The Application of Topological Quantum Chemistry in Electrides

The recently developed theory of topological quantum chemistry (TQC) has built a close connection between band representations in momentum space and orbital characters in real space. It provides an effective way to diagnose topological materials, leading to the discovery of lots of topological materials after the screening of all known nonmagnetic compounds. On the other hand, it can also efficiently reveal spacial orbital characters, including average charge centers and site-symmetry characters. By using TQC theory, we demonstrate that the electrides with excess electrons serving as anions at vacancies can be well identified by analyzing band representations (BRs), which cannot be expressed as a sum of atomic-orbital-induced band representations (aBRs). By computing the irreducible representations of electronic states, we find that the floating bands (formed by the excess electrons) belong to the BRs induced from the "pseudo-orbitals" centered at vacancies, which can be characterized by real-space invariants (RSI), providing a promising avenue to pursue more electrides in ionic crystals.