Effective low-energy theory of superconductivity in carbon nanotube ropes

We derive and analyze the low-energy theory of superconductivity in carbon nanotube ropes. A rope is modelled as an array of metallic nanotubes, taking into account phonon-mediated as well as Coulomb interactions, and arbitrary Cooper pair hopping amplitudes (Josephson couplings) between different tubes. We use a systematic cumulant expansion to construct the Ginzburg-Landau action including quantum fluctuations. The regime of validity is carefully established, and the effect of phase slips is assessed. Quantum phase slips are shown to cause a depression of the critical temperature T-c below the mean-field value, and a temperature-dependent resistance below T-c. We compare our theoretical results to recent experimental data of Kasumov [Phys. Rev. B 68, 214521 (2003) ] for the sub-T-c resistance, and find good agreement with only one free fit parameter. Ropes of nanotubes therefore represent superconductors in the one-dimensional few-channel limit.