Abstract
We have studied the low-temperature electrical transport properties of Pb_x(SiO₂)_1-x (x being the Pb volume fraction) nanogranular films with thicknesses of ∼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 x0.50, the resistivities ρ as functions of temperature T obey ρ∝exp(Δ/k_BT) relation (Δ being the local superconducting gap and the k_B Boltzmann constant) below the superconducting transition temperature T_c (∼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 0.60x0.72 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.