All Topological Bands of All Stoichiometric Materials

The recently introduced theories of Topological Quantum Chemistry and Symmetry-Based Indicators (SIs) have facilitated the discovery of novel topological phases of matter and large-scale searches for materials with experimentally accessible topological properties at the Fermi energy ($E_F$). In this work, we have completed the first catalog of stable and fragile topology in all of the bands both at and away from $E_F$ in the Inorganic Crystal Structure Database (ICSD), which we have made accessible through a substantial upgrade of the Topological Materials Database. We have computed the electronic structure, topological class, and stable and fragile SIs of all bands in the 96,196 processable ICSD entries with stoichiometric chemical formulas in the presence and absence of SOC. Our calculations represent the completion of the symmetry-indicated band topology of known nonmagnetic materials, and a doubling of the number of materials accessible in previous topological material catalogs. Through our calculations, we discover the existence of repeat-topological (RTopo) materials with stable topological insulating (TI) gaps at and just below $E_F$, and supertopological (STopo) materials in which every isolated set of bands above the core shell is stable topological. Our findings recontextualize several previous experimental investigations of topological materials. We find that Ta$_2$NiSe$_5$ and Ta$_2$NiSe$_7$, respectively previously highlighted for hosting exciton-insulator and CDW phases, are 3D TIs in their normal states, and that rhombohedral bismuth and Bi$_2$Mg$_3$ are both RTopo and STopo materials. We present detailed statistics for our computations revealing 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 shockingly, 87.99% of all materials contain at least one topological band.