We have experimentally studied a model system that demonstrates the crossover from a superconductor that is dominated by phase fluctuations, to one in which the amplitude of the order parameter is the controlling influence on $T_c.$ This model system is comprised of two-dimensional granular Pb with an overlayer of Ag. The system displays many aspects of the phase diagram of the concentration dependence of $T_c$ in the high-$T_c$ superconductors, and this crossover has been applied to explain the phase diagram in that case. We point out the similarities and differences between the model system presented in this paper and the high-$T_c$ superconductors.

Tunneling measurements have been performed on both sides of the insulator-superconductor transition in quench-condensed granular Pb films. The results indicate that the Pb film consists of fully superconducting grains with essentially bulk values for the superconducting energy gap Δ and transition temperature ${\mathit{T}}_{\mathit{c}}$, even when the film exhibits insulating behavior in transport measurements. The density of states inferred from measurements in perpendicular magnetic field are consistent with magnetic spin-flip broadening.

Direct measurements of the superconducting superfluid on the surface of vacuum-cleaved ${\text{Bi}}_2{\text{Sr}}_2{\text{CaCu}}_2{\text{O}}_{8+\delta }$ (BSCCO) samples are reported. These measurements are accomplished via Josephson tunneling into the sample using a scanning tunneling microscope (STM) equipped with a superconducting tip. The spatial resolution of the STM of lateral distances less than the superconducting coherence length allows it to reveal local inhomogeneities in the pair wave function of the BSCCO. Instrument performance is demonstrated first with Josephson measurements of Pb films followed by the layered superconductor ${\text{NbSe}}_2$. The relevant measurement parameter, the Josephson $I_C{R}_N$ product, is discussed within the context of both BCS superconductors and the high transition temperature superconductors. The local relationship between the $I_C{R}_N$ product and the quasiparticle density of states (DOS) gap are presented within the context of phase diagrams for BSCCO. Excessive current densities can be produced with these measurements and have been found to alter the local DOS in the BSCCO. Systematic studies of this effect were performed to determine the practical measurement limits for these experiments. Alternative methods for preparation of the BSCCO surface are also discussed.

The rapid rise in resistance occurring in barely conducting quench-condensed Pb films cooled through temperatures characteristic of the bulk superconducting transition is found to be strongly current dependent, the resistance increasing rapidly with decreasing current and temperature. Annealing the same film at temperatures below 40 K changes the behavior to that of a conventional superconductor with resistance that drops as the film current and temperature decrease. Experimental evidence suggests this results from a transition from quasiparticle-dominated to Josephson-dominated tunneling.

We have performed both Josephson and quasiparticle tunneling in vacuum tunnel junctions formed between a conventional superconducting scanning tunneling microscope tip and overdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ single crystals. A Josephson current is observed with a peak centered at a small finite voltage due to the thermal-fluctuation-dominated superconducting phase dynamics. Josephson measurements at different surface locations yield local values for the Josephson $I_C{R}_N$ product. Corresponding energy gap measurements were also performed and a surprising inverse correlation was observed between the local $I_C{R}_N$ product and the local energy gap.

Granular Pb thin films on the insulating side of the two-dimensional superconductor-insulator transition are observed to exhibit a large negative magnetoresistance and electroresistance (change in resistance with electric field) at low temperatures. At high measurement voltages and low temperatures, the film resistances become temperature independent creating a “metallic” state. These phenomena are explained as manifestations of transport due to intergranular quasiparticle tunneling. This explanation might also provide insights into the similar behavior observed in other superconductors.