Wave-packet dynamics and electronic transport properties in 2D materials

Detalhes bibliográficos
Autor(a) principal: Cunha, Sofia Magalhães
Data de Publicação: 2022
Tipo de documento: Tese
Idioma: eng
Título da fonte: Repositório Institucional da Universidade Federal do Ceará (UFC)
Texto Completo: http://www.repositorio.ufc.br/handle/riufc/69291
Resumo: This piece of work is twofold. First, the time evolution of wave-packets in 2D systems is analyzed by the Split-Operator technique in three different scenarios: in multilayer phosphorene, the transient oscillations in the time-dependent average of position and momentum were observed due to the zitterbewegung effect, and the wave packet propagates non-uniformly along the space deforming itself into an elliptical shape. These results were corroborated by the Green’s function formalism except for large values of the wave-vector and long times; in 2D semiconductor quantum wires (QWs) with anisotropic effective masses and different angle orientations with respect to the anisotropic axis. We have shown that the greater this angle, the smaller is the energy levels spacing implying in an increase of the accessible electronic states. Additionally, for non-null magnetic field, the quantum Hall edge states are significantly affected by the edge orientation. In the anisotropic case damped oscillations in the average values of velocity in both x and y directions where obtained. Theses oscillations are originated by the QW geometry but also from subwavepackets with different momentum orientations, whereas for isotropic QWs the wavepacket disperses without splitting; in the third scenario the split-operator technique was used to study the Landau levels, the wave packet trajectories and velocities of electrons in graphene at low-energy regime described by a modified Dirac equation where the momentum-operator is written in a generalized form as result of applying the position-dependent translation operator formalism (PDTO). In the second part of this thesis, the electronic and tunneling properties of α − T 3 lattices were studied. Electrons in these lattices behave analogous to integer-spin Dirac Fermions. The presence of a third atomic site in the unit cell leads to a flat band in the energy spectrum, providing unique electronic and tunneling properties. The presence of a super-periodic potential and the inclusion of symmetry-breaking terms results in deviations of the atomic equivalence between the atomic sites affecting the Dirac points and the band-gap. Small deviations in the equivalence between the atomic sites and the number of barriers change the transmission properties in these lattices. Additionally, new tunneling regions are possible by adjusting the symmetry between the atomic sites and affect the omnidirectional total transmission called super-Klein tunneling observed in these lattices. We compare those results to the tunneling probabilities through regions where the energy spectrum changes from linear with a middle flat band to a hyperbolic dispersion.
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spelling Wave-packet dynamics and electronic transport properties in 2D materialsTécnica Split-OperatorFosforenoGrafenoSuper tunelamento KleinTight-binding approximationThis piece of work is twofold. First, the time evolution of wave-packets in 2D systems is analyzed by the Split-Operator technique in three different scenarios: in multilayer phosphorene, the transient oscillations in the time-dependent average of position and momentum were observed due to the zitterbewegung effect, and the wave packet propagates non-uniformly along the space deforming itself into an elliptical shape. These results were corroborated by the Green’s function formalism except for large values of the wave-vector and long times; in 2D semiconductor quantum wires (QWs) with anisotropic effective masses and different angle orientations with respect to the anisotropic axis. We have shown that the greater this angle, the smaller is the energy levels spacing implying in an increase of the accessible electronic states. Additionally, for non-null magnetic field, the quantum Hall edge states are significantly affected by the edge orientation. In the anisotropic case damped oscillations in the average values of velocity in both x and y directions where obtained. Theses oscillations are originated by the QW geometry but also from subwavepackets with different momentum orientations, whereas for isotropic QWs the wavepacket disperses without splitting; in the third scenario the split-operator technique was used to study the Landau levels, the wave packet trajectories and velocities of electrons in graphene at low-energy regime described by a modified Dirac equation where the momentum-operator is written in a generalized form as result of applying the position-dependent translation operator formalism (PDTO). In the second part of this thesis, the electronic and tunneling properties of α − T 3 lattices were studied. Electrons in these lattices behave analogous to integer-spin Dirac Fermions. The presence of a third atomic site in the unit cell leads to a flat band in the energy spectrum, providing unique electronic and tunneling properties. The presence of a super-periodic potential and the inclusion of symmetry-breaking terms results in deviations of the atomic equivalence between the atomic sites affecting the Dirac points and the band-gap. Small deviations in the equivalence between the atomic sites and the number of barriers change the transmission properties in these lattices. Additionally, new tunneling regions are possible by adjusting the symmetry between the atomic sites and affect the omnidirectional total transmission called super-Klein tunneling observed in these lattices. We compare those results to the tunneling probabilities through regions where the energy spectrum changes from linear with a middle flat band to a hyperbolic dispersion.Este trabalho se divide em duas partes. Na primeira, a evolução temporal dos pacotes de ondas em sistemas 2D é analisada pela técnica Split-Operator em três cenários diferentes: em multicamadas de fósforo negro, as oscilações transientes dependente do tempo nos valores médios de posição e momento foram observadas devido a o efeito zitterbewegung e o pacote de ondas se propagam de maneira não uniforme ao longo do espaço, deformando-se em uma forma elíptica. Esses resultados foram corroborados pelo formalismo da função de Green, exceto para maiores valores de momento e após intervalos maiores de tempo. Em fios quânticos semicondutores 2D com massas efetivas anisotrópicas e diferentes orientações de ângulo em relação ao eixo anisotrópico, mostramos que quanto maior este ângulo, menor é o espaçamento dos níveis de energia, implicando em um aumento dos estados eletrônicos acessíveis. Além disso, para o campo magnético não-nulo, os estados quânticos de Hall edge states são significativamente afetados pela orientação das bordas. No caso anisotrópico, oscilações amortecidas nos valores médios de velocidade nas direções x e y foram obtidas. Essas oscilações são originadas pela geometria do fio quântico, mas também de subpacotes de onda com diferentes orientações de momento, enquanto que para fios quanticos isotrópicos o pacote de onda se dispersa sem se dividir; no terceiro cenário, a técnica split-operator foi usada para estudar os níveis de Landau, as trajetórias do pacote de ondas e as velocidades dos elétrons no grafeno em regime de baixa energia descrito por uma equação de Dirac modificada onde o operador momentum é escrito em uma forma generalizada como resultado da aplicação do formalismo do operador de translação dependente da posição. Na segunda parte desta tese, as propriedades eletrônicas e de tunelamento das redes α − T3 foram estudadas. Os elétrons nessas redes se comportam de forma análoga aos férmions de Dirac de spin inteiro. A presença de um terceiro sítio atômico na célula unitária leva a uma banda plana no espectro de energia, fornecendo propriedades eletrônicas e de tunelamento únicas. A presença de um potencial superperiódico e a inclusão de termos de quebra de simetria resultam em desvios da equivalência atômica entre os sítios atômicos que afetam os pontos de Dirac e o band gap no espectro de energia. Pequenos desvios na equivalência entre os sítios atômicos e o número de barreiras alteram as propriedades de transmissão nessas redes. Além disso, novas regiões de tunelamento são possíveis ajustando a simetria entre os sítios atômicos e afetando a transmissão total omnidirecional chamada super-tunelamento de Klein observada nessas redes. Comparamos esses resultados com as probabilidades de tunelamento por meio de regiões onde o espectro de energia muda de linear com uma banda plana do meio para uma dispersão hiperbólica.Pereira Júnior, João MiltonPeeters, Francois Maria LeopoldCunha, Sofia Magalhães2022-11-21T14:58:37Z2022-11-21T14:58:37Z2022info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdfCUNHA, S. M. Wave-packet dynamics and electronic transport properties in 2D materials. 228 f. Tese (Doutorado em Física) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2022.http://www.repositorio.ufc.br/handle/riufc/69291engreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFCinfo:eu-repo/semantics/openAccess2022-11-21T14:58:37Zoai:repositorio.ufc.br:riufc/69291Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2024-09-11T18:36:52.525956Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false
dc.title.none.fl_str_mv Wave-packet dynamics and electronic transport properties in 2D materials
title Wave-packet dynamics and electronic transport properties in 2D materials
spellingShingle Wave-packet dynamics and electronic transport properties in 2D materials
Cunha, Sofia Magalhães
Técnica Split-Operator
Fosforeno
Grafeno
Super tunelamento Klein
Tight-binding approximation
title_short Wave-packet dynamics and electronic transport properties in 2D materials
title_full Wave-packet dynamics and electronic transport properties in 2D materials
title_fullStr Wave-packet dynamics and electronic transport properties in 2D materials
title_full_unstemmed Wave-packet dynamics and electronic transport properties in 2D materials
title_sort Wave-packet dynamics and electronic transport properties in 2D materials
author Cunha, Sofia Magalhães
author_facet Cunha, Sofia Magalhães
author_role author
dc.contributor.none.fl_str_mv Pereira Júnior, João Milton
Peeters, Francois Maria Leopold
dc.contributor.author.fl_str_mv Cunha, Sofia Magalhães
dc.subject.por.fl_str_mv Técnica Split-Operator
Fosforeno
Grafeno
Super tunelamento Klein
Tight-binding approximation
topic Técnica Split-Operator
Fosforeno
Grafeno
Super tunelamento Klein
Tight-binding approximation
description This piece of work is twofold. First, the time evolution of wave-packets in 2D systems is analyzed by the Split-Operator technique in three different scenarios: in multilayer phosphorene, the transient oscillations in the time-dependent average of position and momentum were observed due to the zitterbewegung effect, and the wave packet propagates non-uniformly along the space deforming itself into an elliptical shape. These results were corroborated by the Green’s function formalism except for large values of the wave-vector and long times; in 2D semiconductor quantum wires (QWs) with anisotropic effective masses and different angle orientations with respect to the anisotropic axis. We have shown that the greater this angle, the smaller is the energy levels spacing implying in an increase of the accessible electronic states. Additionally, for non-null magnetic field, the quantum Hall edge states are significantly affected by the edge orientation. In the anisotropic case damped oscillations in the average values of velocity in both x and y directions where obtained. Theses oscillations are originated by the QW geometry but also from subwavepackets with different momentum orientations, whereas for isotropic QWs the wavepacket disperses without splitting; in the third scenario the split-operator technique was used to study the Landau levels, the wave packet trajectories and velocities of electrons in graphene at low-energy regime described by a modified Dirac equation where the momentum-operator is written in a generalized form as result of applying the position-dependent translation operator formalism (PDTO). In the second part of this thesis, the electronic and tunneling properties of α − T 3 lattices were studied. Electrons in these lattices behave analogous to integer-spin Dirac Fermions. The presence of a third atomic site in the unit cell leads to a flat band in the energy spectrum, providing unique electronic and tunneling properties. The presence of a super-periodic potential and the inclusion of symmetry-breaking terms results in deviations of the atomic equivalence between the atomic sites affecting the Dirac points and the band-gap. Small deviations in the equivalence between the atomic sites and the number of barriers change the transmission properties in these lattices. Additionally, new tunneling regions are possible by adjusting the symmetry between the atomic sites and affect the omnidirectional total transmission called super-Klein tunneling observed in these lattices. We compare those results to the tunneling probabilities through regions where the energy spectrum changes from linear with a middle flat band to a hyperbolic dispersion.
publishDate 2022
dc.date.none.fl_str_mv 2022-11-21T14:58:37Z
2022-11-21T14:58:37Z
2022
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv CUNHA, S. M. Wave-packet dynamics and electronic transport properties in 2D materials. 228 f. Tese (Doutorado em Física) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2022.
http://www.repositorio.ufc.br/handle/riufc/69291
identifier_str_mv CUNHA, S. M. Wave-packet dynamics and electronic transport properties in 2D materials. 228 f. Tese (Doutorado em Física) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2022.
url http://www.repositorio.ufc.br/handle/riufc/69291
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Institucional da Universidade Federal do Ceará (UFC)
instname:Universidade Federal do Ceará (UFC)
instacron:UFC
instname_str Universidade Federal do Ceará (UFC)
instacron_str UFC
institution UFC
reponame_str Repositório Institucional da Universidade Federal do Ceará (UFC)
collection Repositório Institucional da Universidade Federal do Ceará (UFC)
repository.name.fl_str_mv Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)
repository.mail.fl_str_mv bu@ufc.br || repositorio@ufc.br
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