Bogoliubov-de Gennes approach to superconducting states in correlated carbon nanotubes

In contrast to most microscopic theories of superconductivity based on the reciprocal space, the Bogoliubov-de Gennes (BdG) one provides a real-space alternative for addressing inhomogeneous systems with surface and interfaces [1]. In this work, single-walled carbon nanotubes with intertube interactions are addressed through a unitary transformation within an attractive Hubbard model [2], which decouples the self-consistent BdG equations into those of independent superconducting channels and significantly reduces the numerical solution time. The results reveal a close relationship between the local superconducting gap and the local density of states. In the limiting case of independent nanotubes, the superconducting states of carbon nanotubes can be determined by the standard Bardeen-Cooper-Schrieffer equation. Finally, the superconducting gap and critical temperature of correlated carbon nanotubes including curvature and spin-orbital effects are compared with experimental data.

[1] P. G. de Gennes, Superconductivity of Metals and Alloys (Westview Press, 1999) p. 141.

[2] C. G. Galvan, L. A. Perez, and C. Wang, Physica B 553, 36 (2019).