Surface and bulk plasmon excitations in carbon nanotubes. Comparison with the hydrodynamic model

In this work, we compare two models describing the interaction of external charged particles with carbon nanotubes. One is the semiclassical dielectric response model (DRM) in the Drude approximation, which approximate the valence electrons of the system by a gas of non interacting classical particles. The other is the hydrodynamic model (HDM) which uses Fluid Dynamics to describe their collective excitations. We found that both models agree for those cases where it is possible to define a dispersion relation which depends on a single frequency ωpωp. We found that in the description of the electronic response of a single-walled carbon nanotube (SWCNT) with the DRM, the connection between a three- and a two-dimensional system is non trivial and the equivalence is not direct. In spite of this, the DRM can be an important basic tool for the calculation and physical interpretation of the plasmon excitations in a nanodimensions system.