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 $\{\mathrm{\Gamma },S,T,U\}$ fully determines the global band topology, with all topological classes characterized through their simple and double Dirac points.

• Received 17 February 2017

DOI:https://doi.org/10.1103/PhysRevB.95.241101