Frequency dependent effective conductivity of two-dimensional metal-dielectric composites

TL;DR

This paper investigates the frequency-dependent effective conductivity of 2D metal-dielectric composites using a resistor-inductor-capacitor lattice model, highlighting discrepancies with classical effective medium theories caused by conductivity fluctuations.

Contribution

It introduces a detailed analysis of conductivity fluctuations and their impact on effective medium approximations in 2D metal-insulator composites.

Findings

Discrepancies observed between model and classical theories at certain frequencies.

Conductivity fluctuations lead to a two-branches distribution at low frequencies.

The Drude peak vanishes at the percolation threshold as system size increases.

Abstract

We analyze a random resistor-inductor-capacitor $(RLC)$ lattice model of 2-dimensional metal-insulator composites. The results are compared with Bruggeman's and Landauer's Effective Medium Approximations where a discrepancy was observed for some frequency zones. Such a discrepancy is mainly caused by the strong conductivity fluctuations. Indeed, a two-branches distribution is observed for low frequencies. We show also by increasing the system size that at $p_c$ the so-called Drude peak vanishes; it increases for vanishing losses.