Effects of electron exchange-correlation potential on electrostatic oscillations in single-walled carbon nanotubes

Using macroscopic quantum hydrodynamic formulation, we study the dispersion properties of electrostatic electron plasma oscillations in single-walled carbon nanotubes. The electrons and ions are considered uniformly distributed over the cylindrical surface of a nanotube thus forming a two-component (electron-ion) quantum plasma system. Electron degeneracy via Fermi-Dirac statistics as well as electron exchange and correlation effects is taken into account. It is found that the quantum (Bohm) potential arising due to fermionic nature of electrons and exchange-correlations effects has significant impact on the wave. The frequency of wave is influenced by variation in azimuthal index and radius of the nanotube. The results are analyzed numerically for typical systems for relatively longer wavelength waves and possible consequences are discussed. The results can be important in general understanding of the role of exchange-correlation potential in quantum hydrodynamic treatment of charge-carriers in nanotubes.