Plasmon excitations of single-wall carbon nanotubes

Plasmon excitations in isolated single-wall carbon nanotubes are singled out in the optical spectra, and analyzed within density-functional tight-binding method and random-phase approximation. Full symmetry considerations, implemented in both approaches, stressed out that only helical quantum numbers are conserved in processes involving momentum transfer, i.e., only these quantum numbers can be unambiguously attributed to the plasmons. Energy of $\pi$ plasmon is about 5 eV and slightly decreases with diameter with no observable influence of chirality. Energy of $\pi +\sigma$ plasmon is between 20 and 21 eV, and is insensitive to nanotube geometry. Dispersion of the $\pi$ plasmon is mainly linear. Slope of dispersion curve increases with tube’s translational period.

Figure 1

Optical calculations for tube (10, 10): $\text{Re}\left(\epsilon \right)$, $\text{Im}\left(\epsilon \right)$ (top), and EEL function (bottom).

Figure 2

EEL functions for tubes (15, 5), (12, 8), (10, 10), (15, 15), and (20, 20) (from top to bottom). The first three are with almost same diameters $D\approx 1.38\text{nm}$, while the last three are with same chirality $\theta =30°$. For comparison, the results of Refs. 2, 3, 6 are indicated by the vertical lines.

Figure 3

Dispersion of $\pi$ plasmon for tube (10, 10). EEL functions are given for different momentum transfer $q$ (in ${\text{Å}}^{-1}$). For $q=0.2{\text{Å}}^{-1}$, EEL function (gray line), with its values given on the scale on the right side (gray ticks), is much larger than for the other momentums.

Figure 4

(Color online) EEL functions for tube (10, 0) for various momentum transfers $q$.

Figure 5

(Color online) Fit of $\pi$ plasmon energy dependence of momentum transfer $q$ (in ${\text{Å}}^{-1}$) for tubes (10, 2), (12, 2), (18, 2), (10, 10), and (10, 0). Fit curves for chiral tubes are given in the inset with better resolution.