Intervalley Band Crossing and Transition of Fractional Chern Insulators in Floquet Twisted Bilayer MoTe$_2$

We study the twisted MoTe$_2$ homobilayer coupled to periodic driving of a circularly polarized light (CPL). Using Floquet theory in the high-frequency limit, we start from the Dirac model including both the valence and conduction bands of monolayer MoTe$_2$ to derive an effective time-independent Floquet Hamiltonian. The photon processes coupling the valence and conduction bands are captured in this Floquet analysis, and the resulting Floquet Hamiltonian contains explicit time-reversal symmetry breaking terms that are absent if conduction bands are integrated out from the beginning of the derivation. Based on the Floquet Hamiltonian, we find the increase of CPL driving intensity can cause the crossing of Floquet bands and redistribution of holes between the two valleys. When interactions are included, a transition between Floquet Laughlin-type FCIs with different behaviors of valley polarization is identified at total hole filling $5/3$.