Quantum-size effects on T c in superconducting nanofilms

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 c with film thickness. We demonstrate that the Bogoliubov-de Gennes equations are able to describe the thickness-dependent T c in nanofilms, and our results are in good agreement with recent experimental data on 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 c will be more pronounced for Al