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

Abstract: 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. This Floquet Hamiltonian contains explicit time-reversal symmetry breaking terms that are absent if conduction bands are neglected from the beginning of the derivation. Based on the Floquet Hamiltonian, we find the increasing of CPL driving intensity can cause the crossing of Floquet bands between the two valleys. When interactions are included, we identify the redistribution of holes during the intervalley Floquet band crossing. Accordingly, the ground state of the Floquet Hamiltonian at total hole filling $5/3$ evolves from the Laughlin-type FCI in one valley to that in the other valley.