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  • Letter
  • Open Access

Topological-to-topological transition induced by on-site nonlinearity in a one-dimensional topological insulator

Kazuki Sone* and Yasuhiro Hatsugai

  • *Contact author: sone@rhodia.ph.tsukuba.ac.jp
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Phys. Rev. Research 8, L012045 – Published 24 February, 2026

DOI: https://doi.org/10.1103/l2w2-125v

Abstract

Recent studies have extended the notion of band topology to nonlinear systems by defining nonlinear counterparts of eigenvalue problems. They have found the nonlinearity-induced topological transition regarding edge-localized eigenvectors, while it has required complicated nonlinearity such as off-diagonal one. Thus, the existence of nonlinearity-induced edge modes has been unclear under homogeneous on-site nonlinearity, which is ubiquitously found in nature. We here reveal that such on-site nonlinearity can induce transitions of topological modes, where topological modes converging to zero begin to converge to nonzero values. Since such nonlinearity-induced transition keeps the bulk band topology unchanged, we can regard it as a transition from a conventional topological mode to one unique to nonlinear systems. We analyze a nonlinear eigenvalue problem by rewriting it to a dynamical system in the spatial direction and clarify that the nonlinearity-induced transition is a result of the bifurcation in the spatial dynamics. We also propose a possible setup to observe the nonlinearity-induced transition that uses a gradual amplification of nonlinear waves. These results provide a general designing principle of topological insulators controlled by nonlinearity.

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Phys. Rev. Research 8, L012045– Published 24 February, 2026
  • Received 2 February 2025
  • Accepted 19 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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