Static conductivity and superconductivity of carbon nanotubes: Relations between tubes and sheets

We relate the static conductivity of carbon nanotubes to the static in-plane conductivity of a graphite sheet and conclude that isolated single-wall nanotubes are excellent conductors. In contrast, multiwall tubes at low doping may possess conductivities substantially below that of the sum of the constituent tubes. The curvature of small tubes opens new electron-phonon scattering channels that are not available to sheets. This increases the electron-phonon coupling and yields superconducting transition temperatures for small doped tubes intermediate between those of intercalated graphite and alkali-metal-doped ${\mathrm{C}}_{60}$.