Topological materials exhibit edge modes corresponding to topological features of their bulk, which is known as the bulk-boundary correspondence. Recent studies have extended the notion of topology to, e.g., fluid and photonic metamaterials, whose dynamics can be nonlinear. However, since most of the studies of topological materials have focused on linear systems, it was unclear whether nonlinear effects, in particular, chaos can alter the fundamental principle of topological materials such as the bulk-boundary correspondence.
The research group has revealed the transition from topological edge modes to spatially chaotic modes by theoretically analyzing a model of nonlinear topological insulators. This chaos transition leads to the breakdown of the bulk-boundary correspondence. We have also proposed an analytical technique to study the nonlinear extension of topological materials, which combines the theories of nonlinear dynamical systems and topological materials. It is expected that our results will provide a designing principle of nonlinear devices that utilize effects of topology and chaos.

Papers
Journal: Nature Communications
Title: Transition from the topological to the chaotic in the nonlinear Su–Schrieffer–Heeger model
Authors: Kazuki Sone*, Motohiko Ezawa, Zongping Gong, Taro Sawada, Nobuyuki Yoshioka, Takahiro Sagawa
DOI: 10.1038/s41467-024-55237-3