We present a unified view of electric transport in undoped graphene for finite electric field. The weak field results agree with the Kubo approach. For strong electric field, the current increases nonlinearly 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. This is analogous to the generation of defects in a finite-rate quench through a quantum-critical point, which we account for in the framework of the Kibble-Zurek mechanism. These results are also recast in terms of Schwinger’s pair production and Landau-Zener tunneling. Other systems exhibiting a band structure with Dirac cones, in particular, cold atoms in optical lattices, should exhibit the same dynamics as well.

• Received 16 September 2009

DOI:https://doi.org/10.1103/PhysRevB.81.165431