Theory of superconducting fluctuations in the thinest carbon nanotubes

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The low-energy electronic Hamiltonian for the thinest zigzag carbon nanotube, embedded into a dielectric host, is derived and its phase diagram is discussed. The specific multi-band structure and the microscopic form of the electron-electron interaction in this systems is considered. The interband repulsive interaction, which is almost unscreened, leads to a retarded intraband attraction between the electrons and can stabilize the Cooper pairs. For a dielectric constant of the host εd 2-4, the theory predicts that the superconducting fluctuations should develop, which is in agreement with the experiment. For εd 8, the density wave fluctuations should be amplified. Between the two phases, there is a metallic state where all two-particle fluctuations are suppressed.