Density Functional Theory Calculations of Topological Insulators

Density functional theory (DFT) is an approach to overcome the intractability of interacting quantum mechanical many-body problems: DFT recasts an interacting many-body equation into a set of self-consistent noninteracting single-particle equations, the so-called Kohn–Sham (KS) equations. This chapter gives an overview of some of the essential ideas underlying DFT and considers one example of widely used implementation of DFT, the plane-wave pseudopotential method. It focuses on two aspects indispensable for studying topological insulators (TIs): techniques for including spin–orbit interactions (SOIs) and evaluating Z2 topological invariants. The chapter demonstrates how DFT can be used for studying the bismuth chalcogenides Bi2Se3 and Bi2Te3 taken as generic examples of bulk Tls. It discusses some of their very basic properties such as bulk band structures, band dispersions, and spin textures of the topological states at the surfaces of these materials.