Topological semimetals from the perspective of first-principles calculations

Topological semimetals (TSMs) refer to electronic gapless phases that exhibit topological band crossings around the Fermi level and have intrigued enormous research interest in the past few decades. There have been many theoretical and experimental progresses regarding TSMs, and first-principles calculations have been proven to be an instrumental tool in finding candidate materials for TSMs. In this tutorial, we will focus on two representative types of TSMs-Weyl and Dirac semimetals and summarize the recent progress from the perspective of first-principles calculations. First of all, the basic concepts of TSMs, the generic topological invariants, and the frequently used techniques within first-principles calculations are briefly introduced. Second, taking typical materials as representative examples, we summarize the characteristic electronic properties, formation mechanisms, and general methodologies for Weyl and Dirac semimetals, respectively. In the last part, we present a short review of recent progresses on other types of TSMs.