Non-equilibrium electron relaxation in Graphene

Abstract

We apply the powerful method of 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/τ ) 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/τ ∝ T 4 when T << Θ BG and 1/τ ∝ T when T >> Θ BG , where Θ BG is the Bloch-Grüneisen temperature). We report several new results for 1/τ where T = T e relevant in pump-probe spectroscopic experiments. In the finite frequency regime we find that 1/τ ∝ ω 2 when ω << ω BG , and for ω >> ω BG it is ω independent and also electron temperature independent. These results can be verified in a typical pump-probe experimental setting for graphene.