Threshold of Terahertz Population Inversion and Negative Dynamic   Conductivity in Graphene Under Pulse Photoexcitation
  We theoretically study the population inversion and negative dynamic conductivity in intrinsic graphene in the terahertz (THz) frequency range upon pulse photoexcitation with near-/mid-infrared wavelength. The threshold pulse energy required for the population inversion and negative dynamic conductivity can be orders-of-magnitude lower when the pulse photon energy is lower, due to the inverse proportionality of the photoexcited carrier concentration to the pulse photon energy and to the weaker carrier heating. We also investigate the dependence of the dynamic conductivity on the momentum relaxation time. The negative dynamic conductivity takes place either in high- or low-quality graphene, where the Drude absorption by carriers in the THz frequency is weak. 
A. Satou, V. Ryzhii, Y. Kurita, and T. Otsuji
cond-mat.mes-hall