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To date, several experimental groups reported measurements of the thicknessdependence of T_c of atomically uniform single-crystalline Pb nanofilms. Thereported amplitude of the T_c-oscillations varies significantly from oneexperiment to another. Here we propose that the reason for this unresolvedissue is an interplay of the quantum-size variations in the single-electrondensity of states with thickness-dependent oscillations in the phonon mediatedelectron-electron coupling. Such oscillations in the coupling depend on thesubstrate material, the quality of the interface, the protection cover andother details of the fabrication process, changing from one experiment toanother. This explains why the available data do not exhibit one-voiceconsistency about the amplitude of the T_c-oscillations. Our analyses are basedon a numerical solution of the Bogoliubov-de Gennes equations for asuperconducting slab.

physical review. b, condensed matter and materials physics

Superconducting transition temperature of Pb nanofilms: Impact of the  thickness-dependent oscillations of the phonon mediated electron-electron  coupling