Estrutura Eletrônica de Isolantes Topológicos via Teoria de Perturbação de Löwdin e Teoria de Grupos

Abstract

The energy levels of a confined particle are given of discrete form. In solids, due to the big number of atoms (∼ 10²³), the electronic bands appear obeying the principle of exclusion of Pauli. These, explain physics properties of solids as insulators, semiconductors, metals, etc. In semiconductors, we typically analyze two bands: conduction and valence. Due, to the periodicity of the crystal appear regions of prohibited energy (gap), where the electrons have no propagation mobility in the material. The theoretical study of electronic bands is typically based on perturbative methods and the symmetry of the material. In this sense, we investigated the electronic structure of GaAs and graphene using Löwdin perturbation theory, kp method and group theory. For the Kronig-Penney potential we obtained the effective mass. Beyond thereof, in the graphene model we analyzed the characteristics of the points of hight symmetry Γ and K finding the effective Hamiltonian of the material. The results of this monograph can be extended: in the GaAs model the inclusion of spin-orbit interaction can be done using group theory, beyond thereof the invariant method can be applied for different materials, such as PbSe and SnTe.