Fig. 3. Symmetry indicators for antiferromagnetic topological insulators.

(A) Example of the inversion parity combination of valence bands in the ${\mathbb{Z}}_2$ nontrivial phase of MSG 2.7. (B) Realization of the ${\mathbb{Z}}_2$ nontrivial phase by staggered stacking of Chern insulators. The red (blue) disks represent a Chern insulator with C = +1 (C = −1). (C) Breaking the $\tilde{\mathit{T}}$ symmetry (the half translation in z, followed by the TR) leads to a “higher-order” state with a 1D equatorial chiral mode on the surface (62–71).