Electrostatically confined quantum dots in bilayer phosphorene

Detalhes bibliográficos
Ano de defesa: 2025
Autor(a) principal: Paz, Maria Lúcia Alvares
Orientador(a): Farias, Gil de Aquino
Banca de defesa: Não Informado pela instituição
Tipo de documento: Tese
Tipo de acesso: Acesso aberto
Idioma: eng
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
Link de acesso: http://repositorio.ufc.br/handle/riufc/82775
Resumo: Since the isolation of few-layer graphene in 2004 by Geim and Novoselov, materials in their lamellar versions have received great attention from the scientific and technological community due to their peculiar electronic, optical, and transport properties that are not present in their bulk forms. Among these two-dimensional materials, black phosphorus, an allotrope of phosphorus, exhibits high electron mobility and, unlike graphene, is a semiconductor whose energy gap strongly depends on the number of layers. The wide frequency range covered by the tunable gap (~ 2.0 eV for the monolayer down to ~0.3 eV in the bulk, combined with the anisotropic properties of its electronic structure, makes this material promising for various applications, especially in optoelectronics. In this work, we investigate the electronic properties of charge carriers confined in quantum dots defined exclusively through a position-dependent electrostatic potential, without the need for physical patterning of the material. This potential breaks the inversion symmetry of bilayer phosphorene, locally modulating the gap and allowing for charge carrier confinement. We employ the tight-binding method to numerically investigate the electronic states and their wave functions under circularly symmetric potentials, both in the absence and presence of a perpendicular magnetic field. As the main results, we identify the closing of the gap at a critical value of the applied potential, the consequent emergence of Dirac cones, and that the quantum dot energy gap follows a power-law dependence on the dot radius, Eg(R) ∝ 1/R1.38, highlighting the combined role of electrostatic confinement and material anisotropy.
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spelling Paz, Maria Lúcia AlvaresCosta, Diego Rabelo daFarias, Gil de Aquino2025-09-30T13:13:16Z2025-09-30T13:13:16Z2025PAZ, Maria Lúcia Alvares. Electrostatically confined quantum dots in bilayer phosphorene. Tese (Doutorado em Física: Física da Matéria Condensada) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2025.http://repositorio.ufc.br/handle/riufc/82775Since the isolation of few-layer graphene in 2004 by Geim and Novoselov, materials in their lamellar versions have received great attention from the scientific and technological community due to their peculiar electronic, optical, and transport properties that are not present in their bulk forms. Among these two-dimensional materials, black phosphorus, an allotrope of phosphorus, exhibits high electron mobility and, unlike graphene, is a semiconductor whose energy gap strongly depends on the number of layers. The wide frequency range covered by the tunable gap (~ 2.0 eV for the monolayer down to ~0.3 eV in the bulk, combined with the anisotropic properties of its electronic structure, makes this material promising for various applications, especially in optoelectronics. In this work, we investigate the electronic properties of charge carriers confined in quantum dots defined exclusively through a position-dependent electrostatic potential, without the need for physical patterning of the material. This potential breaks the inversion symmetry of bilayer phosphorene, locally modulating the gap and allowing for charge carrier confinement. We employ the tight-binding method to numerically investigate the electronic states and their wave functions under circularly symmetric potentials, both in the absence and presence of a perpendicular magnetic field. As the main results, we identify the closing of the gap at a critical value of the applied potential, the consequent emergence of Dirac cones, and that the quantum dot energy gap follows a power-law dependence on the dot radius, Eg(R) ∝ 1/R1.38, highlighting the combined role of electrostatic confinement and material anisotropy.Desde o isolamento do grafeno em poucas camadas em 2004 por Geim e Novoselov, materiais em suas versões lamelares têm recebido grande destaque na comunidade científica e tecnológica devido às propriedades eletrônicas, ópticas e de transporte peculiares que não estão presentes em suas versões bulk. Entre esses materiais bidimensionais, o fósforo negro, um alótropo do fósforo, apresenta alta mobilidade eletrônica e, ao contrário do grafeno, é um semicondutor cujo gap de energia depende fortemente do número de camadas. O amplo intervalo de frequências coberto pelo gap variável (~ 2.0 eV para monocamada até ~ 0.3 eV no bulk, aliado a propriedades anisotrópicas em sua estrutura eletrônica, torna esse material promissor para diversas aplicações, especialmente em optoeletrônica. Neste trabalho, investigamos as propriedades eletrônicas de portadores de carga confinados em pontos quânticos definidos exclusivamente por meio de um potencial eletrostático dependente da posição, sem necessidade de recorte físico do material. Esse potencial quebra a simetria de inversão da bicamada de fosforeno, modulando localmente o gap e permitindo o confinamento dos portadores de carga. Utilizamos o método tight-binding para investigar numericamente os estados eletrônicos e suas funções de onda em potenciais de simetria circular, na ausência e presença de um campo magnético perpendicular. Como resultados principais, identificamos o fechamento do gap para um valor crítico do potencial, a consequente emergência de cones de Dirac e que o gap de energia dos pontos quânticos segue uma lei de potência com o raio, Eg(R) ∝ 1/R1.38, evidenciando o papel combinado do confinamento eletrostático e da anisotropia do material.PAZ, Maria Lúcia Alvares. Electrostatically confined quantum dots in bilayer phosphorene. Tese (Doutorado em Física: Física da Matéria Condensada) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2025.Electrostatically confined quantum dots in bilayer phosphoreneElectrostatically confined quantum dots in bilayer phosphoreneinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisMateriais bidimensionaisSemicondutores anisotrópicosPropriedades eletrônicasFosforenoPontos quânticosTwo-dimensional materialsAnisotropic semiconductorsElectronic propertiesPhosphoreneQuantum dotsinfo:eu-repo/semantics/openAccessengreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFC2025ORIGINAL2025_tese_mlapaz.pdf2025_tese_mlapaz.pdfapplication/pdf16233448http://repositorio.ufc.br/bitstream/riufc/82775/3/2025_tese_mlapaz.pdfa253da85888757b8542cb6141c9486ccMD53LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.ufc.br/bitstream/riufc/82775/4/license.txt8a4605be74aa9ea9d79846c1fba20a33MD54riufc/827752025-09-30 10:13:16.802oai:repositorio.ufc.br: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Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2025-09-30T13:13:16Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false
dc.title.pt_BR.fl_str_mv Electrostatically confined quantum dots in bilayer phosphorene
dc.title.en.pt_BR.fl_str_mv Electrostatically confined quantum dots in bilayer phosphorene
title Electrostatically confined quantum dots in bilayer phosphorene
spellingShingle Electrostatically confined quantum dots in bilayer phosphorene
Paz, Maria Lúcia Alvares
Materiais bidimensionais
Semicondutores anisotrópicos
Propriedades eletrônicas
Fosforeno
Pontos quânticos
Two-dimensional materials
Anisotropic semiconductors
Electronic properties
Phosphorene
Quantum dots
title_short Electrostatically confined quantum dots in bilayer phosphorene
title_full Electrostatically confined quantum dots in bilayer phosphorene
title_fullStr Electrostatically confined quantum dots in bilayer phosphorene
title_full_unstemmed Electrostatically confined quantum dots in bilayer phosphorene
title_sort Electrostatically confined quantum dots in bilayer phosphorene
author Paz, Maria Lúcia Alvares
author_facet Paz, Maria Lúcia Alvares
author_role author
dc.contributor.co-advisor.none.fl_str_mv Costa, Diego Rabelo da
dc.contributor.author.fl_str_mv Paz, Maria Lúcia Alvares
dc.contributor.advisor1.fl_str_mv Farias, Gil de Aquino
contributor_str_mv Farias, Gil de Aquino
dc.subject.ptbr.pt_BR.fl_str_mv Materiais bidimensionais
Semicondutores anisotrópicos
Propriedades eletrônicas
Fosforeno
Pontos quânticos
topic Materiais bidimensionais
Semicondutores anisotrópicos
Propriedades eletrônicas
Fosforeno
Pontos quânticos
Two-dimensional materials
Anisotropic semiconductors
Electronic properties
Phosphorene
Quantum dots
dc.subject.en.pt_BR.fl_str_mv Two-dimensional materials
Anisotropic semiconductors
Electronic properties
Phosphorene
Quantum dots
description Since the isolation of few-layer graphene in 2004 by Geim and Novoselov, materials in their lamellar versions have received great attention from the scientific and technological community due to their peculiar electronic, optical, and transport properties that are not present in their bulk forms. Among these two-dimensional materials, black phosphorus, an allotrope of phosphorus, exhibits high electron mobility and, unlike graphene, is a semiconductor whose energy gap strongly depends on the number of layers. The wide frequency range covered by the tunable gap (~ 2.0 eV for the monolayer down to ~0.3 eV in the bulk, combined with the anisotropic properties of its electronic structure, makes this material promising for various applications, especially in optoelectronics. In this work, we investigate the electronic properties of charge carriers confined in quantum dots defined exclusively through a position-dependent electrostatic potential, without the need for physical patterning of the material. This potential breaks the inversion symmetry of bilayer phosphorene, locally modulating the gap and allowing for charge carrier confinement. We employ the tight-binding method to numerically investigate the electronic states and their wave functions under circularly symmetric potentials, both in the absence and presence of a perpendicular magnetic field. As the main results, we identify the closing of the gap at a critical value of the applied potential, the consequent emergence of Dirac cones, and that the quantum dot energy gap follows a power-law dependence on the dot radius, Eg(R) ∝ 1/R1.38, highlighting the combined role of electrostatic confinement and material anisotropy.
publishDate 2025
dc.date.accessioned.fl_str_mv 2025-09-30T13:13:16Z
dc.date.available.fl_str_mv 2025-09-30T13:13:16Z
dc.date.issued.fl_str_mv 2025
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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status_str publishedVersion
dc.identifier.citation.fl_str_mv PAZ, Maria Lúcia Alvares. Electrostatically confined quantum dots in bilayer phosphorene. Tese (Doutorado em Física: Física da Matéria Condensada) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2025.
dc.identifier.uri.fl_str_mv http://repositorio.ufc.br/handle/riufc/82775
identifier_str_mv PAZ, Maria Lúcia Alvares. Electrostatically confined quantum dots in bilayer phosphorene. Tese (Doutorado em Física: Física da Matéria Condensada) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2025.
url http://repositorio.ufc.br/handle/riufc/82775
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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dc.source.none.fl_str_mv reponame:Repositório Institucional da Universidade Federal do Ceará (UFC)
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reponame_str Repositório Institucional da Universidade Federal do Ceará (UFC)
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