Topological non-symmorphic crystalline insulators

In this talk, we will describe a new class of Z2 topological insulator protected by non-symmorphic crystalline symmetry, dubbed a ``topological non-symmorphic crystalline insulator.'' We construct a concrete tight-binding model with the non-symmorphic space group pmg and confirm the topological nature of this model by directly calculating topological surface states. In analog to ``Kramers' pairs'' due to time reversal symmetry, we introduce the ``doublet pairs'' originating from non-symmorphic symmetry to define the corresponding Z2 topological invariant for this phase. Based on the projective representation theory, we extend our discussion to other non-symmorphic space groups that allows to host topological non-symmorphic crystalline insulators.