Collective excitations in single-walled carbon nanotubes

In this Brief Report, we study the dispersion relations of plasma waves which propagate parallel to the surface of the single-walled metallic carbon nanotubes. We use the classical electrodynamics in our calculations. Electronic excitations on the nanotube surface are modeled by an infinitesimally thin layer of the $\pi$ and $\sigma$ electrons which is described by means of the two-fluid hydrodynamic theory.

Figure 1

Dispersions curves ${\omega }_{+}∕{\omega }_{\pi p}$ and ${\omega }_{-}∕{\omega }_{\pi p}$ from Eq. (14) versus dimensionless variable $\kappa a$ in SWNT with the radius $a=7\mathrm{\AA }$ corresponding to $\pi +\sigma$ and $\pi$ plasmons, respectively, are shown for $m=0$, 1, 2, 3, and 4, labeled by different line styles, as indicated in the legend. For each $m$, the upper and lower curves are plotted with the same line styles.