Topological insulators from the Perspective of first-principles calculations

TL;DR

This review discusses the use of first-principles calculations to predict, classify, and understand topological insulators, highlighting recent progress and methodologies in the field.

Contribution

It provides a comprehensive summary of how first-principles methods are applied to identify and classify topological insulators into different types based on band inversion.

Findings

Classification of topological insulators into three types: s-p, p-p, and d-f.

Summary of methodologies for discovering new topological insulators.

Discussion of representative examples for each topological insulator type.

Abstract

Topological insulators are new quantum states with helical gapless edge or surface states inside the bulk band gap.These topological surface states are robust against the weak time-reversal invariant perturbations, such as lattice distortions and non-magnetic impurities. Recently a variety of topological insulators have been predicted by theories, and observed by experiments. First-principles calculations have been widely used to predict topological insulators with great success. In this review, we summarize the current progress in this field from the perspective of first-principles calculations. First of all, the basic concepts of topological insulators and the frequently-used techniques within first-principles calculations are briefly introduced. Secondly, we summarize general methodologies to search for new topological insulators. In the last part, based on the band inversion picture first introduced in the context of HgTe, we classify topological insulators into three types with s-p, p-p and d-f, and discuss some representative examples for each type.