Bogoliubov-de Gennes analysis of superconducting gap in nanowires and nanotubes

Most quantum theories of superconductivity have been formulated in the reciprocal space by taking the advantage of translational symmetry. Such symmetry is absent in many nanostructured superconductors, whose study requires a real space approach such as the Bogoliubov-de Gennes formalism [1]. In this work, the inhomogenious superconducting gap [2,3] in nanostructures is studied by means of a simple attractive Hubbard model. The results show a unique critical temperature for each nanostructure despite the variation of its local superconducting gap and the spectral average of such gap over the chemical potential location grows when its coordination number diminishes. The latter suggests that the superconductivity in nanostructures could be enhanced by the quantum confinement of electrons, which reduces its kinetic energy and accentuates the potential one.

This work was partially funded by UNAM-PAPIIT-IN110020 and CONACyT-252943. Computations were performed at Miztli of DGTIC-UNAM. G.E.L. thanks the support from UNAM-PAEP 2020.

[1] P. G. de Gennes, Superconductivity of Metals and Alloys (Westview Press, 1999) p. 141.
[2] C. G. Galvan, J. M. Cabrera, L. A. Perez, and C. Wang, Phys. Status Solidi B 253, 1638 (2016).
[3] C. G. Galvan, L. A. Perez, and C. Wang, Physica B 553, 36 (2019).