Two-dimensional plasmons in the random impedance network model of disordered thin-film nanocomposites

TL;DR

This paper introduces a model for 2D disordered nanocomposites with 3D Coulomb interactions, revealing how plasmon resonances evolve across the metal filling threshold and demonstrating a spectral density gap below percolation.

Contribution

It proposes a novel 2D model with long-range capacitive connections that captures the evolution of plasmon resonances in disordered thin films.

Findings

In the subcritical region, a spectral gap with Lifshitz tails appears.

Above the percolation threshold, the DOS shows a crossover from plane-wave plasmons to cluster resonances.

The model reproduces the known dispersion relation for 2D plasmons.

Abstract

Random impedance networks are widely used as a model to describe plasmon resonances in disordered metal-dielectric nanocomposites. In order to study thin films, two-dimensional networks are often used despite the fact that such networks correspond to a two-dimensional electrodynamics [J.P. Clerc et al, J. Phys. A 29, 4781 (1996)]. In the present work, we propose a model of two-dimensional systems with three-dimensional Coulomb interaction and show that this model is equivalent to a planar network with long-range capacitive connections between sites. In a case of a metal film, we get a known dispersion $\omega \propto \sqrt{k}$ of plane-wave two-dimensional plasmons. In the framework of the proposed model, we study the evolution of resonances with decreasing of metal filling factor. In the subcritical region with metal filling $p$ lower than the percolation threshold $p_c$, we observe a gap with Lifshitz tails in the spectral density of states (DOS). In the supercritical region $p>p_c$, the DOS demonstrates a crossover between plane-wave two-dimensional plasmons and resonances associated with small clusters.