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

TL;DR

This paper investigates the variability in the superconducting transition temperature (T_c) oscillations in Pb nanofilms, attributing differences to quantum-size effects and substrate-dependent electron-electron coupling variations, analyzed through numerical modeling.

Contribution

It introduces a model linking T_c oscillations to quantum-size effects and substrate influences, explaining experimental discrepancies.

Findings

T_c oscillation amplitude varies with substrate and fabrication details

Quantum-size effects influence electron density of states

Coupling oscillations depend on interface quality

Abstract

To date, several experimental groups reported measurements of the thickness dependence of T_c of atomically uniform single-crystalline Pb nanofilms. The reported amplitude of the T_c-oscillations varies significantly from one experiment to another. Here we propose that the reason for this unresolved issue is an interplay of the quantum-size variations in the single-electron density of states with thickness-dependent oscillations in the phonon mediated electron-electron coupling. Such oscillations in the coupling depend on the substrate material, the quality of the interface, the protection cover and other details of the fabrication process, changing from one experiment to another. This explains why the available data do not exhibit one-voice consistency about the amplitude of the T_c-oscillations. Our analyses are based on a numerical solution of the Bogoliubov-de Gennes equations for a superconducting slab.