Topological Weyl semimetal phases in a time reversal invariant spinless model

We investigate the topological Weyl semimetal phases in a time reversal invariant spinless lattice model which has C _4v or C _2v point group symmetries. For the C _4v case, the model is characterized by eight Weyl points in the k _z = π plane, while for the C _2v case, it is characterized by four Weyl points in the k _z = π plane. For both cases, Fermi arcs can be realized on their surfaces. We find that the topological Weyl semimetal can be viewed as an intermediate phase between the topological crystalline insulator (TCI) and normal insulator, and they all can be described by the so-called bent mirror Chern numbers. What's more, in the C _2v case, the TCI phase is still present when the perturbation is small, though the Z ₂ invariant is not well-defined then, however, it can be well described by the bent mirror Chern number.