First Principles Calculations for Topological Quantum Materials.

Discoveries of topological states and topological materials reshape our understanding of physics and materials in the last one and half decades. First-principles calculations have been playing a significant role in bridging the topology theory and experiments by predicting realistic topological materials. In this article, we overview the first-principles methodology on topological quantum materials and provide a beginner's guide. First, we unify different concepts of topological states in the same band inversion scenario. Then, we discuss the topology using first-principles band structures and newly-established topological materials databases. We stress challenges in characterizing the symmetry-independent Weyl semimetals and calculating the topological surface states. We outlook the exciting transport and optical phenomena induced by the topology.