Superconductivity and electrical properties in single-crystalline ultrathin Nb films grown by molecular-beam epitaxy

High-quality superconducting ultrathin Nb films were grown on sapphire single-crystal substrates by molecular-beam epitaxy, of which thicknesses ranged from 1.2 to 9.0 nm. They were found to be single crystalline by reflection high-energy electron diffraction. Size effects appeared remarkably in the normal conduction range. Superconducting transition temperatures (Tc's) of these films were higher than in the past reports for the same thicknesses. The thickness (d) dependence of Tc was ln[Tc(d)]{∝}-1/d, which could be explained in terms of the proximity effect. A theory of localization effects in two-dimensional superconductors by Maekawa and Fukuyama, on the other hand, could not be applied to the present experiments, since the prepared ultrathin films had better crystallinity than those discussed in the theory.