Electron-phonon coupling and Peierls transition in metallic carbon nanotubes

We reexamine the putative Peierls transition in a (5,5) metallic nanotube. We show that the conduction electrons at the Fermi level do not couple to the longitudinal acoustic phonon but rather to a folded-in graphene zone edge phonon having the proper Kekule modulation symmetry. The calculation for the mean-field transition temperature gives 15 K, a value comparable to previous estimates. We discuss the significance of this transition temperature.