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

Abstract

Random impedance networks are widely used as a model to describe plasmon resonances in disordered metal-dielectric nanocomposites. Two-dimensional networks are applied when considering thin films despite the fact that such networks correspond to the two-dimensional electrodynamics [J.P. Clerc et al, J. Phys. A 29, 4781 (1996)]. In the present work, we propose a model of twodimensional systems with the three-dimensional Coulomb interaction and show that this model is equivalent to the planar network with long-range capacitive links between distant sites. In the case of a metallic film, we obtain the well-known dispersion of two-dimensional plasmons ω ∝ √ k. We study the evolution of resonances with a decrease in the metal filling factor within the framework of the proposed model. In the subcritical region with the metal filling p lower than the percolation threshold pc, we observe a gap with Lifshitz tails in the spectral density of states (DOS). In the supercritical region p > pc, the DOS demonstrates a crossover between plane-wave two-dimensional plasmons and resonances of finite clusters. arXiv:1710.00949v4 [cond-mat.mes-hall]