O papel da interação elétron-elétron no regime Hall quântico interio.
Autor(a) principal: | |
---|---|
Data de Publicação: | 2004 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/4894 |
Resumo: | Experimental and theoretical studies of the aspects of particle-like and collective behavior of electrons in the proximity of the edges of two-dimensional (2DES) and quasi-one-dimensional (Q1DES) systems, named quantum wires (QWs), in semiconductor heterostructures reveal the important role of the electron-electron interaction on the edge states in the integer quantum Hall regime (IQHR). In this thesis we treat two essentially different problems concerning the effects of the electron-electron interaction in low-dimensional electron system in the IQHR. The first problem is related to the suppression of the spin-splitting of the lowest Landau level (LL) (n = 0) due to many-body effects (the electron-electron interaction including exchange and correlation effects of the edge states) in QWs in the IQHR, where the electron behavior is particle-like. Two scenarios are discussed for the collapse of the IQHR at ν = 1 for an electron channel of effective width W modelling the QW. In the first scenario we assume that there is no electron redistribution in the region limited by W at a critical magnetic field B(1) cr , for which the Fermi level (FL) coincides with the bottom of the highest empty LL, at the threshold of the spin-splitting. For B < B(1) cr the IQHR at ν = 1 is termodinamically unstable. This scenario is analyzed within the generalized local density approximation (GLDA) developed here for the QW, at high magnetic fields - ωc À Ω, where ωc and Ω are the ciclotronic and lateral confinement (which we assume as parabolic one) frequencies, respectively. In the second scenario, we consider the possibility of a transition for the IQHR at ν = 2 with an effective width W/2, at a critical magnetic field B(2) cr . In this scenario, the collapse of the IQHR at ν = 1 is studied within the Hartree-Fock approximation (HFA), when the bare factor g0 is neglected (this is a good approximation for QWs based on GaAs). We show that the contribution for the total energy coming from the direct interaction (Hartree term) has a strong effect on B(2) cr due to the high electron redistribution inside the narrow channel that defines the QW at B(2) cr . In both scenarios, the enhanced spin-splitting by exchange is suppressed at the critical magnetic field. From our results, we conclude that only the first scenario explains all the experimental findings obtained by Wróbel et al. and Pallecchi et al.. In the second problem, where the collective aspects of the electron system are dominant, we study the influence of the temperature on the dispersion relation and the spatial structure of the edge magnetoplasmons (EMPs) in wide electron channels in the RHQI at ν = 1 (2) and 4, in the range ¯hωc À kB T À ¯hvH gn/2 0, for different dissipation regimes, by extending the pioneering work by Balev and Studart; here, ¯h is the constant of Planck constant (by 2π), kB is the constant of Boltzmann, vH gn is the group velocity (in Hartree approximation) of the edge states of n-th LL, and 0 is the magnetic lenght. A new mode called the edge helicon is found which is the only one that survive for very strong dissipation regime. For a sake of completeness, the general picture of the other modes is presented in the weak dissipation regime. EMPs in the IQHR for ν = 4 are also evaluated for weak dissipation and we find strong renormalization of the pure EMPs when the Coulomb interaction is considered appropriately. In all studied cases the important effect of the gate and the air from a distance d of the wide electron channel is considered. |
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Silva, Sanderson Francisco Fernandes Pereira daStudart Filho, Nelsonhttp://lattes.cnpq.br/0451310772113076http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=B545317c277b16-cad4-4522-b572-cbf54e00ff5f2016-06-02T20:15:16Z2007-10-192016-06-02T20:15:16Z2004-04-02SILVA, Sanderson Francisco Fernandes Pereira da. O papel da interação elétron-elétron no regime Hall quântico interio.. 2004. 117 f. Tese (Doutorado em Ciências Exatas e da Terra) - Universidade Federal de São Carlos, São Carlos, 2004.https://repositorio.ufscar.br/handle/ufscar/4894Experimental and theoretical studies of the aspects of particle-like and collective behavior of electrons in the proximity of the edges of two-dimensional (2DES) and quasi-one-dimensional (Q1DES) systems, named quantum wires (QWs), in semiconductor heterostructures reveal the important role of the electron-electron interaction on the edge states in the integer quantum Hall regime (IQHR). In this thesis we treat two essentially different problems concerning the effects of the electron-electron interaction in low-dimensional electron system in the IQHR. The first problem is related to the suppression of the spin-splitting of the lowest Landau level (LL) (n = 0) due to many-body effects (the electron-electron interaction including exchange and correlation effects of the edge states) in QWs in the IQHR, where the electron behavior is particle-like. Two scenarios are discussed for the collapse of the IQHR at ν = 1 for an electron channel of effective width W modelling the QW. In the first scenario we assume that there is no electron redistribution in the region limited by W at a critical magnetic field B(1) cr , for which the Fermi level (FL) coincides with the bottom of the highest empty LL, at the threshold of the spin-splitting. For B < B(1) cr the IQHR at ν = 1 is termodinamically unstable. This scenario is analyzed within the generalized local density approximation (GLDA) developed here for the QW, at high magnetic fields - ωc À Ω, where ωc and Ω are the ciclotronic and lateral confinement (which we assume as parabolic one) frequencies, respectively. In the second scenario, we consider the possibility of a transition for the IQHR at ν = 2 with an effective width W/2, at a critical magnetic field B(2) cr . In this scenario, the collapse of the IQHR at ν = 1 is studied within the Hartree-Fock approximation (HFA), when the bare factor g0 is neglected (this is a good approximation for QWs based on GaAs). We show that the contribution for the total energy coming from the direct interaction (Hartree term) has a strong effect on B(2) cr due to the high electron redistribution inside the narrow channel that defines the QW at B(2) cr . In both scenarios, the enhanced spin-splitting by exchange is suppressed at the critical magnetic field. From our results, we conclude that only the first scenario explains all the experimental findings obtained by Wróbel et al. and Pallecchi et al.. In the second problem, where the collective aspects of the electron system are dominant, we study the influence of the temperature on the dispersion relation and the spatial structure of the edge magnetoplasmons (EMPs) in wide electron channels in the RHQI at ν = 1 (2) and 4, in the range ¯hωc À kB T À ¯hvH gn/2 0, for different dissipation regimes, by extending the pioneering work by Balev and Studart; here, ¯h is the constant of Planck constant (by 2π), kB is the constant of Boltzmann, vH gn is the group velocity (in Hartree approximation) of the edge states of n-th LL, and 0 is the magnetic lenght. A new mode called the edge helicon is found which is the only one that survive for very strong dissipation regime. For a sake of completeness, the general picture of the other modes is presented in the weak dissipation regime. EMPs in the IQHR for ν = 4 are also evaluated for weak dissipation and we find strong renormalization of the pure EMPs when the Coulomb interaction is considered appropriately. In all studied cases the important effect of the gate and the air from a distance d of the wide electron channel is considered.Diversos estudos experimentais e teóricos, envolvendo tanto o comportamento do tipo partícula quanto coletivo dos elétrons numa estreita região próxima às fronteiras de sistemas bidimensionais (SE2Ds) e quase-unidimensionais (SEQ1Ds), ou fios quânticos (FQs), em heteroestruturas semicondutoras, vêm revelando o importante papel da interação elétron-elétron dos estados de borda no regime Hall quântico inteiro (RHQI). Dois problemas essencialmente diferentes quanto à natureza de sua manifestação, mas interligados quanto ao meio e regime em que são inseridos, são tratados nesta tese. O primeiro problema aborda a supressão do desdobramento de spin do mais baixo nível de Landau (NL) (n = 0) devido a efeitos de muitos corpos (interação elétron-elétron incluindo troca e correlação dos estados de borda) em FQs no RHQI, cujo comportamento eletrônico se manifesta como sendo do tipo de partícula. Aqui são discutidos dois cenários para o colapso do RHQI com ν = 1 no FQ com largura efetiva W . No primeiro cenário assumimos que não há redistribuição dos elétrons na região limitada por W na presença de um campo magnético crítico B(1) cr , tal que o nível de Fermi (NF) coincide com o fundo do mais alto NL vazio, no limiar do desdobramento de spin. Para B < B(1) cr o RHQI com ν = 1 é instável termodinamicamente. Este cenário é tratado dentro da aproximação da densidade local generalizada (ADLG) desenvolvida aqui para o FQ, em altos campos magnéticos - ωc À Ω, onde ωc e Ω são as freqüências ciclotrônica e de confinamento lateral (que nós consideramos como sendo parabólico), respectivamente. No segundo cenário, consideramos a possibilidade de uma transição para o RHQI com ν = 2 com uma largura duas vezes menor, W/2, no caso de um campo magnético crítico B(2) cr . Neste cenário, o colapso do RHQI com ν = 1 é estudado dentro da aproximação de Hartree-Fock (AHF), quando o fator g0 puro é desprezado (uma boa aproximação para FQs baseados em GaAs). Mostramos que a contribuição para a energia total da interação direta (termo de Hartree) tem um grande efeito sobre B(2) cr por causa da forte redistribuição dentro do canal estreito que cr . Em ambos os cenários, o desdobramento de spin realçado pelo termo de troca é suprimido no campo magnético crítico. De acordo com tais resultados, fomos levados a concluir que somente nosso primeiro cenário explica todas as observações experimentais, obtidas por Wróbel et al. e Pallecchi et al., pertinentes ao nosso estudo. O segundo problema, cujo comportamento eletrônico se manifesta como sendo do tipo coletivo, aborda os efeitos da temperatura sobre a dispersão e a estrutura espacial dos magnetoplasmons de borda (MPBs) em canais eletrônicos largos (ou SE2Ds) no RHQI com ν = 1(2) e 4, considerando o intervalo de temperaturas T não-muito-baixas, ¯hωc À kB T À ¯hvH gn/2 0, e diferentes regimes de dissipação, numa extensão ao trabalho pioneiro desenvolvido por Balev e Studart; aqui, ¯h é a constante de Planck (por 2π), kB é a constante de Boltzmann, vH gn é a velocidade de grupo (na aproximação Hartree) dos estados de borda do n-ésimo NL e 0 é o comprimento magnético. Assim, um novo modo denominado hélicon de borda foi encontrado, sendo o único dentre os vários outros modos presentes a sobreviver sob o regime de dissipação muito forte, revelando o importante papel da interação elétron-elétron. Por questão de completeza, um quadro geral dos outros modos é apresentado no regime de fraca dissipação. MPBs no RHQI com ν = 4 são também avaliados na região de fraca dissipação, onde é verificada uma forte renormalização dos MPBs puros quando considerada a interação coulombiana entre eles. Em todos casos o importante efeito do portão (gate) e ar a uma distância d dos canais largos é considerado.Financiadora de Estudos e Projetosapplication/pdfporUniversidade Federal de São CarlosPrograma de Pós-Graduação em Física - PPGFUFSCarBRFísica da matéria condensadaInteração elétron-elétronRegime Hall quântico inteiroMagnetoplasmonsCIENCIAS EXATAS E DA TERRA::FISICA::FISICA DA MATERIA CONDENSADAO papel da interação elétron-elétron no regime Hall quântico interio.info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis-1-1e4639cc6-864e-4cd1-b1c7-53741556e8c3info:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALTeseSFFPS.pdfapplication/pdf1833696https://repositorio.ufscar.br/bitstream/ufscar/4894/1/TeseSFFPS.pdf2dcb008b4bd422c525fbffa1eb94608cMD51THUMBNAILTeseSFFPS.pdf.jpgTeseSFFPS.pdf.jpgIM Thumbnailimage/jpeg8180https://repositorio.ufscar.br/bitstream/ufscar/4894/2/TeseSFFPS.pdf.jpg6eb236b9937ab612a077efd61f2d2da1MD52ufscar/48942023-09-18 18:31:04.769oai:repositorio.ufscar.br:ufscar/4894Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:31:04Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.por.fl_str_mv |
O papel da interação elétron-elétron no regime Hall quântico interio. |
title |
O papel da interação elétron-elétron no regime Hall quântico interio. |
spellingShingle |
O papel da interação elétron-elétron no regime Hall quântico interio. Silva, Sanderson Francisco Fernandes Pereira da Física da matéria condensada Interação elétron-elétron Regime Hall quântico inteiro Magnetoplasmons CIENCIAS EXATAS E DA TERRA::FISICA::FISICA DA MATERIA CONDENSADA |
title_short |
O papel da interação elétron-elétron no regime Hall quântico interio. |
title_full |
O papel da interação elétron-elétron no regime Hall quântico interio. |
title_fullStr |
O papel da interação elétron-elétron no regime Hall quântico interio. |
title_full_unstemmed |
O papel da interação elétron-elétron no regime Hall quântico interio. |
title_sort |
O papel da interação elétron-elétron no regime Hall quântico interio. |
author |
Silva, Sanderson Francisco Fernandes Pereira da |
author_facet |
Silva, Sanderson Francisco Fernandes Pereira da |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=B54531 |
dc.contributor.author.fl_str_mv |
Silva, Sanderson Francisco Fernandes Pereira da |
dc.contributor.advisor1.fl_str_mv |
Studart Filho, Nelson |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/0451310772113076 |
dc.contributor.authorID.fl_str_mv |
7c277b16-cad4-4522-b572-cbf54e00ff5f |
contributor_str_mv |
Studart Filho, Nelson |
dc.subject.por.fl_str_mv |
Física da matéria condensada Interação elétron-elétron Regime Hall quântico inteiro Magnetoplasmons |
topic |
Física da matéria condensada Interação elétron-elétron Regime Hall quântico inteiro Magnetoplasmons CIENCIAS EXATAS E DA TERRA::FISICA::FISICA DA MATERIA CONDENSADA |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::FISICA::FISICA DA MATERIA CONDENSADA |
description |
Experimental and theoretical studies of the aspects of particle-like and collective behavior of electrons in the proximity of the edges of two-dimensional (2DES) and quasi-one-dimensional (Q1DES) systems, named quantum wires (QWs), in semiconductor heterostructures reveal the important role of the electron-electron interaction on the edge states in the integer quantum Hall regime (IQHR). In this thesis we treat two essentially different problems concerning the effects of the electron-electron interaction in low-dimensional electron system in the IQHR. The first problem is related to the suppression of the spin-splitting of the lowest Landau level (LL) (n = 0) due to many-body effects (the electron-electron interaction including exchange and correlation effects of the edge states) in QWs in the IQHR, where the electron behavior is particle-like. Two scenarios are discussed for the collapse of the IQHR at ν = 1 for an electron channel of effective width W modelling the QW. In the first scenario we assume that there is no electron redistribution in the region limited by W at a critical magnetic field B(1) cr , for which the Fermi level (FL) coincides with the bottom of the highest empty LL, at the threshold of the spin-splitting. For B < B(1) cr the IQHR at ν = 1 is termodinamically unstable. This scenario is analyzed within the generalized local density approximation (GLDA) developed here for the QW, at high magnetic fields - ωc À Ω, where ωc and Ω are the ciclotronic and lateral confinement (which we assume as parabolic one) frequencies, respectively. In the second scenario, we consider the possibility of a transition for the IQHR at ν = 2 with an effective width W/2, at a critical magnetic field B(2) cr . In this scenario, the collapse of the IQHR at ν = 1 is studied within the Hartree-Fock approximation (HFA), when the bare factor g0 is neglected (this is a good approximation for QWs based on GaAs). We show that the contribution for the total energy coming from the direct interaction (Hartree term) has a strong effect on B(2) cr due to the high electron redistribution inside the narrow channel that defines the QW at B(2) cr . In both scenarios, the enhanced spin-splitting by exchange is suppressed at the critical magnetic field. From our results, we conclude that only the first scenario explains all the experimental findings obtained by Wróbel et al. and Pallecchi et al.. In the second problem, where the collective aspects of the electron system are dominant, we study the influence of the temperature on the dispersion relation and the spatial structure of the edge magnetoplasmons (EMPs) in wide electron channels in the RHQI at ν = 1 (2) and 4, in the range ¯hωc À kB T À ¯hvH gn/2 0, for different dissipation regimes, by extending the pioneering work by Balev and Studart; here, ¯h is the constant of Planck constant (by 2π), kB is the constant of Boltzmann, vH gn is the group velocity (in Hartree approximation) of the edge states of n-th LL, and 0 is the magnetic lenght. A new mode called the edge helicon is found which is the only one that survive for very strong dissipation regime. For a sake of completeness, the general picture of the other modes is presented in the weak dissipation regime. EMPs in the IQHR for ν = 4 are also evaluated for weak dissipation and we find strong renormalization of the pure EMPs when the Coulomb interaction is considered appropriately. In all studied cases the important effect of the gate and the air from a distance d of the wide electron channel is considered. |
publishDate |
2004 |
dc.date.issued.fl_str_mv |
2004-04-02 |
dc.date.available.fl_str_mv |
2007-10-19 2016-06-02T20:15:16Z |
dc.date.accessioned.fl_str_mv |
2016-06-02T20:15:16Z |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/doctoralThesis |
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doctoralThesis |
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publishedVersion |
dc.identifier.citation.fl_str_mv |
SILVA, Sanderson Francisco Fernandes Pereira da. O papel da interação elétron-elétron no regime Hall quântico interio.. 2004. 117 f. Tese (Doutorado em Ciências Exatas e da Terra) - Universidade Federal de São Carlos, São Carlos, 2004. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/4894 |
identifier_str_mv |
SILVA, Sanderson Francisco Fernandes Pereira da. O papel da interação elétron-elétron no regime Hall quântico interio.. 2004. 117 f. Tese (Doutorado em Ciências Exatas e da Terra) - Universidade Federal de São Carlos, São Carlos, 2004. |
url |
https://repositorio.ufscar.br/handle/ufscar/4894 |
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por |
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openAccess |
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Universidade Federal de São Carlos |
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Programa de Pós-Graduação em Física - PPGF |
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UFSCar |
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BR |
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Universidade Federal de São Carlos |
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