Consistency of Superconducting Correlations with One-Dimensional Electron Interactions in Carbon Nanotubes

We show that a model of interacting electrons in one dimension is able to explain the order of magnitude as well as the temperature dependence of the critical supercurrents recently measured in nanotube samples placed between superconducting contacts. We use bosonization methods to deal with the long-range Coulomb interaction, ending up with a picture in which the critical current does not follow the temperature dependence of the gap in the contacts. Our results also reveal the presence of a short-range attractive interaction in the nanotubes, which accounts for a significant enhancement of the critical supercurrents.