Weak Localization and Magnetoconductance in Percolative Superconducting Aluminum Films

TL;DR

This study investigates the transition from homogeneous to inhomogeneous behavior in granular aluminum films by analyzing temperature and magnetic field effects on resistance, revealing critical exponents and scaling laws related to percolation.

Contribution

It introduces a method to extract the diffusion constant and critical exponent in percolative superconducting films through magnetoconductance data analysis.

Findings

The diffusion constant D(T) shows anomalous temperature dependence.

The critical exponent θ varies abruptly near 1.5kΩ, indicating a crossover.

The prefactor α_T in conductivity scales inversely with sheet resistance R_⊠.

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 $\theta$, 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.