High-Energy Phonon Branches of an Individual Metallic Carbon Nanotube

Abstract

We present excitation-energy dependent Raman measurements between 2.05 and 2.41 eV on the same individual carbon nanotube. We find a change in the Raman frequencies of both the $D$ mode ($63{\mathrm{c}\mathrm{m}}^{-1}/\mathrm{e}\mathrm{V}$) and the high-energy modes. The observed frequencies of the modes at $\approx 1600{\mathrm{c}\mathrm{m}}^{-1}$ as a function of laser-energy map the phonon dispersion relation of a metallic tube near the $\Gamma$ point of the Brillouin zone. Our results prove the entire first-order Raman spectrum in single-wall carbon nanotubes to originate from double-resonant scattering. Moreover, we confirm experimentally the phonon softening in metallic tubes by a Peierls-like mechanism.