Breakdown of quantization in nonlinear Thouless pumping

TL;DR

This paper investigates how nonlinear effects influence quantized soliton transport in Thouless pumps, revealing a critical nonlinearity threshold where quantization breaks down due to loop structures in nonlinear topological bands.

Contribution

It uncovers the intermediate nonlinearity regime where quantized pumping fails, linking it to loop structures in nonlinear topological bands, a previously unexplored aspect.

Findings

Quantized pumping persists at weak nonlinearity

Pumping breaks down at a critical nonlinearity strength

Loop structures in nonlinear bands cause quantization failure

Abstract

The dynamics of solitons driven in a nonlinear Thouless pump and its connection with the system's topology were recently explored for both weak and strong nonlinear strength. This work uncovers the fate of nonlinear Thouless pumping in the regime of intermediate nonlinearity, thus establishing a fascinating crossover from the observation of nonzero and quantized pumping at weak nonlinearity to zero pumping at strong nonlinearity. We identify the presence of critical nonlinearity strength at which quantized pumping of solitons breaks down regardless of the protocol time scale. Such an obstruction to pumping quantization is attributed to the presence of loop structures of nonlinear topological bands. Our results not only unveil a missing piece of physics in nonlinear Thouless pumping, but also provide a means to detect loop structures of nonlinear systems investigated in real space.