Topological insulators on the Lieb and Perovskite lattices

We study a system of tight-binding electrons on both the 2D Lieb and 3D edge-centered cubic (Perovskite) lattices. With spin-orbit coupling between next-nearest neighbor sites these systems become band insulators with non-trivial Z2 topological invariants. We calculate the Z2 invariants for various fillings and study the emergence of topologically protected gapless edge and surface modes. Aside from establishing simple models for topological insulators with cubic symmetry, we also discuss some possible candidates among the naturally occurring Perovskites.