Weak Localization and Magnetoconductance in Percolative Superconducting Aluminum Films

In order to investigate the crossover from the homogeneous behavior to inhomogeneous (percolative) one, the temperature $T$ and magnetic field H dependence of the sheet resistance $R_\square$ have been measured for two-dimensional granular aluminum films. Fitting the theory to data of 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 the analysis of $D(T)$, the electron diffusion index $\theta$, a certain critical exponent in percolation theory, has been obtained. In the relation $R_\square-\theta$, the value of $\theta$ varies abruptly near $1.5k\omega$. This behavior suggesting the above mentioned crossover is similar to our previous results determined from the temperature dependence of the upper critical field. For percolative films in $H = 5\mathrm{T}$, we have found the strong $R_\square$ dependence of the prefactor $\alpha_T$ in the expression$\sigma=[\alpha_T e^2/(2\pi^2\hbar)]\ln T+\sigma_0$. The relation $\alpha_T\propto1/R_\square$ can be explained qualitatively by a model of scaling law for percolation.