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 with the computed irreducible representations in the first-principles calculations, 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). In fact, the floating bands (formed by the excess electrons) belong to the BRs induced from the pseudo-orbitals centered at vacancies. In other words, the electrides are proved to be unconventional ionic crystals, where a set of occupied bands is not a sum of aBRs but necessarily contains a BR from vacancies. The TQC theory provides a promising avenue to pursue more electride candidates in ionic crystals.
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