Thresholdless nonlinearity-induced edge solitons in trimer arrays

TL;DR

This paper demonstrates that in a trimer array modeled by a nonlinear Schrödinger equation, weak nonlinearity can induce localized edge states even when linear edge states are absent, with analytical descriptions near the band edge.

Contribution

It reveals the phenomenon of thresholdless nonlinear edge state formation in a trimer array, expanding understanding of nonlinear topological edge modes.

Findings

Weak nonlinearity induces edge states without linear counterparts

Edge modes bifurcate from linear band edges

Analytical description matches numerical results near gap edges

Abstract

We consider a one-dimensional discrete nonlinear Schr\"odinger (DNLS) model with Kerr-type on-site nonlinearity, where the nearest-neighbor coupling constants take two different values ordered in a three-periodic sequence. The existence of localized edge states in the linear limit (Su-Schrieffer-Heeger trimer, SSH3) is known to depend on the precise location of the edge. Here, we show that for a termination that does not support linear edge states, an arbitrarily weak on-site nonlinearity will induce an edge mode with asymptotic exponential localization, bifurcating from a linear band edge. Close to the gap edge, the shape of the mode can be analytically described in a continuum approximation as one half of a standard gap soliton. The linear stability properties of nonlinear edge modes are also discussed.