  In contrast to most microscopic theories of superconductivity based on the
reciprocal space, the Bogoliubov-de Gennes (BdG) formalism provides a
real-space alternative for addressing inhomogeneous systems. In this article,
we study the superconducting states in correlated single-walled carbon
nanotubes (SWNTs) with curvature and spin-orbit corrections, as well as the
inter-tube interaction through a connecting molecule using an attractive
Hubbard model. The results reveal a close relationship between the on-site
superconducting gap and the single-electron local density of states. For the
limiting case of independent large-diameter nanotubes, the BdG equations can be
reduced to the standard Bardeen-Cooper-Schrieffer one with analytical
solutions. Moreover, an optimal separation between nanotubes is found, which
leads to a maximal superconducting critical temperature. This finding has a
remarkable accordance with the experimental data obtained from Buckypapers
built of boron doped SWNTs under external pressure.
