Topological nonsymmorphic crystalline insulators

In this work, we identify a class of topological phases protected by nonsymmorphic crystalline symmetry dubbed ``topological nonsymmorphic crystalline insulators.'' We construct a concrete tight-binding model for a lattice with nonsymmorphic symmetry and confirm its topological nature by directly calculating topological surface states. Analogous to ``Kramers' pairs'' originating from time-reversal symmetry, we introduce ``doublet pairs'' originating from nonsymmorphic symmetry to define the corresponding Z₂ topological invariant for this phase. Based on projective representation theory, we extend our discussion to other nonsymmorphic symmetry groups that can host this topological phase which will provide guidance for the systematic search for new topological materials.