Persistent superconductivity in ultrathin Pb films: a scanning tunneling spectroscopy study.

By using a low temperature scanning tunneling microscope we have probed the superconducting energy gap of epitaxially grown Pb films as a function of the layer thickness in an ultrathin regime (5-18 ML). The layer-dependent energy gap and transition temperature (Tc) show persistent quantum oscillations down to the lowest thickness without any sign of suppression. Moreover, by comparison with the quantum-well states measured above Tc and the theoretical calculations, we found that the Tc oscillation correlates directly with the density of states oscillation at E(F) . The oscillation is manifested by the phase matching of the Fermi wavelength and the layer thickness, resulting in a bilayer periodicity modulated by a longer wavelength quantum beat.