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We have studied the low-temperature electrical transport properties ofPb$_x$(SiO$_2$)$_{1-x}$ ($x$ being the Pb volume fraction) nanogranular filmswith thicknesses of $\sim$1000 nm and $x$ spanning the dielectric,transitional, and metallic regions. It is found that the percolation threshold$x_c$ lies between 0.57 and 0.60. For films with $x$$\lesssim$0.50, theresistivities $\rho$ as functions of temperature $T$ obey$\rho\propto\exp(\Delta/k_BT)$ relation ($\Delta$ being the localsuperconducting gap and the $k_B$ Boltzmann constant) below the superconductingtransition temperature $T_c$ ($\sim$7 K) of Pb granules. The value of the gapobtained via this expression is almost identical to that by single electrontunneling spectra measurement. The magnetoresistance is negative below $T_c$and its absolute value is far larger than that above $T_c$ at a certain field.These observations indicate that single electron hopping (or tunneling), ratherthan Cooper pair hopping (or tunneling) governs the transport processes below$T_c$. The temperature dependence of resistivities shows reentrant behavior forthe 0.50$<$$x$$<$0.57 films. It is found that single electron hopping (ortunneling) also dominates the low-temperature transport process for thesefilms. The reduction of the single electron concentration leads to anenhancement of the resisivity at sufficiently low temperature. For the0.60$\lesssim$$x$$\lesssim$0.72 films, the resistivities sharply decrease withdecreasing temperature just below $T_c$, and then show dissipation effect withfurther decreasing temperature. Treating the conducting paths composed of Pbparticles as nanowires, we have found that the $R(T)$ data below $T_c$ can bewell explained by a model that includes both thermally activated phase slipsand quantum phase slips.

Hopping conductance and macroscopic quantum tunneling effect in three dimensional Pb$_x$(SiO$_2$)$_{1-x}$ nanogranular films