Floquet formalism for tunable optically induced orbital magnetization in twisted bilayers

Substantial interest has been sparked by experimental observations of spontaneous orbital magnetism in moir\'e materials and multilayer graphene, with a particular focus on phenomena related to orbital magnetization (OM). Nonetheless, optical manipulation of OM remains largely unexplored. In this work, we develop a Floquet formalism for calculating OM induced by a low-intensity, adiabatically switched, circularly polarized field in extended systems. Using this formalism, we investigate the optically induced OM in twisted ${\text{MoTe}}_{2}$, and reveal that it can be substantially modulated through adjusting chemical potential, interlayer bias, and optical field (specifically intensity, frequency, and chirality). Remarkably, we discover a significant inverse Faraday effect that is inversely proportional to the cube of the frequency. Our findings highlight the potential of circularly polarized light to induce and manipulate magnetism in moir\'e materials.