Surface plasmons in a semi-bounded massless Dirac plasma

TL;DR

This paper investigates the unique properties of surface plasmons in massless Dirac plasmas like graphene, highlighting their nonclassical frequency dependence and differences from Fermi plasmas, with implications for relativistic quantum plasma behavior.

Contribution

It introduces a relativistic quantum fluid model to analyze surface plasmons in massless Dirac plasmas, revealing their nonclassical frequency characteristics and differences from traditional Fermi plasmas.

Findings

Surface plasmon frequency in Dirac plasmas is nonclassical, proportional to 1/√ħ.

Distinct differences between Dirac and Fermi plasma surface plasmons are identified.

Relativistic and quantum effects significantly influence surface plasmon propagation.

Abstract

The collective excitation of surface plasmons in a massless Dirac plasma (e.g., graphene) half-space (bounded by air) is investigated using a relativistic quantum fluid model. The unique features of such surface waves are discussed and compared with those in a Fermi plasma. It is found that in contrast to Fermi plasmas, the long-wavelength surface plasmon frequency $(\omega)$ in massless Dirac plasmas is explicitly nonclassical, i.e., $\omega\propto1/\sqrt{\hbar}$, where $h=2\pi\hbar$ is the Planck's constant. Besides some apparent similarities between the surface plasmon frequencies in massless Dirac plasmas and Fermi plasmas, several notable differences are also found and discussed. Our findings elucidate the properties of surface plasmons that may propagate in degenerate plasmas where the relativistic and quantum effects play a vital role.