  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.
