Non-linear electric transport in graphene: quantum quench dynamics and the Schwinger mechanism

We present a unified view of electric transport in undoped clean graphene for finite electric field. The weak field results agree with the Kubo approach. For strong electric field, the current increases non-linearly with the electric field as E^{3/2}. As the Dirac point is moved around in reciprocal space by the field, excited states are generated, in a way analogous to the generation of defects in a quench through a quantum critical point. These results are also analyzed in terms of Schwinger's pair production and Landau-Zener tunneling. An experiment for cold atoms in optical lattices is proposed to test these ideas.