Metastable breathers and local diamagnetism in two-dimensional nonlinear metamaterials

Abstract

This article investigates the dynamic properties of two-dimensional nonlinear magnetic metamaterials consisting of nanoscale elements. The authors propose a model for a two-dimensional lattice of capacitively and inductively coupled split rectangular nanoresonators. It has been shown that the long-wave dynamics of this two-dimensional lattice are described by a regularized two-dimensional nonlinear Klein–Gordon equation, which has been solved in the form of two sequences of two-dimensional dynamic solitons on a pedestal of homogeneous forced oscillations, using an asymptotic method and taking into account the action of electromotive force (EMF) induced by an electromagnetic wave. The authors have calculated a diamagnetic response to an electromagnetic field in the terahertz range in the metamaterial region, where a breather is excited and oscillates in antiphase to a homogeneous background. The evolution of long-lived metastable breathers has been numerically studied, and two scenarios – collapse and decay – have been established for the development of their instability depending on the parameters of the induced EMF and inductive coupling between nanoresonators. It has been found that at the boundary between these scenarios, the final result of the transformation of the breathers is the chimera state of the metamaterial with a large-amplitude breather that generates stochastic waves.