Topological phases in the periodically kicked Chern insulators

Novel topological properties that arose in the periodically driven system are unique, in which there are two kinds of quasienergy gaps, the zero quasienergy gap and the $\pi$ quasienergy gap. The corresponding edge modes would traverse either the zero quasienergy gap or the $\pi$ quasienergy gap, or traverse both two quasienergy gaps. And the characterization of these two kinds of edge modes might not be the same. However, in this paper, we find that both the zero edge modes and the $\pi$ edge modes in the Floquet Chern insulators can be characterized by the same topological invariant, where the corresponding Dirac mass term is periodically kicked. Particularly, we take the periodically kicked Qi-Wu-Zhang model as an illustrative example. In this model, the topology is characterized by the Floquet Chern number $C_F$, and there are six different topological phases in total, denoted as $C_F=\{-1_0,-2,-1_\pi,1_\pi,2,1_0\}$. Furthermore, we find that the Floquet operator associated with the periodically kicked Qi-Wu-Zhang model reduces to a Dirac Hamiltonian in the low-energy limit. Then, the phase diagram is uncovered by examining the topology of this Dirac Hamiltonian. Additionally, we explore the orders of topological phase transitions in the context of Floquet stationary states by analyzing the von Neumann entropy of these states. Our work provides further insights into the topological phases in periodically driven systems.