First-principles calculations for topological quantum materials

Discoveries of topological states and topological materials have reshaped our understanding of physics and materials over the past 15 years. First-principles calculations have had an important role in bridging the theory of topology and experiments by predicting realistic topological materials. In this Review, we offer an overview of the first-principles methodology on topological quantum materials. First, we unify different concepts of topological states in the same band inversion scenario. We then discuss the topology using first-principles band structures and newly established topological materials databases. We stress challenges in characterizing symmetry-independent Weyl semimetals and calculating topological surface states, closing with an outlook on the exciting transport and optical phenomena induced by the topology.