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Novel topological properties that arose in the periodically driven system areunique, in which there are two kinds of quasienergy gaps, the zero quasienergygap and the $\pi$ quasienergy gap. The corresponding edge modes would traverseeither the zero quasienergy gap or the $\pi$ quasienergy gap, or traverse bothtwo quasienergy gaps. And the characterization of these two kinds of edge modesmight not be the same. However, in this paper, we find that both the zero edgemodes and the $\pi$ edge modes in the Floquet Chern insulators can becharacterized by the same topological invariant, where the corresponding Diracmass term is periodically kicked. Particularly, we take the periodically kickedQi-Wu-Zhang model as an illustrative example. In this model, the topology ischaracterized by the Floquet Chern number $C_F$, and there are six differenttopological 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 periodicallykicked Qi-Wu-Zhang model reduces to a Dirac Hamiltonian in the low-energylimit. Then, the phase diagram is uncovered by examining the topology of thisDirac Hamiltonian. Additionally, we explore the orders of topological phasetransitions in the context of Floquet stationary states by analyzing the vonNeumann entropy of these states. Our work provides further insights into thetopological phases in periodically driven systems.

Topological phases in the periodically kicked Chern insulators