Explorando a Equação de Dirac: um passeio por Isolantes Topológicos e Férmions de Majorana

Abstract

In this monography, we sought to understand the physical and mathematical reasoning that led Paul Dirac to build his famous equation, and why it has attracted the attention of the condensed matter physicists in the last decades. We then make a historically based discussion about the process of building the Dirac equation and describe some of it's main properties. With all that well established, we base ourselves in an already rich literature, to argue in favor of using the Dirac equation to build effective models to describe Topological Insulators. We start with a very general discussion which is finished with the investigation of Bismuth Selenide (Bi2Se3). We also present a brief discussion about how Majorana Fermions can be predicted by an investigation of real solutions to the Dirac equation, and how those fermions have been used to describe topological superconductors.