Metastable breathers and local diamagnetism in two-dimensional nonlinear metamaterials
O.V. Charkina1 and M.M. Bogdan1,2
1B.Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine47 Nauky Ave., Kharkiv 61103, Ukraine
2V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 61077, Ukraine
Received April 20, 2020, published online May 26, 2020
The dynamic properties of two-dimensional nonlinear magnetic metamaterials consisting of nanoscale elements are investigated. A model of a two-dimensional lattice of capacitively and inductively coupled rectangle nanoresonators is proposed, and it is shown that its long-wave dynamics is described by the regularized nonlinear two-dimensional Klein–Gordon equation. The asymptotic method found solutions of this equation, taking into account the action of the emf induced by an electromagnetic wave, in the form of two sequences of two-dimensional dynamic solitons on a pedestal of homogeneous forced oscillations. The diamagnetic response to the electromagnetic field of the terahertz range in the metamaterial region, in which a breather is excited, oscillating in antiphase to a uniform background, is calculated. The evolution of long-lived metastable breathers is numerically studied and two scenarios, collapse, and decay are found in the development of its instability, depending on the parameters of the induced emf and inductive coupling between nanoresonators. At the boundary of these scenarios, it has been found that 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.
Key words: two-dimensional metamaterials, nanoscale resonators, nonlinear dynamics, metastable breathers.