Negative dynamic Drude conductivity in pumped graphene

We theoretically reveal a new amplification mechanism of terahertz and far-infrared radiation in graphene under interband pumping. It is enabled by indirect interband electron transitions, where in the photon emission is preceded or followed by disorder scattering. The emerging contribution to the optical conductivity, which we call the interband Drude conductivity, is negative for photon energies below the double quasi-Fermi energy of the pumped carriers. Moreover, for Gaussian correlated disorder, the real part of the net Drude conductivity becomes negative, whereas the radiation amplification by a single graphene sheet substantially exceeds 2.3%. This effect enables terahertz lasing in disordered graphene.