Extended Haldane's model and its simulation with ultracold atoms

Haldane's model is extended to a square lattice related close to the so-called d + id state, in which the on-site energy is staggered and the next-nearest-neighbor hopping is anisotropic. From the phase diagram obtained, two types of phases are found, i.e. , the normal insulator with Chern number C =0 and the Hall insulator with C =±1. We propose a way of simulating this model with cold atoms in an optical lattice. By measuring the atomic density profile, one can detect this phase diagram.