Isolantes Triviais e Topológicos

Abstract

The topological insulators (TI), form a new quantum phase of matter. These mate- rials when being placed in contact with a trivial insulator, like vacuum, on the surfaces (three dimesional (3D)) or on the edges (two dimensional (2D)), emerge metallic states that have a single or a odd number of crossing between the cunductions bands e and valence band, giving rise to Dirac cones, as well as graphene. The strong spin-orbit coupling generates an inversion of symmetry of the band bottom states of the conduction band with the band top states of the valence band, leading the emergence of a topological phase. This kind of material has great potential for application in high speed devices, since due to the linear dispersions of the conduction states can present a high mobility. This states obey the Dirac equation, having null mass, were protect of scattering, and can be not destroyed if they undego continius and infinitesimal changes. Such properties are highly desired for technological applications. The objective of the development of this work is to investigate the effect of spin-orbit interaction on the structure of bands of two materials, the bulk silicon and the bismuth layer. As predicted by theory, when we put a material with trivial topology in contact with a material with non-trivial topology, edge states topologically protected by the symmetry of the system and which do not exhibit energy dissipation, will arise. In order to observe the appearance of these states, we will construct a nanoribbon, which is a confined system, whose interface is composed of a trivial topology material and one with a non-trivial topology, and we will analyze its band structure and of the effect of the spin-orbit coupling on it. Also, we will verify the effect of the width of this nanoribbon on its edge states. In our results we verified that, as predicted by the theory, textit bulk is a system with trivial topology, while the bismuth sheet has a non-trivial topology. And from the construction of the nanoribbon of the bismuth sheet it was possible to observe the edge states provided by theory.