Electronic band structure, electron-phonon interaction, and superconductivity of (5,5), (10,10), and (5,0) carbon nanotubes

The electronic band structure, electron-phonon interaction, and superconducting transition are investigated for the (5,5), (10,10) armchair and (5,0) zigzag single walled carbon nanotubes (SWCNT). While the electron-phonon interaction and superconducting transition temperature are very small in (5,5) and negligibly small in (10,10) armchair tubes, they are considerable in the (5,0) zigzag tube. The (5,0) tube, which is a semiconductor with π-bands alone contributing to the band structure, exhibits metallic character with π-σ bands hybridization. As a result the van Hove like singularity in the density of states moves towards the top of the valance band enhancing the effective density of states near the Fermi energy. Consequently the electron-phonon interaction increases and the (5,0) tube turns out to be a superconductor with appreciable transition temperature and found to be the most probable member of the family of 4 Å diameter carbon nanotubes for which the superconducting transition temperature is experimentally measured.