Superconductivity of multi-walled carbon nanotubes

\newcounter{bean} We investigate the superconductivity of multi-walled carbon nanotubes, paying attention to the balance between the Coulomb interaction and the effective {\em e-e} interaction mediated by phonon-exchange. Our main aim is to confront the recent observation of sharp transitions in the resistance of multi-walled nanotubes, in situations where most part of the shells are electrically active [1]. For this purpose we will adapt the mechanism already shown for the superconductivity of nanotube ropes, where the electrostatic coupling among a large number of nanotubes leads to a drastic reduction of the Coulomb interaction [2]. We will consider in particular the interaction and Cooper-pair tunneling among a large number of shells in the multi-walled nanotubes, drawing a connection between the superconductivity of these structures and the more conventional one in the intercalated compounds of graphite. \begin{list}{[\arabic{bean}]}{\usecounter{bean} } \item I. Takesue {\em et al.}, to appear in Phys. Rev. Lett. \item J. Gonz\'alez, Phys. Rev. Lett. {\bf 88}, 076403 (2002); J. V. Alvarez and J. Gonz\'alez, Phys. Rev. Lett. {\bf 91}, 076401 (2003). \end{list}