Nonlinear dc transport in graphene

Considering electron-impurity, electron-acoustic-phonon and electron-optical-phonon scatterings, the nonlinear steady-state transport properties of graphene are studied theoretically by means of the balance equation approach. We find that the conductivity as a function of electric field strength, E, exhibits strongly nonlinear behavior for E larger than a critical value, Ec∼0.1 kV cm-1. With the increase of E from zero, the conductivity first decreases slowly and then it falls rapidly when E>Ec. The dependence of electron temperature on E is also demonstrated.