibilidade de se obter sistemas bidimensionais a partir de materiais com estrutura cristalina lamelar tem atraído muitas pesquisas nesses materiais, pois as propriedades de poucas camadas diferem bastante dos seus respectivos bulks, o que abre uma gama de possibilidades em aplicações tecnológicas. O fósforo negro apresenta muitas propriedades interessantes, dentre elas, um gap de energia, que garante a construção de dispositivos eletrônicos (bem diferente do grafeno que é um semi metal sem gap). Esse gap pode ser ajustado aumentando o número de camadas, variando de 0.3 eV para uma monocamada até cerca de 2.0 eV para o bulk, cobrindo um espectro de energia de gap relativamente grande de dispositivos ópticos. Além disso, esse material é altamente anisotrópico em sua estrutura de bandas. Neste trabalho, derivamos a aproximação da massa efetiva a partir do modelo tight-binding e usamos o Hamiltoniano aproximado para estudar nanoestruturas de fósforo negro. Nesse modelo, o caráter anisotrópico do fósforo negro é refletido na diferença entre as massas efetivas quando se toma diferentes direções. Primeiramente, comparamos os resultados numérico obtido através da técnica de diferenças finitas com o modelo analítico para um ponto quântico circular, que devido à estrutura de bandas ter um contorno elíptico, é descrito pelas equações de Mathieu quando se resolve a equação de Schrödinger. Os resultados analítico e numérico mostram boa concordância. Ainda na aproximação da massa efetiva, estudamos o efeito de campos externos sobre um anel quântico de fósforo negro e analisamos o efeito da interação entre esses campos e a anisotropia de massa do sistema sobre seus estados eletrônicos. Devido à anisotropia de massa, esse sistema quando sujeito a um campo magnético, não apresenta oscilações Aharonov-Bohm, que podem ser recuperadas aplicando-se um potencial de confinamento elíptico. Estudamos também o efeito de um campo elétrico nas direções x e y em um anel quântico, e verificamos como a energia é alterada pelo campo. Nossos resultados mostram que, como consequência de uma localização da função de onda causada pela anisotropia de massa, os níveis de energia decrescem quadraticamente (efeito Stark) com o campo aplicado apontando para a direção armchair, enquanto um decréscimo quase linear (efeito Stark linear) aparece para um campo aplicado na direção zigzag, com uma série de estados que se cruzam, levando a um comportamento semelhante ao de um poço quântico duplo sob um campo elétrico perpendicular a ele.FósforoFísica da matéria condensadaFísica do estado sólidoAnéis e pontos quânticos de fósforo negro investigadas por modelo contínuoinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisporreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFCinfo:eu-repo/semantics/openAccessORIGINAL2016_dis_godesousa.pdf2016_dis_godesousa.pdfapplication/pdf3920169http://repositorio.ufc.br/bitstream/riufc/20058/1/2016_dis_godesousa.pdf4528605d05b33e81edffcede7905ea07MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.ufc.br/bitstream/riufc/20058/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52riufc/200582018-12-13 16:18:55.613oai:repositorio.ufc.br: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Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2018-12-13T19:18:55Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false
dc.title.pt_BR.fl_str_mv Anéis e pontos quânticos de fósforo negro investigadas por modelo contínuo
title Anéis e pontos quânticos de fósforo negro investigadas por modelo contínuo
spellingShingle Anéis e pontos quânticos de fósforo negro investigadas por modelo contínuo
Sousa, Gabriel Oliveira de
Fósforo
Física da matéria condensada
Física do estado sólido
title_short Anéis e pontos quânticos de fósforo negro investigadas por modelo contínuo
title_full Anéis e pontos quânticos de fósforo negro investigadas por modelo contínuo
title_fullStr Anéis e pontos quânticos de fósforo negro investigadas por modelo contínuo
title_full_unstemmed Anéis e pontos quânticos de fósforo negro investigadas por modelo contínuo
title_sort Anéis e pontos quânticos de fósforo negro investigadas por modelo contínuo
author Sousa, Gabriel Oliveira de
author_facet Sousa, Gabriel Oliveira de
author_role author
dc.contributor.co-advisor.none.fl_str_mv Costa, Diego Rabelo da
dc.contributor.author.fl_str_mv Sousa, Gabriel Oliveira de
dc.contributor.advisor1.fl_str_mv Chaves, Andrey
contributor_str_mv Chaves, Andrey
dc.subject.por.fl_str_mv Fósforo
Física da matéria condensada
Física do estado sólido
topic Fósforo
Física da matéria condensada
Física do estado sólido
description The possibility of obtaining two-dimensional systems from layered materials has been attracting a lot of research on these materials, since their few layer properties are very different from their respective bulk ones, which opens up great possibilities in technological applications. Black phosphorus exhibit several interesting properties, among them, a direct energy gap, that enables the possibility of fabricating electronic devices (in contrast e.g. with the gapless semi-metallic graphene), and which can be tuned by the number of layers, varying from 0.3 eV for a bulk up to 2.0 eV for a monolayer, thus covering a relatively large range of the energy spectrum for optical devices. Besides, the fact that this is a very anisotropic material has brought even more attention to it, towards novel ways of exploring this anisotropy in new technologies. In this work, we have derived the effective mass approximation from the tight binding model and used the out coming approximate Hamiltonian to study nanostructures based on monolayer black phosphorus. In this model, the anisotropic features of black phosphorus are reflected in the difference between effective masses in different directions. Firstly, we compare the finite difference methods with the analytical solution for a circular quantum dot, which, due to its elliptical contour of energy bands, is given by Mathieu functions for solving the resulting Schrödinger equation. With this comparison, we verify the compatibility between these methods. Within the effective mass approximation, we investigate the effect of external electromagnetic fields on a black phosphorus quantum ring, thus analysing the effect of the interplay between these fields and the system anisotropy on its electronic states. Due to the anisotropy, under an applied magnetic field, this ring does not exhibit Aharonov-Bohm oscillations, which can be recovered by assuming an elliptic ring-like confinement. We also investigate the effect of an external electric field applied in x and y directions in a black phosphorus quantum ring on its energy levels. Our results show that, as a consequence of a wave function localization induced by mass anisotropy, energy levels decay quadratically (Stark effect) with the field if it is applied along the armchair direction, whereas an almost linear Stark effect, along with a series of crossing excited states, is observed for a field applied in the zigzag direction, leading to a behavior that is in close resemblance to a double quantum well under a perpendicular electric field.
publishDate 2016
dc.date.accessioned.fl_str_mv 2016-10-07T15:49:06Z
dc.date.available.fl_str_mv 2016-10-07T15:49:06Z
dc.date.issued.fl_str_mv 2016
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
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dc.identifier.citation.fl_str_mv SOUSA, G. O. Anéis e pontos quânticos de fósforo negro investigadas por modelo contínuo. 2016. 73 f. Dissertação (Mestrado em Física) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2016.
dc.identifier.uri.fl_str_mv http://www.repositorio.ufc.br/handle/riufc/20058
identifier_str_mv SOUSA, G. O. Anéis e pontos quânticos de fósforo negro investigadas por modelo contínuo. 2016. 73 f. Dissertação (Mestrado em Física) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2016.
url http://www.repositorio.ufc.br/handle/riufc/20058
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