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-e and density n. We find an intrinsic power loss weakly dependent on carrier density and nonvanishing 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 similar to 10(-12)-10(-7) W within the range of electron temperatures similar to 20-1000 K. We find optical (acoustic) phonon emission to dominate the energy loss for T-e > (<)200-300 K in the density range n = 10(11)-10(13) cm(-2).