Estudo teórico de transições de fase topológica na franqueita: uma heteroestrutura de van der Waals de formação natural

Abstract

In this work, we intended to investigate the electronic and topological proprieties of the franckeite, a non- stoichiometric material formed by alternated stacking layers. The layers have different compositions, symmetries and periodicity. This characteristics lead to an incommensurate crystal structure e held partially by van der Waals and partially by ionic interactions. For our research we used the Functional Density Theory | DFT, with it was possible to predict a topological phase transition caused by the stoichiometric changes in one the franckeite`s layers. To study this matter our work was divided in three main parts. We began by exploring the theoretical bases that sustain the Functional Density Theory, in order to better comprehend the tools used in our study of franckeite. The following step was, starting from the simplified interpretation proposed by Haldane we study the Berry`s Theory, both helped us to better gasp at some proprieties that are a present in all topological materials. At last, in order to explore the franckeite`s topological phases we concluded the following steps: 1) direct calculation of Z2 topological invariant; 2) study the rising of band inversion around S point as well as it`s orbital composition; 3) compute the surface`s states; and 4) calculate the band structure for a few layers system. With this stages it was possible to build a topological phase space for the chemical composition changes occurring in individual layers.