Wigner-Weyl description of massless Dirac plasmas

TL;DR

This paper develops a quantum kinetic model for graphene electrons using the Wigner--Weyl formalism, deriving plasmon dispersion relations and fluid equations to enhance understanding of graphene plasmonics.

Contribution

It introduces a phase space quantum kinetic model for Dirac electrons in graphene, including Coulomb interactions and deriving fluid equations from first principles.

Findings

Derived plasmon dispersion relations for graphene in different configurations.

Established a consistent fluid model with correct effective mass for Dirac electrons.

Provided insights into the quantum dynamics of graphene electrons in phase space.

Abstract

We derive a quantum kinetic model describing the dynamics of graphene electrons in phase space based on the Wigner--Weyl formalism. To take into account the quantum nature of the carriers, we make use of the quantum Liouville equation for the density matrix. By relating the density matrix elements with the Wigner function, the equation of motion for the latter is established, with the Coulomb interaction being introduced self-consistently (i.e., in the Hartree approximation). The long-wavelength limit for the plasmon dispersion relation is obtained, for both ungated and gated situations. As an application, we derive the corresponding fluid equations from first principles and discuss the correct value of the effective hydrodynamic mass of the carriers. This constitutes a crucial point in establishing the appropriate fluid description of Dirac electrons, thus paving the way to a more comprehensive description of graphene plasmonics.