Suppression of electron-electron repulsion and superconductivity in ultra-small carbon nanotubes

Recently, ultra-small diameter single wall nanotubes with diameter of similar to 0.4 nm have been produced and many unusual properties were observed, such as superconductivity, leading to a transition temperature T-c similar to 15 K, much larger than that observed in the bundles of larger diameter tubes. By a comparison between two different approaches, we discuss the issue of whether a superconducting behaviour in these carbon nanotubes can arise by a purely electronic mechanism in the armchair geometry. The first approach is based on the Luttinger model while the second one, which emphasizes the role of the lattice and short range interaction, is developed starting from the Hubbard Hamiltonian. By using the latter model we predict a transition temperature of the same order of magnitude as the measured one.