Valley Hall Transport of Photon-Dressed Quasiparticles in 2D Dirac Semiconductors

We present a theory of the photovoltaic valley-dependent Hall effect in a two-dimensional Dirac semiconductor subject to an intense near-resonant electromagnetic field. Our theory captures and elucidates the influence of both the field-induced resonant interband transitions and the nonequilibrium carrier kinetics on the resulting valley Hall transport in terms of photon-dressed quasiparticles. The non-perturbative renormalization effect of the pump field manifests itself in the dynamics of the photon-dressed quasiparticles, with a quasienergy spectrum characterized by {dynamical gaps $\delta_\eta$ ($\eta$ is the valley index)} that strongly depend on field amplitude and polarization. Nonequilibrium carrier distribution functions are determined by the pump field frequency $\omega$ as well as the ratio of intraband relaxation time $\tau$ and interband recombination time $\tau_{\mathrm{rec}}$. We obtain analytic results in three regimes, when (I) all relaxation processes are negligible, (II) $\tau \ll \tau_{\mathrm{rec}}$, and (III) $\tau \gg \tau_{\mathrm{rec}}$, and display corresponding asymptotic dependences on $\delta_\eta$ and $\omega$. We then apply our theory to two-dimensional transition-metal dichalcogenides, and find a strong enhancement of valley-dependent Hall conductivity as the pump field frequency approaches the transition energies between the pair of spin-resolved conduction and valence bands at the two valleys.