Non-equilibrium electron relaxation in Graphene

TL;DR

This paper uses the memory function formalism within the Two Temperature Model to analyze non-equilibrium electron relaxation in graphene, deriving explicit expressions for the scattering rate and revealing new temperature and frequency dependencies relevant for pump-probe experiments.

Contribution

It provides explicit formulas for the generalized Drude scattering rate in non-equilibrium graphene, extending known equilibrium results to cases where electron and phonon temperatures differ.

Findings

Reproduces known equilibrium temperature dependence of scattering rate.

Derives new temperature-dependent results for non-equilibrium conditions.

Identifies frequency dependence of scattering rate in different regimes.

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-Gr\"{u}neisen temperature). We report several new results for $1/ \tau$ where $T \neq T_e$ 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.