Non-equilibrium electron relaxation in Graphene

Abstract

We apply the powerful method of memory function formalism to investigate non-equilibrium 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. $1/\tau \propto T^4$ when $T<<{\Theta }_{BG}$ and $1/\tau \propto T$ when $T>>{\Theta }_{BG}$, where ${\Theta }_{BG}$ is the Bloch-Grüneisen temperature). We report several new results for $1/\tau$ where $T\ne T_e$ relevant in pump-probe spectroscopic experiments. In the finite frequency regime, we find that $1/\tau \propto {\omega }^2$ when $\omega <<{\omega }_{BG}$, and for $\omega >>{\omega }_{BG}$ it is $\omega$ independent and also electron temperature independent. These results can be verified in a typical pump-probe experimental setting for graphene.

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