Europhys. Lett.
Volume 76, Number 3, November 2006
Page(s) 498 - 504
Section Condensed matter: electronic structure, electrical, magnetic, and optical properties
Published online 22 September 2006
Europhys. Lett., 76 (3), pp. 498-504 (2006)
DOI: 10.1209/epl/i2006-10274-6

Quantum-size effects on $T_{\rm c}$ in superconducting nanofilms

A. A. Shanenko1, 2, M. D. Croitoru1 and F. M. Peeters1

1  Departement Fysica, Universiteit Antwerpen - Groenenborgerlaan 171 B-2020 Antwerpen, Belgium
2  Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research 141980 Dubna, Russia

received 17 August 2006; accepted 1 September 2006
published online 22 September 2006

An essential property of a high-quality metallic nanofilm is the quantization of the electron spectrum due to dimensional confinement in one direction. Quantum confinement has a substantial impact on the superconducting characteristics and leads to quantum-size variations of the critical temperature $T_{\rm c}$ with film thickness. We demonstrate that the Bogoliubov-de Gennes equations are able to describe the thickness-dependent $T_{\rm c}$ in nanofilms, and our results are in good agreement with recent experimental data on ${\rm Pb}$ flat terraces grown on silicon (Science, 306 (2004) 1915 and Nature Phys., 2 (2006) 173). We predict that the quantum-size oscillations of $T_{\rm c}$ will be more pronounced for ${\rm Al}$.

74.78.-w - Superconducting films and low-dimensional structures.
74.78.Na - Mesoscopic and nanoscale systems.
74.62.-c - Transition temperature variations.

© EDP Sciences 2006