Anomalous quantized nonlinear Thouless pumping

TL;DR

This paper uncovers anomalous and quantized nonlinear Thouless pumping of solitons, revealing behaviors that deviate from topological predictions and introducing a general theory for these phenomena.

Contribution

It demonstrates the existence of anomalous and quantized nonlinear Thouless pumps, and develops a theory explaining soliton transitions between Wannier functions due to nonlinearity.

Findings

Discovery of anomalous soliton displacement exceeding Chern number predictions.

Identification of nonlinearity-induced integer quantized soliton pumping.

Development of a general theory for soliton transitions between Wannier functions.

Abstract

It has recently been theoretically predicted and experimentally observed that a soliton resulting from nonlinearity can be pumped across an integer or fractional number of unit cells as a system parameter is slowly varied over a pump period. Nonlinear Thouless pumping is now understood as the flow of instantaneous Wannier functions, ruling out the possibility of pumping a soliton across a nonzero number of unit cells over one cycle when a corresponding Wannier function does not exhibit any flow, i.e., when the corresponding Bloch band that the soliton bifurcates from is topologically trivial. Here we surprisingly find an anomalous nonlinear Thouless pump where the displacement of a soliton over one cycle differs from the Chern number of the Bloch band from which the soliton comes. We develop a general theory showing that this anomalous behavior arises from a transition of a soliton between different Wannier functions by passing through an intersite-soliton (or dipole-soliton) state. Furthermore, we find a nonlinearity-induced integer quantized Thouless pump of a soliton, allowing a soliton to travel across one unit cell during a pump period, even when the corresponding band is topologically trivial. Our results open the door to studying nonlinearity-induced Thouless pumping of solitons.