Three-Dimensional Real Space Invariants and Obstructed Atomic Insulators: Catalogues and Applications

Topologically trivial Insulators come into two kinds: Atomic, where the Wannier centers are localized on the atoms, and obstructed atomic, where the Wannier centers are located away from the atoms. The latter, which can exhibit interesting interface states with much larger gaps than the topological insulators, have so far not been classified in 3-dimensions (3-d). Here, we develop the 3-d real space invariants with band representations in 1651 Shubnikov space groups, which include 230 paramagnetic and 1421 magnetic space groups. By applying the RSIs to all the topological trivial insulators in Topological material database (https://www.topologicalquantumchemistry.com), we obtain about 4000 paramagnetic obstructed atomic Insulators (OAI), which should exhibit surface states and filling anomalies. Combined with symmetry analysis, we further filter out hundreds of OAIs with surface topological states such as quantum spin Hall effect and fragile bands and flat bands on the top of the surface. Finally, we comment on several potential applications of the OAIs, including first and foremost, catalysis.