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

The superconducting transition temperature (TC) in nanostructured Pb remains nearly constant as the particle size is reduced from 65 to 7nm, below which size the superconductivity is lost rather abruptly. In contrast, there is a large enhancement in the upper critical field (HC2) in the same size regime. We explore the origin of the unusual robustness of the TC 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/Al2O3/nano-Pb. We show that below 22nm, 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 TC.