Energy Relaxation of Hot Dirac Fermions in Graphene

TL;DR

This paper develops a theoretical model for energy relaxation in hot Dirac fermions in graphene, quantifying power loss due to phonon emission across various temperatures and densities, highlighting the dominance of optical or acoustic phonons depending on conditions.

Contribution

It introduces a generic expression for energy relaxation rate in graphene, accounting for both optical and acoustic phonon interactions, including effects at the Dirac point.

Findings

Power loss per carrier ranges from 10^{-12} to 10^{-7} W.

Optical phonon emission dominates above 200-300 K.

Intrinsic power loss persists at the Dirac point, independent of carrier density.

Abstract

We develop a theory for the energy relaxation of hot Dirac fermions in graphene. We obtain a generic expression for the energy relaxation rate due to electron-phonon interaction and calculate the power loss due to both optical and acoustic phonon emission as a function of electron temperature $T_{\mathrm{e}}$ and density $n$. We find an intrinsic power loss weakly dependent on carrier density and non-vanishing at the Dirac point $n = 0$, originating from interband electron-optical phonon scattering by the intrinsic electrons in the graphene valence band. We obtain the total power loss per carrier $\sim 10^{-12} - 10^{-7} \mathrm{W}$ within the range of electron temperatures $\sim 20 - 1000 \mathrm{K}$. We find optical (acoustic) phonon emission to dominate the energy loss for $T_{\mathrm{e}} > (<) 200-300 \mathrm{K}$ in the density range $n = 10^{11}-10^{13} \mathrm{cm}^{-2}$.