Topological materials discovery by large-order symmetry indicators

Crystalline symmetries play an important role in the classification of band structures, and their richness leads to various topological crystalline phases. On the basis of our recently developed method for the efficient discovery of topological materials using symmetry indicators, we explore topological materials in five space groups (SGs), which are diagnosed by large-order symmetry indicators (Z(8) and Z(12)) and support the coexistence of several kinds of gapless boundary states in a single compound. We predict many candidate materials; some representatives include Pt3Ge (SG 140), graphite (SG 194), XPt3 (SG221, X = Sn, Pb), Au4Ti (SG87), and Ti2Sn (SG194). As by-products, we also find that AgXF3 (SG140, X = Rb, Cs) and AgAsX (SG194, X = Sr, Ba) are good Dirac semimetals with clean Fermi surfaces. The proposed materials provide a good platform for studying the novel properties emerging from the interplay between different types of boundary states.