Floquet topological phase transition in two-dimensional quadratic band crossing system

We investigate the Hall effects of quadratic band crossing (QBC) fermions in a square optical lattice with spin-orbit coupling and orbital Zeeman term. We find that the orbital Zeeman term and shaking play critical roles in the systems, which can drive a topological transition from spin Hall phases to anomalous Hall phase with nonvanishing (spin) Chern numbers. Due to the interplay among the orbital Zeeman term, spin-orbit coupling, and the shaking, the phase diagram of the system exhibits rich phases, which are characterized by Chern number.