Collective modes of the massless Dirac plasma

TL;DR

This paper develops a quantum theory for long-wavelength plasma oscillations in massless Dirac particle systems like doped graphene, revealing non-classical behavior and differences from traditional metal plasmons.

Contribution

It introduces a novel quantum plasma oscillation theory for massless Dirac particles, highlighting non-classical frequency scaling and dimensional differences.

Findings

Plasmon frequency scales as h^{-1/2} in all dimensions.

D-dimensional superlattice plasmon frequency differs from (D+1)-dimensional bulk.

Dirac plasmons exhibit non-classical behavior unlike traditional metal plasmons.

Abstract

We develop a theory for the long-wavelength plasma oscillation of a collection of charged massless Dirac particles in a solid, as occurring for example in doped graphene layers, interacting via the long-range Coulomb interaction. We find that the long-wavelength plasmon frequency in such a doped massless Dirac plasma is explicitly non-classical in all dimensions with the plasma frequency being proportional to \hbar^{-1/2}. We also show that the long wavelength plasma frequency of the D-dimensional superlattice made from such a plasma does not agree with the corresponding (D + 1)-dimensional bulk plasmon frequency. We compare and contrast such Dirac plasmons with the well-studied regular palsmons in metals and doped semiconductors which manifest the usual classical long wavelength plasma oscillation.