Electrons hopping on the sites of a two-dimensional Lieb lattice and three-dimensional edge centered cubic (perovskite) lattice are shown to form topologically non-trivial insulating phases when spin-orbit coupling is introduced. These simple models on lattices with cubic symmetry show a Dirac-like structure in the excitation spectrum but with the unusual feature that there is a dispersionless band through the center of the spectrum and only a single Dirac cone per Brillouin zone.
@article{arxiv.1004.5172,
title = {Topological Insulators on the Lieb and Perovskite Lattices},
author = {C. Weeks and M. Franz},
journal= {arXiv preprint arXiv:1004.5172},
year = {2010}
}