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

## TL;DR

This paper develops an algebraic method combining space group theory and Wilson loops to classify the global band topology of simple and double Dirac-point semimetals, exemplified by space group #19.

## Contribution

It introduces a novel algebraic approach that links irreducible representation ordering at high-symmetry points to global topological classification.

## Key findings

- Energy ordering at high-symmetry points determines topology
- All topological classes characterized by Dirac points
- Method applied to space group #19 case study

## 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.