Dielectric response of isolated carbon nanotubes investigated by spatially resolved electron energy-loss spectroscopy: From multiwalled to single-walled nanotubes

To investigate the dielectric response of isolated single-walled carbon nanotubes, (SWCNTs), spatially resolved electron energy-loss spectroscopy measurements have been carried out using a scanning transmission electron microscope in a near-field geometry. Spectra have been compared with those acquired on multiwalled carbon nanotubes (MWCNTs) made of different numbers of layers, and with simulations performed within the framework of the continuum dielectric theory, taking into account the local anisotropic character of these nanostructures and adapted to the cylindrical geometry. Experimental data show a dispersion of mode energies as a function of the ratio of the internal and external diameters, as predicted by the continuum dielectric model. For thin MWCNTs, two polarization modes have been identified at 15 and 19 eV, indexed as tangential and radial surface-plasmon modes, respectively, resulting from the coupling of the two surface modes on the internal and external surfaces of the nanotubes. We finally show that the dielectric response of a SWCNT, displaying a single energy mode at 15 eV, can be understood in the dielectric model as the thin layer limit of surface-plasmon excitation of MWCNTs.