Higher order topological insulators in anti-perovskites

We prove that a family of anti-perovskite materials realize a higher order topological insulator (HOTI) phase, characterized by a previously introduced Z4 index. A tight binding model and a k.p model are used to capture the physics of the bulk, surface and hinge states of these anti-perovskites. A phase diagram of the Z4 index and weak topological invariant is obtained for the tight binding model. The mirror Chern number is also discussed. In order to reveal the gapless hinge states in the presence of mirror Chern surface states, several ways of opening the surface gap are proposed and confirmed by calculation, including cleaving the lattice to reveal a low-symmetry surface, building a heterostructure, and applying strain. Upon opening the surface gap, we are able to study the hinge states by computing the momentum space band structure and real space distribution of mid-gap states.