Room Temperature Peierls Distortion in Small Diameter Nanotubes

By means of ab initio simulations, we investigate the phonon band structure and electron-phonon coupling in small $4\mathrm{\text{−}}\AA$ diameter nanotubes. We show that both the C(5,0) and C(3,3) tubes undergo above room temperature a Peierls transition mediated by an acoustical long wavelength and an optical $q=2k_F$ phonon, respectively. In the armchair geometry, we verify that the electron-phonon coupling parameter $\lambda$ originates mainly from phonons at $q=2k_F$ and is strongly enhanced when the diameter decreases. These results question the origin of superconductivity in small diameter nanotubes.