Global band topology of simple and double Dirac-point semimetals

We combine space group representation theory together with the scanning of closed subdomains of the Brillouin zone with Wilson loops to algebraically determine the global band-structure topology. Considering space group No. $19$ as a case study, we show that the energy ordering of the irreducible representations at the high-symmetry points Γ,S,T,U fully determines the global band topology, with all topological classes characterized through their simple and double Dirac points.