From local symmetry to band structure topology*

Weyl semi-metals and their symmetry-protected generalizations are sought after for their exotic Fermi arcs and unconventional transport properties. Symmetry can force these degeneracies to lie on special points or lines. However, it can be a challenge to find materials that realize these band crossings near the Fermi level. Using the theory of topological quantum chemistry, we describe how the local symmetry properties of a chemical compound (i.e., its orbitals and crystal structure) determine which symmetry representations appear at each point in the Brillouin zone and, ultimately, the topology of the band structure. This theory unites symmetry-enforced semi-metals and topological crystalline insulators. We describe algorithms to search for materials that realize these phases.