Optically tunable spin Hall effect in periodically driven monolayer transition metal dichalcogenides

We show that the driving field of circularly polarized light (CPL) can be used to enhance and reverse the spin current generated in the spin Hall effect for some transition-metal dichalcogenides. This is demonstrated by analyzing the time-averaged spin Hall conductivities in the nonequilibrium steady states of monolayers WS$_{2}$, MoS$_{2}$, MoTe$_{2}$, and WTe$_{2}$ driven by CPL with the Floquet linear-response theory. We argue that the enhancement and reversals of the spin current come from a combination of the non-Rashba effect of broken inversion symmetry and the nonperturbative effect of CPL beyond the dynamical localization. This work allows optical control of the magnitude and direction of the pure spin current.