Superconductivity of individual Pb islands on Si(111): pseudogap, critical region, density of states, and island size

Abstract

With high energy resolution scanning tunneling spectroscopy, we have studied the superconductivity of a set of individual Pb islands grown on a Si(111) surface. By systematically examining 8 and 9 ML thick Pb islands with a large range of lateral sizes, we have found that their superconducting transition temperatures follow the same trend of gradual suppression on decreasing the size of the island, despite having a different density of states (DOS) at the Fermi level. This behavior is completely different from the sudden drop of transition temperature observed in the ensemble Pb particles system. Our systematic analysis in treating the temperature-dependent pseudogap state for the Pb islands has revealed a critical region in superconductivity that originates from fluctuations and was predicted by theory. Our further analysis has indicated that when the size decreases, the DOS change at EF due to the discretization of electronic levels wins over the phonon softening for Pb islands and results in a net decrease of the superconductivity temperature.