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 Tₑ 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 ~10^-12--10^-7 W within the range of electron temperatures ~20--1000 K. We find optical (acoustic) phonon emission to dominate the energy loss for Tₑ>(<)200--300 K in the density range n=10¹¹--10¹³ cm^-2.