Three-Dimensional Real Space Invariants: Theory and Applications

In this work, we have developed the three-dimensional real space invariants (3D RSIs) for all the 1,651 Shubnikov space groups (SSGs) with spin-orbit coupling (SOC), including the 230 paramagnetic space groups (SGs) and the 1,421 magnetic space groups (MSGs), and provide the expressions of all the RSIs in the Bilbao Crystallographic Server. The 3D RSIs have allowed for the identification of a special set of 3D topologically trivial insulators which we call Obstructed Atomic Insulators (OAIs), and electrides which we call obstructed metals. Using the theoretical formulation of RSIs, we have performed the high throughput scanning of the Topological Quantum Chemistry database materials and found more than 3300  OAIs. and  5000 obstructed metals. Furthermore, we analyze the potential applications of OAIs and obstructed metals in catalysis and superconductivities.