Competing effects of surface phonon softening and quantum size effects on the superconducting properties of nanostructured Pb

The superconducting transition temperature (T(C)) in nanostructured Pb decreases from 7.24 to 6.4 K as the particle size is reduced from 65 to 7 nm, below which superconductivity is lost rather abruptly. In contrast, there is a large enhancement in the upper critical field (H(C2)) in the same size regime. We explore the origin of the unusual robustness of T(C) over such a large particle size range in nanostructured Pb by measuring the temperature dependence of the superconducting energy gap in planar tunnel junctions of Al/Al(2)O(3)/nano-Pb. We show that below 22 nm, the electron-phonon coupling strength increases monotonically with decreasing particle size, and almost exactly compensates for the quantum size effect, which is expected to suppress T(C).