Hot electron dynamics and Schwinger mechanism 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 isotropic elastic electron-phonon scattering, we show that, in the limit of weak external electric field one recovers Ohm's law, while above a threshold field $E=(k_B T)/(ev_F \tau)$ the dc conductivity varies as the inverse of the external electric field. In particular, we obtain an explicit form for the scaling of the conductivity with respect to $E/T$. We then investigate how this result is affected by the Schwinger mechanism, which leads to particle-hole creation and, consequently, to interband transitions.