Energy Relaxation of Hot Dirac Fermions in Graphene

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 $n = 10^{11}-10^{13} \mathrm{cm}^{-2}$.