Antiferromagnetic topological insulators

We consider antiferromagnets breaking both time-reversal () and a primitive-lattice translational symmetry (T₁/₂) of a crystal but preserving the combination S=T₁/₂. The S symmetry leads to a Z₂ topological classification of insulators, separating the ordinary insulator phase from the ``antiferromagnetic topological insulator'' phase. This state is similar to the ``strong'' topological insulator with time-reversal symmetry and shares with it such properties as a quantized magnetoelectric effect. However, for certain surfaces the surface states are intrinsically gapped with a half-quantum Hall effect ₗₘ=e^2/ (2h), which may aid experimental confirmation of = quantized magnetoelectric coupling. Step edges on such a surface support gapless, chiral quantum wires. In closing we discuss GdBiPt as a possible example of this topological class.