Superconductivity in correlated carbon nanotubes under pressure: A Bogoliubov-de Gennes study

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.