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 weak time-reversal invariant perturbations without closing the bulk band gap, 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. [GRAPHICS] Surface states of topological insulator Bi2Se3 consist of a single Dirac cone, as obtained from first-principles calculations. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
