Wigner model for quantum transport in graphene

Abstract

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 transport of electrons in graphene including quantum effects. Our full-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 the 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 a rigid potential step is investigated. The connection of our formalism with the Barry-phase approach is also discussed.

Phase-space methods for the spin dynamics in condensed matter systems

“…In order to study the macroscopic properties of the system, it is convenient to project F onto the Pauli basis set [41,42] …”

Dirac open-quantum-system dynamics: Formulations and simulations

“…Additionally, our method can be used to simulate effective systems modeled by relativistic mechanics, e.g., graphene [127,128], trapped ions [14], optical lattices [129], and semiconductors [130,131]. Finally, the developed techniques can be generalized to treat Abelian [50,132,133] as well as non-Abelian [2,134] (e.g., quark gluon) plasmas.…”

“…This conclusion is obtained, e.g., by comparing Eqs. (128) and (129) (setting A µ = 0) with Eqs. (19)- (21) in Ref.…”

A kinetic model for the transport of electrons in a graphene layer

“…Previous kinetic models have been discussed by O. Morandi and F. Schürrer in [33] and a quite similar strategy as ours has been developed at the same moment where we were writing this paper by A. Faraj and S. Jin in [12]. We refer to Section 1.6 below for further details.…”

“…The kinetic system proposed by O. Morandi and F. Schürrer in [33] is obtained by expliciting some of the neglected terms in the pseudodifferential approach which gives (1.4) at first approximation. Indeed, the O(ε) term in (1.4) is no longer small when ξ is close to 0, and O. Morandi and F. Schürrer explicits this term which couples the equations.…”