Redshift and optical anisotropy of collectiveπ-volume modes in multiwalled carbon nanotubes

Abstract

A combined study concerning localized electron energy-loss spectroscopy (EELS) and modeling of collective $\ensuremath{\pi}$-volume modes in multiwalled carbon nanotubes (MWCNT) is presented. The changing line width and eigenfrequency of the $\ensuremath{\pi}$-volume mode can be ascribed solely to optical anisotropy and ``cylindrical anisotropy.'' Optical anisotropy results from the weighting of various nearly degenerate and nondegenerate states allowed for the ${\mathbf{E}}_{\ensuremath{\Vert}c}$ and ${\mathbf{E}}_{\ensuremath{\perp}c}$ polarizations. Cylindrical anisotropy arises from a lowering of the symmetry arising from the nanotube geometry. The eigenfrequency of the $\ensuremath{\pi}$-volume mode corresponds to polarization eigenmodes of graphite, and not to new maxima in the joint density of states, since momentum transfer $\mathrm{\ensuremath{\Delta}}{\mathbf{q}}_{\ensuremath{\pi}}\ensuremath{\rightarrow}0$. Results are also included from multiwalled hexagonal-boron nitride nanotubes (MWBNNT). An accurate description of the $\ensuremath{\pi}$-volume mode in multiwalled nanotubes has not been attempted so far, and is essential to resolve coupled MWCNT $\ensuremath{\pi}$-surface features, which are usually obscured in spectra obtained in penetrating-beam geometry. Volume mode-extracted EEL spectra demonstrate eigenfrequency modification of coupled $\ensuremath{\pi}$-surface features in the presence of a MWCNT dielectric filling. It was found, owing to dielectric screening effects and smearing of the dipole mode, that aloof-beam EELS which is conventionally applied to surface plasmon investigations, cannot give this information.