Global band topology of simple and double Dirac-point (semi-)metals

Abstract

We combine space group representation theory together with scanning of closed subdomains of the Brillouin zone with Wilson loops to algebraically determine global band structure topology. Considering space group #19 as a case study, we show that the energy ordering of the irreducible representations at the high-symmetry points $\{\Gamma,S,T,U\}$ fully determines the global band topology, with all topological classes characterized through their simple and double Dirac-points.