Coherent photogalvanic valley Hall effect

The theory of the coherent photogalvanic valley Hall effect in two-dimensional systems with the Dirac spectrum of charge carriers is formulated. The study deals with a two-dimensional sample irradiated by two electromagnetic waves, at the fundamental and doubled frequencies. Both frequencies exceed the band gap of the material, whereas the wave with the fundamental frequency having circular polarization and a high intensity is taken into account in a nonperturbative manner. The wave at the doubled frequency is linearly polarized and the electrical conductivity of the two-dimensional system is calculated with respect to it. The effect under study manifests itself as the dc Hall current in the direction orthogonal to the electric field of the weak electromagnetic wave. It is assumed that, in equilibrium, the sample is in the insulating state with the completely occupied valence band and empty conduction band. The strong electromagnetic wave induces a nonequilibrium filling of the bands and the system passes to a strongly nonequilibrium steady state. The behavior of the Hall current in the case of nonequilibrium distribution functions is analyzed both including and disregarding the intraband relaxation and interband recombination.