Wigner model for quantum transport in graphene

The single graphene layer is a novel material consisting of a flat monolayer of carbon atoms packed in a two-dimensional honeycomb lattice, in which the electron dynamics is governed by the Dirac equation. A pseudo-spin phase-space approach based on the Wigner-Weyl formalism is used to describe the ballistic transport of electrons in graphene including quantum effects. Our two-band quantum mechanical representation of the particles reveals itself to be particularly close to the classical description of the particle motion. We analyze the Klein tunneling and correction to the total current in graphene induced by this phenomenon. The equations of motion are analytically investigated and some numerical tests are presented. The temporal evolution of the electron-hole pairs in the presence of an external electric field and rigid potential step is investigated. The connection of our formalism with the Berry phase approach is also discussed.