Negative dynamic Drude conductivity in pumped graphene
  We theoretically reveal a new mechanism of light amplification in graphene under the conditions of interband population inversion. It is enabled by the indirect interband transitions, with the photon emission preceded or followed by the scattering on disorder. The emerging contribution to the optical conductivity, which we call the interband Drude conductivity, appears to be negative for the photon energies below the double quasi-Fermi energy of pumped electrons and holes. We find that for the Gaussian correlated distribution of scattering centers, the real part of the net Drude conductivity (interband plus intraband) can be negative in the terahertz and near-infrared frequency ranges, while the radiation amplification by a single graphene sheet can exceed 2.3%. 
D. Svintsov, V. Ryzhii, T. Otsuji
cond-mat.mes-hall