Repulsive Fermi gases in a two-dimensional lattice with non-Abelian gauge fields

Motivated by the recent experiment realizing bidirectional spin-orbit–coupled Bose-Einstein condensates (BEC), we theoretically explore the properties of repulsive fermions in the two-dimensional (2D) optical lattice with such non-Abelian gauge fields. Within the mean-field level, we find a novel phase of topological antiferromagnetic (TAFM) order which incorporates both the non-trivial topology due to spin-flip hopping and spontaneous symmetry breaking (SSB) for the in-plane spin order. We argue that the appearance of such a phase is generic for repulsive fermions in Chern bands achieved through spin-orbit coupling. Our work paves the way for further studies of fermionic generalization of 2D non-Abelian spin-orbit–coupled quantum gases.