Estimation of superconducting transition temperature in metallic carbon nanotubes

The superconducting transition temperature ($T_c$) for a metallic carbon nanotube [tube ($n, n$)] has been estimated considering the electron-phonon interaction. The intraband backward scattering by the longitudinal modes plays an important role for the occurrence of the superconducting state. Specifically for tube (5,5) with a diameter of ∼7 Å, the $T_c$ was found to be 1.5×${10}^{-4\mathrm{}}$ K.