Quantized soliton pumping governed by high-dimensional Chern invariants.

Area of Science:

• Topological physics
• Non-linear dynamics
• Condensed matter physics

Background:

• Non-linear topological pumping describes quantized solitary wave transport in driven systems.
• Existing research primarily focuses on first Chern number-governed soliton transport.
• The interplay between high-dimensional band topology and soliton pumping is largely unexplored.

Purpose of the Study:

• To theoretically establish and experimentally demonstrate soliton topological pumping governed by both first and second Chern numbers.
• To investigate the influence of non-linear strength on soliton pumping phenomena, including phase transitions.
• To explore anisotropic soliton pumping with engineered linear band structures.

Main Methods:

• Development of a theoretical framework for multi-dimensional topological pumping.
• Experimental implementation using non-linear time-modulated topolectrical circuits.
• Analysis of phase transitions and anisotropic transport through system parameter modulation.

Main Results:

• Demonstration of soliton topological pumping governed by first and second Chern numbers.
• Observation of phase transitions into integer-quantized, fractional-quantized, and soliton trapping states.
• Experimental realization of anisotropic soliton pumping with distinct integer and fractional characteristics along orthogonal axes.

Conclusions:

• This work bridges topological physics and non-linear dynamics by exploring high-dimensional band topology in soliton pumping.
• A scalable experimental platform for advanced non-linear topological phases is established.
• The findings offer broad applications for systems at the intersection of topological matter and non-linear wave physics.