Nonlinearity induced topological physics in momentum space and real space

TL;DR

This paper explores how nonlinearity induces novel topological phenomena in lattice systems, revealing new phases, edge states, and solitons through theoretical analysis and potential photonic experiments.

Contribution

It introduces a nonlinear extension of the SSH model, derives a general nonlinear Zak phase, and uncovers topological features and solitons arising from nonlinearity.

Findings

Nonlinear Zak phase sum becomes quantized at strong nonlinearity.

Strong interplay between solitons and topological edge states.

Topological in-gap solitons can exist in trivial regimes.

Abstract

Nonlinearity induced topological properties in nonlinear lattice systems are studied in both momentum space and real space. Experimentally realizable through the Kerr effect on photonic waveguide systems, our working model depicts on-site nonlinearity added to the Su-Schrieffer-Heeger (SSH) model plus a chiral-symmetry breaking term. Under the periodic-boundary condition, two of the nonlinear energy bands approach the energy bands of the chiral-symmetric SSH model as nonlinearity strength increases. Further, we account for a correction to the Zak phase and obtain a general expression for nonlinear Zak phases. For sufficiently strong nonlinearity, the sum of all nonlinear Zak phases (not the sum of all conventional Zak phases) is found to be quantized. In real space, it is discovered that there is a strong interplay between nonlinear solitons and the topologically protected edge states of the associated chiral-symmetric linear system. Nonlinearity can recover the degeneracy between two edge soliton states, albeit a chiral-symmetry breaking term. We also reveal the topological origin of in-gap solitons even when the associated linear system is in the topological trivial regime. These momentum-space and real-space results have clearly demonstrated new topological features induced by nonlinearity, indicating that topological physics in nonlinear lattice systems is far richer than previously thought.