Nonlinear excitonic spin Hall effect in monolayer transition metal dichalcogenides

We propose and analyze a mechanism for inducing spin Hall currents in ordinary (1H phase) monolayer transition metal dichalcogenides (TMDs) due to the nonlinear process of optical rectification. The photo-induced spin current is proportional to the light intensity, and originates from the intrinsic spin-orbit coupling in TMDs. The spin current spectrum is strongly influenced by electron-hole interactions, i.e. excitonic effects, analogous to the optical absorption. Remarkably, excitons change the temperature dependence of the induced spin current, to the point that the current direction can even be reversed by varying the temperature. This peculiar excitonic behavior is shown to emerge from the relative strength of two distinct mechanisms contributing to the optical response, i.e. a purely interband part and a mixed inter/intraband contribution. Furthermore, we investigate the valley dichrosim of second-harmonic charge and spin currents, and demonstrate different valley polarization of $s$ and $p$ excitons that stem from their distinct angular momenta. Our findings pave the path to the generation of dc spin currents in ordinary TMDs without external static electric or magnetic fields.