Abstract
Graphene is a novel material constituted by a two-dimensional carbon lattice. The electron dynamics in graphene is governed by the Dirac equation. The Wigner-Weyl formalism is used to describe the transport of electrons in graphene including quantum effects. A diagonalization procedure regarding the pseudo-spin degree of freedom is proposed. Our approach highlights the effect of Klein tunneling and we study the correction of the total current in intrinsic graphene induced by this phenomena. The connection of our formalism with the Berry phase approach is also investigated.
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