Antiferromagnetic topological insulators in cold atomic gases

We propose a spin-dependent optical lattice potential that realizes a three-dimensional antiferromagnetic topological insulator in a gas of cold, two-state fermions such as alkaline earths, as well as a model that describes the tight-binding limit of this potential. We discuss the physically observable responses of the gas that can verify the presence of this phase, in particular rapid rotation in response to the trap potential. We also point out how this model can be used to obtain two-dimensional flat bands with nonzero Chern number.