Weak localization and magnetoconductance in percolative superconducting aluminum films

In order to investigate the crossover from a homogeneous behavior to an inhomogeneous (percolative) one, the temperature T and magnetic field H dependence of the sheet resistance R_□ have been measured for two-dimensional granular aluminum films. Fitting the theory to data on magnetoconductance near T_C with use of the diffusion constant D(T) as a fitting parameter, we have obtained the anomalous T-dependent diffusion constant D. From D(T), the electron diffusion index θ, a certain critical exponent in the percolation theory, has been obtained. In the relation R _□-θ, the value of θ varies abruptly near 1.5 kΩ. This behavior suggests the abovementioned crossover is similar to our previous results determined from the T dependence of the upper critical magnetic field. For percolative films at H=5 T, we have found the strong R _□ dependence of the prefactor α_T in the expression σ=[α_Te²/(2π²ℏ) ]ln T+σ₀. The relation α_T∝1/R _□ can be explained qualitatively by a model of scaling law for percolation.