Collisionless Hydrodynamics of Doped Graphene in a Magnetic Field

TL;DR

This paper develops a collisionless hydrodynamic model for doped graphene's electrodynamics, deriving plasmon dispersion relations with and without magnetic fields, and compares classical and quantum approaches.

Contribution

It introduces a hydrodynamic framework for graphene's collective modes and compares classical and quantum results, highlighting the model's validity range.

Findings

Derived low-energy plasmon dispersion relations in magnetic fields

Compared hydrodynamic and quantum RPA results, showing good agreement at small wave vectors

Discussed limitations of the classical approach at higher orders

Abstract

The electrodynamics of a two-dimensional gas of massless fermions in graphene is studied by a collisionless hydrodynamic approach. A low-energy dispersion relation for the collective modes (plasmons) is derived both in the absence and in the presence of a perpendicular magnetic field. The results for graphene are compared to those for a standard two-dimensional gas of massive electrons. We further compare the results within the classical hydrodynamic approach to the full quantum mechanical calculation in the random phase approximation. The low-energy dispersion relation is shown to be a good approximation at small wave vectors. The limitations of this approach at higher order is also discussed.