Glide-symmetric topological crystalline insulators with nonprimitive lattices

Topological crystalline insulators (TCIs) with glide symmetry have been theoretically proposed recently. Such glide-symmetric TCIs are characterized by a Z2 topological number. In our previous work, we studied a phase transition between the TCI phase and a normal insulator (NI) phase, and show that the Weyl semimetal phase intervenes between the TCI and the NI phases. In this presentation, we consider this glide-symmetric TCI in nonprimitive lattices. In this case, the previous formula of the Z2 topological number does not apply. We give a new formula of the Z2 topological number for glide-symmetric TCI on nonprimitive lattices, and describe how TCI-NI phase transitions occur via emergence of Weyl nodes. We also apply the results to magnon systems and photonic crystals with glide symmetries.