By theoretically analyzing nonlinear topological materials, a research group including Assistant Professor Kazuki Sone of the Institute of Pure and Applied Sciences at the University of Tsukuba (Graduate Student at the Graduate School of Engineering, the University of Tokyo at the time of research); Lecturer Motohiko Ezawa, Associate Professor Zongping Gong, Graduate Student Taro Sawada, and Professor Takahiro Sagawa of the Graduate School of Engineering, the University of Tokyo; and Associate Professor Nobuyuki Yoshioka of the International Center for Elementary Particle Physics at the same university (Assistant Professor at the Graduate School of Engineering at the time of research), clarified that these materials underwent a transition from a topological phase to chaos. The results are published in Nature Communications.
In physics, the concept of topology has various applications. In a topological material, a peculiar electronic state called an edge state is predicted to appear at the sample edge, corresponding to topological features of their bulk. This relationship between the bulk topology and edge states is called bulk edge correspondence. Recent studies address not only solids but also the extension of this concept to fluid waves and optical metamaterials have also been discussed. Some of these extensions exhibit nonlinear dynamics.
An important concept in the dynamical system theory, a field of mathematics that analyzes nonlinear dynamics, is the instability of dynamics called chaos. This is a phenomenon in which small deviations in the initial conditions increase with time, even in the absence of noise, and the long-term behavior becomes unpredictable. This concept is related to familiar phenomena, such as weather changes. Furthermore, most previous studies on topological materials have focused on linear systems. Therefore, fundamental questions such as the relationship between the dynamical system theory and nonlinear topological materials, especially whether chaos causes changes in bulk edge correspondence, have not been clarified.
By theoretically analyzing the edge states of nonlinear materials, the research group showed that a transition from a topological edge state to a spatially chaotic unstable state occurred when nonlinearity was strong. They also revealed that bulk edge correspondence could be broken in nonlinear systems via chaotic transition. The key idea here was to apply the dynamical system theory to analyze the spatial direction of the edge state, which would reveal not only chaos but also the correspondence with the topological index, a quantity that characterized topology.
The present study is significant from the viewpoint of fundamental physics because it provides a theoretical framework for analyzing bulk-edge correspondence in topological materials in nonlinear systems, which has so far primarily been investigated in linear systems. This method will lead to the development of design principles for nonlinear optical and quantum devices that utilize the effects of topology and chaos and are stable against noise.
Journal Information
Publication: Nature Communications
Title: Transition from the topological to the chaotic in the nonlinear Su-Schrieffer-Heeger model
DOI: 10.1038/s41467-024-55237-3
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