Antiferromagnetic topological insulators

We consider antiferromagnets breaking both time-reversal $(\ensuremath{\Theta})$ and a primitive-lattice translational symmetry $({T}_{1/2})$ of a crystal but preserving the combination $S=\ensuremath{\Theta}{T}_{1/2}$. The $S$ symmetry leads to a ${\mathbb{Z}}_{2}$ 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 $[{\ensuremath{\sigma}}_{xy}={e}^{2}/(2h)]$, which may aid experimental confirmation of $\ensuremath{\theta}=\ensuremath{\pi}$ 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.