Wigner model for Klein tunneling in graphene

Quantum corrections to the electron-hole motion in graphene are investigated by applying the multiband Wigner approach. A diagonalization procedure regarding the pseudo-spin degree of freedom is proposed. The resulting formulation of the equation of motion reveals to be particularly close to the classical description of the particle motion. This formal analogy offers a framework in which quantum phenomena can be described with a classical language and the question of the quantum-classical correspondence can be directly investigated. Some numerical results are presented showing the ability of our quasi-diagonal Wigner model to reproduce Klein tunneling in graphene under the application of an external electric field