Percolation and weak localization in thin discontinuous aluminum films

In order to investigate the crossover from the homogeneous behavior to percolative one for two-dimensional system, the temperature T and magnetic field H dependence of the sheet resistance Rsq have been measured for thin granular aluminum films. In a magnetic field of View the MathML source, the conductance σ decreases with decreasing T as View the MathML source due to weak localization effect. The value of αT decreases when Rsq increases beyond View the MathML source. In the network which does not contain loops smaller than the phase relaxation length, weak localization effect is considered to be suppressed. We have obtained the anomalous T-dependent diffusion constant D from the analysis of the magnetoconductance above TC with use of the fitting parameter D(T). These behaviors can be explained qualitatively by a model of scaling law for percolation.