Topological-to-Topological Transition Induced by On-Site Nonlinearity in a One-Dimensional Topological Insulator

TL;DR

This paper demonstrates that on-site nonlinearity can induce topological mode transitions in a one-dimensional topological insulator without changing the bulk band topology, revealing a new nonlinear topological phenomenon.

Contribution

It shows that homogeneous on-site nonlinearity can cause topological mode transitions, a phenomenon previously thought to require more complex nonlinearities.

Findings

On-site nonlinearity induces topological mode transitions.

Transition is a bifurcation in the spatial dynamical system.

Proposed experimental setup to observe the transition.

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, while it has required complicated nonlinearity such as off-diagonal one. Thus, the existence of nonlinearity-induced transitions 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 remains 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.