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 of hot Dirac fermions in graphene 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 $n = 0$, originating from interband electron-optical phonon scattering from the intrinsic electrons in the graphene valence band. We also obtain the total power loss per carrier to be $\sim 10^{-12}\,-\,10^{-7}\,\mathrm{W}$ within the range of electron temperatures $\sim 20\,-\,1000\,\mathrm{K}$, finding that the temperature for the optical phonon emission to overtake acoustic phonon emission as the dominant energy loss mechanism ranges $\sim 200-300\,\mathrm{K}$ for $n = 10^{11}-10^{13}\,\mathrm{cm}^{-2}$.