Interplay between geometry and topology on a conical quantum dot

• Ano de defesa: 2020
• Autor(a) principal: Veiga, Leonardo Gomides
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal de Viçosa
• Palavras-chave em Português: Pontos quânticos; Isolantes topológicos; Superfícies (Matemática); Física da Matéria Condensada
• Link de acesso: https://locus.ufv.br//handle/123456789/28449

This work is aimed to the study of the interplay between quantum confinement and topo- logical features in condensed matter systems with complex geometry. More specifically we studied a conical topological insulator quantum dot (CTIQD), where the local non- triviality of the cone tip (the cone has null curvature everywhere but at the tip, where there is a singularity) can lead to global effects in the surface charge carriers and its energies spectrum and properties. We start by introducing an ordinary conical quantum dot (i.e., a semiconductor) through an effective model , and we make an introduction to topology in condensed matter and topological insulators. The effective Dirac operator that acts on the charge carriers on the surface of the conical topological insulator is calcu- lated, and the Dirac equation that describes the dynamics of these carriers is completely solved. We discussed the geometric and topological effects associated with the singularity and how the wave function and the energy spectrum are affected by these effects. Keywords: Quantum dots. Topological insulators. Quantum confinement. Dirac equation on curved spaces.