Theory of high-harmonic generation in graphene under a DC current

High-harmonic generation (HHG) is a typical nonlinear optical effect, and it denotes the phenomenon that when an intense laser pulse with frequency ω is applied to a material, a laser pulse with multiple frequencies nω (n is an arbitrary positive integer) is emitted from the material. Recently, HHGs in graphene and related systems have been actively studied both experimentally and theoretically. For HHGs in electron systems, even-order harmonics are known to be prohibited by their inversion symmetry. This fact indicates that even-order harmonics can be controlled by an injected dc-current which breaks the inversion symmetry. In fact, dc-current-driven even-order harmonics have been observed in some systems. However, it is not easy to theoretically treat the dc-current, the applied laser, and the dissipation effect simultaneously. Existing theoretical studies are limited only to the perturbation theory for second harmonics. We here report a new approach for dc-current-driven high-harmonic generation in graphene. Combining the quantum master equation with the Boltzmann equation, we numerically calculate the reliable HHG spectra. We show the laser-frequency, laser-intensity, and dc-current-strength dependences of the spectra, focusing on even-order harmonics especially.