Statistical and Scaling Properties of the $ac$ Conductivity in Thin Metal-Dielectric Composites

TL;DR

This paper investigates the statistical and scaling behaviors of ac conductivity in thin metal-dielectric composites, revealing divergence of correlation length, fluctuation patterns, and a phase transition at zero loss using a 2D network model.

Contribution

It introduces a real space renormalization group analysis of ac conductivity in metal-dielectric films, highlighting the phase transition at zero loss and the distribution shift to log-normal.

Findings

Conductivity fluctuations are significant at very low losses.

Correlation length diverges as loss approaches zero.

Distribution of conductivity becomes log-normal below a critical loss.

Abstract

We Study in this paper the scaling and statistical properties of the $ac$ conductivity of thin metal-dielectric films in different regions of the loss in the metallic components and particularly in the limit of vanishing loss. We model the system by a 2D $RL-C$ network and calculate the effective conductivity by using a real space renormalization group method. It is found that the real conductivity strongly fluctuates for very small losses. The correlation length, which seems to be equivalent to the localization length, diverges for vanishing losses confirming our previous results for the decay of the real conductivity with the loss. We found also that the distribution of the real conductivity becomes log-normal below a certain critical loss $R_{c}$ which is size dependent for finite systems. For infinite systems this critical loss vanishes and corresponds to the phase transition between localized modes for finite losses and the extended ones at zero loss.