Plasmon exchange model for superconductivity in carbon nanotubes and metallic nanowires
Recent investigations of superconductivity in carbon nanotubes have shown that a single-wall zig-zag nanotube can become superconducting at around 15 K. Theoretical studies of superconductivity in nanotubes using the traditional phonon exchange model, however, give a superconducting transition temperature T c less than 1 K. To explain the observed higher critical temperature we explore the possibility of the plasmon exchange mechanism for superconductivity in nanotubes. We first calculate the effective interaction between electrons in a nanotube mediated by plasmon exchange and show that this interaction can become attractive. Using this attractive interaction in the modified Eliashberg theory for strong coupling superconductors, we then calculate the critical temperature T c in a single-wall nanotube. Our theoretical results can explain the observed T c in a single-wall nanotube. In particular, we find that T c is sensitively dependent on the dielectric constant of the medium, the effective mass of the electrons and the radius of the nanotube. We then consider superconductivity in a bundle of single-wall nanotubes and find that bundling of nanotubes does not change the critical temperature significantly. Going beyond carbon nanotubes we show that in a metallic hollow nanowire T c has some sort of oscillatory behaviour as a function of the surface number density of electrons.