UC Berkeley

Although the richness of spatial symmetries has led to a rapidly expanding inventory of possible topological crystalline (TC) phases of electrons, physical realizations have been slow to materialize due to the practical difficulty in ascertaining band topology in realistic calculations. Here, we integrate the recently established theory of symmetry indicators of band topology into first-principles band-structure calculations, and test it on a database of previously synthesized crystals. On applying our algorithm to just 8 out of the 230 space groups, we are able to efficiently unearth topological materials and predict a diversity of topological phenomena, including: a screw-protected three-dimensional TC insulator, β-MoTe 2 , with gapped surfaces except for one-dimensional helical hinge states; a rotation-protected TC insulator, BiBr, with coexisting surface Dirac cones and hinge states; non-centrosymmetric Z 2 topological insulators undetectable using the well-established parity criterion, AgXO (X = Na, K, Rb); a Dirac semimetal MgBi 2 O 6 ; a Dirac nodal-line semimetal AgF 2 ; and a metal with three-fold degenerate band crossing near the Fermi energy, AuLiMgSn. Our work showcases how recent theoretical insights into the fundamentals of band structures can aid in the practical goal of discovering new topological materials.