Superconductivity in carbon nanotube ropes

We investigate the conditions in which superconductivity may develop in ropes of carbon nanotubes. It is shown that the interaction among a large number of metallic nanotubes favors the appearance of a metallic phase in the ropes, intermediate between respective phases with spin-density-wave and superconducting correlations. These arise in samples with about 100 metallic nanotubes or more, where the long-range Coulomb interaction is very effectively reduced and it may be overcome by the attractive interaction from the exchange of optical phonons within each nanotube. We estimate that the probability for the tunneling of Cooper pairs between neighboring nanotubes is much higher than that for single electrons in a disordered rope. The effect of pair hopping is therefore what establishes the intertube coherence, and the tunneling amplitude of the Cooper pairs dictates the scale of the transition to the superconducting state.