Antiferromagnetic topological insulators

We consider antiferromagnets breaking both time-reversal ($\Theta$) and a primitive lattice translational symmetry ($T_{1/2}$) of a crystal but preserving the combination $S = \Theta T_{1/2}$. The $S$ symmetry leads to a $Z_2$ topological classification of insulators, separating the ordinary insulator phase from the ``antiferromagnetic topological insulator'' (AFTI) 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 [$\sigma_{xy} = e^2 / (2 h)$], which may aid experimental confirmation of $\theta = \pi$ 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.