Coulomb blockade regime of a single-wall carbon nanotube

We study a model of carbon nanotube with a half filled conduction band. At this filling the system is a Mott insulator. The Coulomb interaction is assumed to be unscreened. It is shown that this allows to develop the adiabatic approximation which leads to considerable simplifications in calculations of the excitation spectrum. We give a detailed analysis of the spectrum and the phase diagram at half filling, and discuss effects of small doping. In the latter case several phases develop strong superconducting fluctuations corresponding to various types of pairing.