Radius and chirality dependence of the radial breathing mode and the G-band phonon modes of single-walled carbon nanotubes

The radial breathing and G-band vibrational modes of all 300 single-walled carbon nanotubes in the radius range from 2 to 12 angstrom were calculated within a symmetry-adapted nonorthogonal tight-binding model. The dynamical matrix was calculated within this model using the linear-response approximation. The obtained phonon frequencies show well-expressed radius and chirality dependence and family behavior. The curvature-induced effects on the frequencies are found to be important for small- and moderate-radius tubes. The strong electron-phonon interactions in metallic tubes bring about Kohn anomalies of certain phonon branches. Among the Raman-active phonons, these interactions have strongest effect on the longitudinal tangential A(1) phonons of metallic tubes, whose frequency becomes lower than that of the transverse tangential A(1) phonons. The calculated frequencies are compared to available theoretical and experimental data.