Wigner model for quantum transport in graphene

TL;DR

This paper develops a Wigner-Weyl phase-space model for quantum electron transport in graphene, capturing quantum effects like Klein tunneling and analyzing electron-hole dynamics under external fields.

Contribution

It introduces a full-quantum Wigner-Weyl formalism for graphene transport, bridging quantum and classical descriptions and analyzing phenomena like Klein tunneling.

Findings

Close to classical particle motion in quantum regime

Analytical equations of motion derived and numerically tested

Insights into electron-hole pair dynamics under external fields

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.