Topologically nontrivial states in one-dimensional nonlinear bichromatic superlattices

TL;DR

This paper explores how nonlinearity influences topological states in one-dimensional bichromatic superlattices, revealing edge solitons, their topological characterization, and stability properties.

Contribution

It introduces the concept of topological edge solitons in nonlinear superlattices and characterizes their topological nature via Chern numbers in an extended parameter space.

Findings

Existence of topological edge solitons sensitive to phase parameters

Topological properties characterized by Chern numbers in extended space

Stability analysis of nonlinear edge states

Abstract

We study topological properties of one-dimensional nonlinear bichromatic superlattices and unveil the effect of nonlinearity on topological states. We find the existence of nontrivial edge solitions, which distribute on the boundaries of the lattice with their chemical potential located in the linear gap regime and are sensitive to the phase parameter of the superlattice potential. We further demonstrate that the topological property of the nonlinear Bloch bands can be characterized by topological Chern numbers defined in the extended two-dimensional parameter space. In addition, we discuss that the composition relations between the nolinear Bloch waves and gap solitions for the nonlinear superlattices. The stabilities of edge solitons are also studied.