Wave-packet transport in topological nonlinear dynamical systems is of broad interest. In nonlinear lattices, wave packets can self-localize into solitons that maintain their spatial profile during evolution, providing a natural setting to study transport beyond linear-wave physics.
A new study demonstrates quantized soliton pumping enabled by high-dimensional topology. Using a time-modulated lattice and its corresponding topolectrical circuits, the researchers observe two-dimensional soliton pumping whose displacement per driving cycle is determined by distinct-order Chern invariants, including the first and second Chern numbers.
In conventional one-dimensional linear pumps, quantized transport is typically characterized by a first Chern number. The present work extends this framework to a nonlinear setting and to high-dimensional topology, where higher-order invariants become relevant and can shape transport in multiple spatial directions.
The study further shows that the pumping behavior changes qualitatively when the nonlinearity and the band structure are tuned. In one regime, solitons display integer-quantized pumping, shifting by an integer number of unit cells per cycle. In another regime, the pumping becomes fractional-quantized, yielding a displacement that corresponds to a rational fraction of a lattice unit per cycle. The work also identifies trapped regimes at strong nonlinearity, where the soliton remains near its initial position over a driving cycle. In addition, the researchers observe anisotropic pumping, where the transport behavior differs along the two spatial directions, including mixed regimes with different quantization characteristics along different axes.
To validate these effects experimentally, the team implements the model using nonlinear, time-modulated topolectrical circuits. The results establish a circuit-based platform for exploring the interplay between high-dimensional topology and nonlinear wave transport. More broadly, they provide a route to study how distinct-order Chern invariants manifest in nonlinear dynamics, and they motivate future extensions to larger lattices and to other driven-wave platforms, including photonic and acoustic systems, where controlled transport of localized nonlinear excitations is of interest.
This work received support from the National Key R&D Program of China and the National Natural Science Foundation of China.
National Science Review
Experimental study