Nonequilibrium electron relaxation in graphene

Abstract

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/ττ) are obtained. In the DC limit and in equilibrium case where electron temperature (Te) is equal to phonon temperature (T), we reproduce the known results (i.e., 1/τ∝τ∝T4 when T≪ΘBG≪ΘBG and 1/τ∝τ∝T when T≫ΘBG≫ΘBG, where ΘBGΘBG is the Bloch–Grüneisen temperature). We report several new results for 1/ττ where T≠≠Te relevant in pump–probe spectroscopic experiments. In the finite-frequency regime we find that 1/τ∝ω2τ∝ω2 when ω≪ωBGω≪ωBG, and for ω=ωBGω=ωBG it is ωω-independent. These results can be verified in a typical pump–probe experimental setting for graphene.