Non-reciprocal topological solitons in active metamaterials.

Abstract

From protein motifs¹ to black holes², topological solitons are pervasive nonlinear excitations that are robust and can be driven by external fields³. So far, existing driving mechanisms all accelerate solitons and antisolitons in opposite directions^3,4. Here we introduce a local driving mechanism for solitons that accelerates both solitons and antisolitons in the same direction instead: non-reciprocal driving. To realize this mechanism, we construct an active mechanical metamaterial consisting of non-reciprocally coupled oscillators^5-8 subject to a bistable potential^9-14. We find that such nonlinearity coaxes non-reciprocal excitations-so-called non-Hermitian skin waves^5-8,15-22, which are typically unstable-into robust one-way (anti)solitons. We harness such non-reciprocal topological solitons by constructing an active waveguide capable of transmitting and filtering unidirectional information. Finally, we illustrate this mechanism in another class of metamaterials that shows the breaking of 'supersymmetry'^23,24 causing only antisolitons to be driven. Our observations and models demonstrate a subtle interplay between non-reciprocity and topological solitons, whereby solitons create their own driving force by locally straining the material. Beyond the scope of our study, non-reciprocal solitons might provide an efficient driving mechanism for robotic locomotion²⁵ and could emerge in other settings, for example, quantum mechanics^26,27, optics^28-30 and soft matter³¹.