Evidence for the existence of two breathinglike phonon modes in infinite bundles of single-walled carbon nanotubes

We study the low-frequency region of the Raman spectra of infinite bundles of identical single-walled carbon nanotubes within a valence force field model of the lattice dynamics and a bond-polarizability model for the Raman intensity. It is obtained that two breathinglike phonon modes are present in such bundles for each tube type. Based on this prediction, an alternative interpretation of the experimental Raman spectra is proposed. In particular, an explanation is given for the appearence of resonant Raman lines that are predicted as nonresonant within the noninteracting tube picture.