Topological magnetic crystalline insulators and co-representation theory

We introduce a new type of topological insulator protected by magnetic group symmetry, which is a combined symmetry of point group symmetry and time reversal symmetry. Based on the Herring rule of the co-representation theory of magnetic group, we systematically show that systems with certain magnetic group symmetries can have Kramers'-like degeneracies and admit a Z2 classification. We establish a tight-binding model describing a layered magnetic structure with combined C4 rotation and time reversal symmetry. We show that this model can support non-trivial topological phases by calculating its gapless surface states and defining its Z2 topological invariant.