Population Inversion and Negative Dynamic Conductivity in Optically Pumped Graphene

Abstract

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 frequen- cies, suggesting the possibility of utilization of graphene under optical pumping for optoelectronic applications, in particular, lasing at such frequencies. I. INTRODUCTION The features of the dynamics of electrons and holes in graphene result in the exceptional properties of graphene. The studies of optical phenomena in graphene can be utilized for revealing the mechanisms of carrier scattering (1), (2). The gapless energy spectrum of graphene provides its nontrivial optical properties which can be utilized in novel optoelectronic devices (3)-(5). Due to zero band gap, the carrier distributions near the Dirac point in intrinsic graphene can exceed one half by even weak optical pumping, corresponding to population inversion. Previously we demonstrated that under the assumption that the distributions become quasi-equilibrium due to carrier-carrier collisions, population inversion and negative dynamic conduc- tivity in the terahertz/far-infrared range are possible (3). At low temperatures and not too strong pumping where carrier-carrier collisions can be ineffective, however, the carrier distributions are determined by an interplay between acoustic phonon scattering and thermal generation/recombination processes (6). In this paper, we study nonequilibrium carriers (electrons and holes) in an intrinsic graphene at low temperatures under near-infrared optical pumping following the cascade of optical phonons. We calculate the energy distributions of carriers using a quasi-classical kinetic equation which accounts for the energy relaxation due to acoustic phonons and the radiative generation-recombination processes associated with thermal radiation, the the cascade emission of optical phonons, and the carrier photoexcitation by incident radiation. 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