All topological bands of all nonmagnetic stoichiometric materials

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 implementation 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, which represent the completion of the symmetry-indicated band topology of known nonmagnetic materials, have enabled the discovery of repeat-topological and supertopological materials, including rhombohedral bismuth and Bi₂Mg₃. We find that 52.65% of all materials are topological at E_F, roughly two-thirds of bands across all materials exhibit symmetry-indicated stable topology, and 87.99% of all materials contain at least one stable or fragile topological band.