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 Bi$2$Mg$_3$. 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.