  We study the properties of a family of anti-pervoskite materials, which are
topological crystalline insulators with an insulating bulk but a conducting
surface. Using ab-initio DFT calculations, we investigate the bulk and surface
topology and show that these materials exhibit type-I as well as type-II Dirac
surface states protected by reflection symmetry. While type-I Dirac states give
rise to closed circular Fermi surfaces, type-II Dirac surface states are
characterized by open electron and hole pockets that touch each other. We find
that the type-II Dirac states exhibit characteristic van-Hove singularities in
their dispersion, which can serve as an experimental fingerprint. In addition,
we study the response of the surface states to magnetic fields.
