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A circularly polarized a.c. pump field illuminated near resonance ontwo-dimensional transition metal dichalcogenides (TMDs) produces an anomalousHall effect in response to a d.c. bias field. In this work, we develop a theoryfor this photo-induced anomalous Hall effect in undoped TMDs irradiated by astrong coherent laser field. The strong field renormalizes the equilibriumbands and opens up a dynamical energy gap where single-photon resonance occurs.The resulting photon dressed states, or Floquet states, are treated within therotating wave approximation. A quantum kinetic equation approach is developedto study the non-equilibrium density matrix and time-averaged transportcurrents under the simultaneous influence of the strong a.c. pump field and theweak d.c. probe field. Dissipative effects are taken into account in thekinetic equation that captures relaxation and dephasing. The photo-inducedlongitudinal and Hall conductivities display notable resonant signatures whenthe pump field frequency reaches the spin-split interband transition energies.Rather than valley polarization, we find that the anomalous Hall current ismainly driven by the intraband response of photon-dressed electron populationsnear the dynamical gap at both valleys, accompanied by a smaller contributiondue to interband coherences. These findings highlight the importance ofphoton-dressed bands and non-equilibrium distribution functions in achieving aproper understanding of photo-induced anomalous Hall effect in a strong pumpfield.

Photo-Induced Anomalous Hall Effect in Two-Dimensional Transition-Metal Dichalcogenides