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A theoretical analysis of the superconductivity observed recently in Carbonnanotubes is proposed. We argue that ultra-small (diameter $ \sim 0.4 nm$)single wall carbon nanotubes (with transition temperature $T_c\sim 15 ^{o}K$)and entirely end-bonded multi-walled ones ($T_c\sim 12 ^{o}K$) can superconductby an electronic mechanism, basically the same in both cases. By a Luttingerliquid -like approach, one finds enhanced superconducting correlations due tothe strong screening of the long-range part of the Coulomb repulsion. Based onthis finding, we perform a detailed analysis on the resulting  Hubbard-like model, and calculate transition temperatures of the same orderof magnitude as the measured ones.Comment: 6 pages, 1 figure, PACS: 71.10.Pm,74.50.+r,71.20.Tx, to appear in  Phys. Rev.

Theoretical approach to electronic screening and correlated superconductivity in carbon nanotubes