Dynamic Scaling near the Percolation Threshold in Thin Au Films

Abstract

We report on measurements of both the ac conductivity ($\sigma$) and the ac dielectric constant ($\epsilon$) of thin Au films near their percolation threshold for frequencies between 100 Hz and 10 MHz. In the critical regime, $\sigma \simeq {\omega }^x$ and $\epsilon \simeq {\omega }^{-y}$. We obtain $x=0.95\mathrm{}\pm 0.05$ and $y=0.13\mathrm{}\pm 0.05$, in agreement with a general relation $x+y=1\mathrm{}$. These results are significantly different from predictions based on finite size scaling of the dc conductivity or diffusion on independent percolation clusters, providing evidence for the importance of electron-electron interaction effects.