Nonequilibrium electron relaxation in graphene

We apply memory function formalism to investigate nonequilibrium electron relaxation in graphene. Within the premises of two-temperature model (TTM), explicit expressions of the imaginary part of the memory function or generalized Drude scattering rate (1/tau) are obtained. In the DC limit and in equilibrium case where electron temperature (T-e) is equal to phonon temperature (T), we reproduce the known results (i.e., 1/tau proportional to T-4 when T << Theta(BG) and 1/tau proportional to T when T >> Theta(BG), where Theta(BG) is the Bloch-Gruneisen temperature). We report several new results for 1/tau where T not equal Te relevant in pump-probe spectroscopic experiments. In the finite-frequency regime we find that 1/tau proportional to omega(2) when omega << omega(BG), and for omega = omega(BG) it is omega-independent. These results can be verified in a typical pump-probe experimental setting for graphene.