Topological edge solitons in the non-Hermitian nonlinear Su-Schrieffer-Heeger model

The Su-Schrieffer-Heeger model is the simplest one-dimensional model showing the characteristic features of topological insulators. Its most interesting property is the appearance of a solution of the edge state or edge soliton in a topologically nontrivial phase determined by the system parameters. Recently, the authors have been investigating generalizations of such a system in two different aspects, both through the inclusion of nonlinearity in the model, and considering the effects of gain and loss. This paper provides an example of accounting for both of these mechanisms. It is shown that for a given gain parameter, there is a region of loss parameters where protected edge solitons are also implemented. Passing the critical value of the loss parameter, the stationary edge soliton becomes oscillating. It is interesting that there are regimes in which the edge soliton, while maintaining spatial localization, demonstrates chaotic temporal dynamics. Analytical estimates characterizing the properties of solutions are given.

Automated summary

This paper investigates the effects of nonlinearity and gain and loss in the one-dimensional Su-Schrieffer-Heeger model, and demonstrates that protected edge solitons can also be implemented within a certain range of loss parameters. When the loss parameter exceeds the critical value, the stationary edge soliton transitions into an oscillating state. Interestingly, there are regions where the edge soliton exhibits chaotic temporal dynamics while maintaining spatial localization. The paper provides analytical estimates characterizing the properties of the solutions.