Hot electron dynamics in graphene

We investigate the nonlinear dc conductivity of graphene by explicitly solving the Boltzmann equation with relaxation and particle-hole pair production contributions and obtain the non-equilibrium electronic distribution function. First by considering electron-phonon scattering and the Schwinger mechanism, which leads to particle-hole creation and, consequently, to interband transitions, we show that, in the limit of weak external electric field one recovers Ohm\u27s law, while above a threshold field E=(T2)/(evF) the dc conductivity varies as the inverse of the square root of external electric field. In particular, we obtain nontrivial result for the effective temperature of this electronic system by scaling