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We present a theory of the photovoltaic valley-dependent Hall effect in atwo-dimensional Dirac semiconductor subject to an intense near-resonantelectromagnetic field. Our theory captures and elucidates the influence of boththe field-induced resonant interband transitions and the nonequilibrium carrierkinetics on the resulting valley Hall transport in terms of photon-dressedquasiparticles. The non-perturbative renormalization effect of the pump fieldmanifests itself in the dynamics of the photon-dressed quasiparticles, with aquasienergy spectrum characterized by {dynamical gaps $\delta_\eta$ ($\eta$ isthe valley index)} that strongly depend on field amplitude and polarization.Nonequilibrium carrier distribution functions are determined by the pump fieldfrequency $\omega$ as well as the ratio of intraband relaxation time $\tau$ andinterband recombination time $\tau_{\mathrm{rec}}$. We obtain analytic resultsin three regimes, when (I) all relaxation processes are negligible, (II) $\tau\ll \tau_{\mathrm{rec}}$, and (III) $\tau \gg \tau_{\mathrm{rec}}$, and displaycorresponding asymptotic dependences on $\delta_\eta$ and $\omega$. We thenapply our theory to two-dimensional transition-metal dichalcogenides, and finda strong enhancement of valley-dependent Hall conductivity as the pump fieldfrequency approaches the transition energies between the pair of spin-resolvedconduction and valence bands at the two valleys.

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