Topological Materials Discovery using Electron Filling Constraints

Nodal semimetals, materials systems with nodal-point or -line Fermi surfaces, are much sought after for their novel transport and topological properties. Identification of experimental materials candidates, however, has mainly relied on exhaustive database searches. Here we show how recent studies on the interplay between electron filling and nonsymmorphic space-group symmetries can guide the search for nodal semimetals which are `filling-enforced'. We recast the previously-derived constraints on the allowed electron fillings for band insulators in the 230 space groups into a new form, which enables effective screening of materials candidates based solely on their (1) space group, (2) electron count in the formula unit, and (3) multiplicity of the formula unit. This criterion greatly reduces the computation load for discovering topological materials in a database of previously-synthesized compounds. Of the more than 30,000 entires listed in a few selected nonsymmorphic space groups, our filling criterion alone eliminates 96% of the entries before they are passed on for further analysis. From this guided search, we discover a handful of candidates, including the monoclinic crystals Ca$_2$Pt$_2$Ga, AgF$_2$, and Ca$_2$InOsO$_6$, and the orthorhombic crystal CsHg$_2$. Based on ab initio calculations, we show that these materials have filling-enforced Dirac nodes near the Fermi energy. In addition, we also identify CaPtGa as a promising filling-enforced Dirac-ring semimetal candidate.