  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%.
