Thermal-radiation-induced nonequilibrium carriers in an intrinsic   graphene
  We examine an intrinsic graphene connected to the phonon thermostat at temperature T under irradiation of thermal photons with temperature T_r, other than T. The distribution of nonequilibrium electron-hole pairs was obtained for the cases of low and high concentration of carriers. For the case when the interparticle scattering is unessential, the distribution function is determined by the interplay of intraband relaxation of energy due to acoustic phonons and interband radiative transitions caused by the thermal radiation. When the Coulomb scattering dominates, then the quasi-equilibrium distribution with effective temperature and non-equilibrium concentration, determined through balance equations, is realized. Due to the effect of thermal radiation with temperature $T_r\neq T$ concentration and conductivity of carriers in graphene modify essentially. It is demonstrated, that at $T_r>T$ the negative interband absorption, caused by the inversion of carriers distribution, can occur, i.e. graphene can be unstable under thermal irradiation. 
P.N. Romanets, F.T. Vasko, and M.V. Strikha