Observing Topological Chiral Orders in 2D Optical Lattices without Spin-orbit Coupling

We propose to observe topological chiral orders with cold atoms without spin-orbit coupling in a two-dimensional optical lattice directly based on the recent experiments which use Raman beams to induce the hopping between nearest-neighbor sites. In the simplest case with s-orbital model, the chiral Chern insulating phases are predicted in the single-particle regime. Moreover, by considering a spin-1/2 system, we predict that the chiral spin liquid phase may exist in the interacting regime. This work proposes realistic cold atom platforms to observe topological chiral orders in the experiment.