Population inversion in electrically and optically pumped graphene

We find the electron and hole distribution functions and calculate the dynamic conductivity of nonequilibrium two-dimensional (2D) electron–hole systems in graphene-based structures under the injection or optical pumping. Both the interband transitions and intraband transitions associated with the electron and hole scattering on impurities and acoustic and optical phonons are considered. It is shown that under sufficiently strong pumping, the population inversion may result in the negative net dynamic AC conductivity in a certain range of photon frequencies. Since the frequencies corresponding to the negative conductivity fall into the terahertz range, the predicted effects might be used in coherent sources of terahertz radiation.