Dynamic Scaling near the Percolation Threshold in Thin Au Films

Abstract

We report on measurements of both the ac conductivity ($\ensuremath{\sigma}$) and the ac dielectric constant ($\ensuremath{\epsilon}$) of thin Au films near their percolation threshold for frequencies between 100 Hz and 10 MHz. In the critical regime, $\ensuremath{\sigma}\ensuremath{\simeq}{\ensuremath{\omega}}^{x}$ and $\ensuremath{\epsilon}\ensuremath{\simeq}{\ensuremath{\omega}}^{\ensuremath{-}y}$. We obtain $x=0.95\ifmmode\pm\else\textpm\fi{}0.05$ and $y=0.13\ifmmode\pm\else\textpm\fi{}0.05$, in agreement with a general relation $x+y=1$. 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.