Publicação
Excitonic properties of hBN from a time-dependent hartree-fock mean-field theory
| Resumo: | In this work we perform a generic derivation on how collective excitations emerge from a many-body system of interacting particles within a time-dependent Hartree-Fock mean-field theory at zero-temperature. To this end, we study the linear response of the system’s reduced density matrix in a many-body perturbation theory and demonstrate that it can be expressed in terms of a generalized eigen-problem of the effective two-particle Hamiltonian of the electron-hole interaction. We then specify this formalism for the case of a crystal system and an atomistic electron-electron interaction, structuring the generalized eigen-problem in terms of the Bloch momentum and spin degrees of freedom. At last, we apply this theory to the case of hexagon boron nitride structures in a nearest-neighbor tight-binding model for the electronic Bloch states. We then solve the generalized eigen-problem numerically and obtain the excitonic states energies and wavefunctions. Also, we comment on the role of screening in the Hartree and Fock interaction, on the numerical details of the generalized eigen-problem and on the reliability of the Tamm-Dancoff approximation. |
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| Autores principais: | Ribeiro, Francisco Ricardo Lobo |
| Assunto: | Time-dependent Mean-field approximation Hartree-Fock Screening Reduced density matrix Zero temperature Linear response Effective two-particle Hamiltonian Generalized eigen-problem Crystal Tight-binding mode Exciton Hexagonal boron nitride Dependente do tempo Aproximação de campo médio Blindagem Matriz de densidade reduzida Temperatura zero Resposta linear Hamiltonian efetivo de dois-partículas Model de tight-binding Problema generalizado aos valores próprios Cristais excitão Nitreto de boro hexagonal Ciências Naturais::Ciências Físicas |
| Ano: | 2023 |
| País: | Portugal |
| Tipo de documento: | dissertação de mestrado |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | In this work we perform a generic derivation on how collective excitations emerge from a many-body system of interacting particles within a time-dependent Hartree-Fock mean-field theory at zero-temperature. To this end, we study the linear response of the system’s reduced density matrix in a many-body perturbation theory and demonstrate that it can be expressed in terms of a generalized eigen-problem of the effective two-particle Hamiltonian of the electron-hole interaction. We then specify this formalism for the case of a crystal system and an atomistic electron-electron interaction, structuring the generalized eigen-problem in terms of the Bloch momentum and spin degrees of freedom. At last, we apply this theory to the case of hexagon boron nitride structures in a nearest-neighbor tight-binding model for the electronic Bloch states. We then solve the generalized eigen-problem numerically and obtain the excitonic states energies and wavefunctions. Also, we comment on the role of screening in the Hartree and Fock interaction, on the numerical details of the generalized eigen-problem and on the reliability of the Tamm-Dancoff approximation. |
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