Electronic correlations of small diameter carbon nanotubes

The transport properties of 4 A diameter carbon nanotubes have been studied in recent experiments by Tang et al, and evidence of superconductivity at about 15 K has been claimed. The only metallic nanotubes compatible with such a small radius are the (3, 3) armchair and the (5, 0) zigzag respectively. In this paper we study the electronic properties of both these systems, paying special attention to the screening effects coming from the surrounding environment characterizing the experimental set-up. We look for the low temperature instabilities in the Luttinger liquid description of the correlated electron system. The phase diagram is investigated by taking into account the competition between the Coulomb repulsion and the phonon-mediated electron-electron interaction