Ballistic transport in graphene beyond linear response

Abstract

The process of coherent creation of particle-hole excitations by an electric field in graphene is quantitatively described beyond linear response. We calculate the evolution of current density, number of pairs and energy in ballistic regime for electric field $E$ using the tight-binding model. While for ballistic flight times smaller than ${t}_{nl}\ensuremath{\propto}{E}^{\ensuremath{-}1/2}$ current is linear in $E$ and independent of time, for larger ballistic times the current increases after ${t}_{nl}$ as $J\ensuremath{\propto}{E}^{3/2}t$ and finally at yet larger times $(t>{t}_{B}\ensuremath{\propto}{E}^{\ensuremath{-}1})$ Bloch oscillations set in. It is shown that the number of pairs follows the 2D generalization of the Schwinger's creation rate $n\ensuremath{\propto}{E}^{3/2}$ only on certain time segments with a prefactor different from that obtained using the asymptotic formula.