Graph Theory Data for Topological Quantum Chemistry

Understand

Topological phases of noninteracting particles are distinguished by global properties of their band structure and eigenfunctions in momentum space.

• On the other hand, group theory as conventionally applied to solid-state physics focuses only on properties which are local (at high symmetry points, lines, and planes) in the Brillouin zone.
• To bridge this gap, we have previously [B.
• Bradlyn et al., Nature 547, 298--305 (2017)] mapped the problem of constructing global band structures out of local data to a graph construction problem.