Superconducting and density-wave correlation functions in carbon nanotubes

We discuss the phase diagrams obtained by calculating temperature dependences of superconducting and density-wave correlation functions for a single (5,0) carbon nanotube (CN). We use one-loop renormalization group method within logarithmic accuracy. In this system, we must specify scattering channels in terms of momentum along the circumferential direction as well as the axis direction, because (5,0) CN has two degenerate bands crossing the Fermi energy with circumferential momenta. We find that the most divergent order is singlet superconducting or charge-density wave with 0 or 10πℏ/2πR circumferential momentum, where R is the tube radius.