Population Inversion and Negative Dynamic Conductivity in Optically Pumped Graphene

We study nonequilibrium carriers (electrons and holes) in an intrinsic graphene at low temperatures under infrared optical pumping. We calculate the energy distributions of carriers using a quasi-classical kinetic equation. It is found that the nonequilibrium distributions are determined by an interplay between weak energy relaxation on acoustic phonons and generation-recombination processes as well as by the effect of pumping saturation. We show that at certain pumping power density the population inversion as well as the dynamic negative conductivity can take place in terahertz and far-infrared frequencies, suggesting the possibility of utilization of graphene under optical pumping for optoelectronic applications, in particular, lasing at such frequencies.