We study nonlinear dc transport in graphene using a hydrodynamic approach and conclude that in clean samples the drift velocity saturates at a weakly density-dependent value $v_{sat}\sim {10}^7\text{cm}/\text{s}$. We show that saturation results from the interactions between graphene’s Dirac quasiparticles and both acoustic and optical phonons. Saturation is accompanied by substantial electron heating and is not reached at realistic driving fields in moderately or strongly disordered samples. We find that it is essential to account for interactions among graphene’s Dirac quasiparticles, which increase the linear-response resistivity at high temperatures or low densities.

• Received 16 June 2009

DOI:https://doi.org/10.1103/PhysRevB.80.085109