Finite-size effect on the Raman spectra of carbon nanotubes

Using nonresonant bond polarization theory, we have calculated the Raman intensity of a single-wall carbon nanotube of finite length. The calculations show that the Raman peaks in the intermediate frequency range $(500\mathrm{}–1200{\mathrm{cm}}^{\mathrm{-}1})$ have no intensity for infinite nanotubes, but do have some intensity for finite nanotubes. These intermediate frequency modes, which are sensitive to the nanotube length, correspond to vibrations along the nanotube axis. We also found an edge state of the breathing phonon mode at an open end of the carbon nanotube, which is Raman active.