Nonequilibrium excitations and transport of Dirac electrons in electric-field-driven graphene

We investigate nonequilibrium excitations and charge transport in charge-neutral graphene driven with dc electric field by using the nonequilibrium Green's-function technique. Due to the vanishing Fermi surface, electrons are subject to nontrivial nonequilibrium excitations such as highly anisotropic momentum distribution of electron-hole pairs, an analog of the Schwinger effect. We show that the electron-hole excitations, initiated by the Landau-Zener tunneling with a superlinear IV relation I proportional to E-3/2, reaches a steady state dominated by the dissipation due to optical phonons, resulting in a marginally sublinear IV with I proportional to E, in agreement with recent experiments. The linear IV starts to show the sign of current saturation as the graphene is doped away from the Dirac point, and recovers the semiclassical relation for the saturated velocity. We give a detailed discussion on the nonequilibrium charge creation and the relation between the electron-phonon scattering rate and the electric field in the steady-state limit. We explain how the apparent Ohmic IV is recovered near the Dirac point. We propose a mechanism where the peculiar nonequilibrium electron-hole creation can be utilized in a infrared device.