All topological bands of all nonmagnetic stoichiometric materials

Abstract

Topological Quantum Chemistry and Symmetry-Based Indicators have facilitated large-scale searches for materials with topological properties at the Fermi energy (E_F). We report the completion of a publicly accessible catalog of stable and fragile topology in all of the bands both at and away from E_F in the 96,196 processable entries in the Inorganic Crystal Structure Database. Our calculations represent the completion of the symmetry-indicated band topology of known nonmagnetic materials, and enable the discovery of repeat-topological and supertopological materials, which include rhombohedral bismuth and Bi₂Mg₃. We find that 52.65% of all materials are topological at E_F, roughly 2/3 of bands across all materials exhibit symmetry-indicated stable topology, and that 87.99% of all materials contain at least one stable or fragile topological band.