Phonon Softening in Metallic Nanotubes by a Peierls-like Mechanism

The radial dependency of the vibrational frequencies of single-wall carbon nanotubes in the $G$ band $(1500–1600{\mathrm{cm}}^{-1\mathrm{}})$ is studied by density functional theory. In metallic nanotubes, a mode with $A_1$ symmetry is found to be significantly softer than the corresponding mode in insulating tubes or graphite. The mechanism that leads to the mode softening is explored. It is reminiscent of the driving force inducing Peierls distortions. At ambient temperature, the energy gained by opening the gap is, however, not sufficient for a static lattice distortion. Instead the corresponding vibrational frequency is lowered.