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.