Nonlinearity-Induced Thouless Pumping in Quasiperiodic Lattices

TL;DR

This paper demonstrates nonlinear topological Thouless pumping of gap solitons in quasiperiodic lattices, revealing controllable switching among topological pumping, drifting, and localization driven by nonlinearity and lattice scaling.

Contribution

It uncovers a novel mechanism for nonlinearity-induced topological behavior in quasiperiodic lattice potentials, extending Thouless pumping to nonlinear regimes.

Findings

Gap solitons can adiabatically occupy a single topological band in quasiperiodic lattices.

Lattice perturbations can disrupt quantized pumping, leading to drifting regimes.

Tuning nonlinearity or lattice scaling enables switching among topological pumping, drifting, and localization.

Abstract

Nonlinear Thouless pumping has been established in periodic lattices; its counterpart in quasiperiodic lattices remains unexplored. Here, we show a nonlinear topological pumping of gap solitons in quasiperiodic lattices where the local nonlinear self-consistent potentials lead to a lattice potential reconstruction; as a result, an emergent topological structure induced by this local reconstruction governs the dynamics of the gap solitons. This enables solitons to adiabatically occupy a single topological band, realizing quasi-quantized Thouless pumping. In addition, the intrinsic lattice perturbations disrupt this band occupation, which drives solitons into a non-quantized drifting regime. However, even in this regime, we also find that the soliton transport is constrained by the topological properties of a critical rational approximant. Tuning nonlinearity or lattice scaling reveals a controllable switching among topological pumping, drifting, and localization. Our work uncovers a mechanism for nonlinearity-induced topological behavior in complex lattice potentials.