Weak Localization and Magnetoconductance in Percolative Superconducting Aluminum Films

Abstract

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 $\hat{I}¸$, a certain critical exponent in percolation theory, has been obtained. In the relation $R_{\square }-\hat{I}¸$, the value of $\hat{I}¸$ varies abruptly near $1.5k\ddot{I}‰$. 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 $\hat{I}{\pm }_T$ in the expression$\ddot{I}ƒ=[\hat{I}{\pm }_T{e}^2/(2\ddot{I}{€}^2\hslash )]\ln T+\ddot{I}{ƒ}_0$. The relation $\hat{I}{\pm }_T\propto 1/R_{\square }$ can be explained qualitatively by a model of scaling law for percolation.