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 (ω) in massless Dirac plasmas is explicitly nonclassical, i.e., ω ∝ 1/ √ , where h = 2π 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.

The propagation characteristics of low-frequency (in comparison with the electron cyclotron frequency) surface (LFS) plasma waves propagating at the interface of a quantum plasma slab are studied in the presence of a uniform external magnetic field. A quantum hydrodynamic model is used, and the effects of the Fermi pressure, the quantum force (as a gradient of the Bohm potential), as well as the Coulomb exchange interaction force, associated with the spin polarization of electrons, are considered to derive the dispersion relation for LFS waves. It is found that the dispersion properties of such LFS waves are significantly modified by this new quantum effect. It is also shown that when the spin polarization effect is increased, the contribution of the Coulomb exchange potential becomes higher than those of the Fermi-pressure and the particle dispersion (Bohm potential). Furthermore, the frequency of the surface wave is seen to be down-shifted by the influence of the Coulomb exchange interaction force.

The effect of graphene on unique features of surface plasmon-polariton excitations near the interface of vacuum and quantum plasma half-space is explored using a quantum hydrodynamic model including the Fermi electron temperature and the quantum Bohm potential together with the full set of Maxwell equations. It is found that graphene as a conductive layer significantly modifies the propagation properties of surface waves by making a change on the corresponding wave dispersion relation. It is shown that the presence of graphene layer on the interface of vacuum and plasma leads to a blue-shift in the surface Plasmon frequency. The results of present study must be contributed to the modern electronic investigations.

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