High-field transport in graphene: the impact of Zener tunneling

We study, theoretically, the impact of Zener tunneling (the generation of electron-hole pairs by the electric field) on the charge-transport properties of graphene in the high-field regime. We model Zener tunneling in a rigorous way, using the quantum master equation for the density matrix. In the presence of Zener tunneling, a steady-state can be reached only by further including an efficient mechanism for the electron thermalization such as electron-electron scattering. We treat the effects of electron-electron relaxation within a simplified model, that assumes an instantaneous separate thermalization of the electrons in the conduction band and of the holes in the valence band. The inclusion of both Zener tunneling and electron-electron relaxation improves the agreement with measurements performed in graphene in the high-field regime at low doping.