Dark solitons in nonlinear Su-Schrieffer-Heeger lattices

TL;DR

This paper explores dark solitons in nonlinear Su-Schrieffer-Heeger lattices, revealing their spectral properties, stability conditions, and potential for novel topological soliton states.

Contribution

It systematically investigates the existence, spectral placement, and stability of dark solitons in nonlinear SSH lattices, a topic not previously explored in detail.

Findings

Dark solitons maintain a constant background with intensity dips.

Some dark solitons are linearly stable when intracell coupling exceeds intercell coupling.

Dark solitons are generally dynamically unstable across broad parameters.

Abstract

The introduction of nonlinearities into lattices with topological band structures has led to the discovery of various types of solitons. The Su-Schrieffer-Heeger (SSH) lattice, as the most fundamental topological model, has been extended into the nonlinear regime. In particular, nonlinear edge states and bulk solitons exhibiting intensity humps against a zero background have been extensively studied in nonlinear SSH lattices. In this paper, we systematically investigate dark solitons in nonlinear SSH lattices. These dark solitons maintain a nonzero and constant background, featuring intensity dips either in the bulk of the lattice or at its edges, and residing spectrally in the semi-infinite gap or the middle finite gap. Regardless of the specific type of dark soliton, the intensity dip remains wellpreserved and is not affected by the band structure of the original linear lattice. Although the dark solitons we have identified are generally dynamically unstable across a broad range of parameters, several types exhibit linear stability when the intracell coupling is much larger than the intercell coupling. Our findings may provide valuable insights for the exploration of novel types of solitons in nonlinear topological lattices.