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. 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.

arXiv comment8 pages, 3 figures, revtex; references added

References in corpus (12)

• The Kernel Polynomial Method
• Anderson localisation in tight-binding models with flat bands
• Boson peak and Ioffe-Regel criterion in amorphous silicon-like materials: the effect of bond directionality
• Dielectric resonances of binary random networks
• On random symmetric matrices with a constraint: the spectral density of random impedance networks
• Dielectric resonances of lattice animals and other fractal structures
• Spectral Properties of Random Reactance Networks and Random Matrix Pencils
• Purcell effect at metal-insulator transitions
• Optical reconfiguration and polarization control in semi-continuous gold films close to the percolation threshold
• Enhancement of High-Frequency Field in Near-Ideal Metal Mixture
• Optical and Electrical Properties of Nanostructured Metallic Electrical Contacts
• Dielectric resonances of ordered passive arrays