  We have studied the low-temperature electrical transport properties of
Pb$_x$(SiO$_2$)$_{1-x}$ ($x$ being the Pb volume fraction) nanogranular films
with 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$$\lesssim$0.50, the
resistivities $\rho$ as functions of temperature $T$ obey
$\rho\propto\exp(\Delta/k_BT)$ relation ($\Delta$ being the local
superconducting gap and the $k_B$ Boltzmann constant) below the superconducting
transition temperature $T_c$ ($\sim$7 K) of Pb granules. The value of the gap
obtained via this expression is almost identical to that by single electron
tunneling spectra measurement. The magnetoresistance is negative below $T_c$
and its absolute value is far larger than that above $T_c$ at a certain field.
These observations indicate that single electron hopping (or tunneling), rather
than Cooper pair hopping (or tunneling) governs the transport processes below
$T_c$. The temperature dependence of resistivities shows reentrant behavior for
the 0.50$<$$x$$<$0.57 films. It is found that single electron hopping (or
tunneling) also dominates the low-temperature transport process for these
films. The reduction of the single electron concentration leads to an
enhancement of the resisivity at sufficiently low temperature. For the
0.60$\lesssim$$x$$\lesssim$0.72 films, the resistivities sharply decrease with
decreasing temperature just below $T_c$, and then show dissipation effect with
further decreasing temperature. Treating the conducting paths composed of Pb
particles as nanowires, we have found that the $R(T)$ data below $T_c$ can be
well explained by a model that includes both thermally activated phase slips
and quantum phase slips.

Mesoscale and Nanoscale Physics