Surface plasmons in a semi-bounded massless Dirac plasma

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.