Symmetry breaking creates electro-momentum coupling in piezoelectric metamaterials

The momentum of deformable materials is coupled to their velocity. Here, we show that in piezoelectric composites which deform under electric fields, the momentum can also be coupled to the electric stimulus by a designed macroscopic property. To this end, we assemble these materials in a pattern with asymmetric microstructure, develop a theory to calculate the relations between the macroscopic fields, and propose a realizable system that exhibits this coupling. In addition to its fundamental importance, our design thus forms a metamaterial for mechanical wave control, as traversing waves are governed by the balance of momentum, and, in turn, the engineered electro-momentum coupling. While introduced for piezoelectric materials, our analysis immediately applies to piezomagnetic materials, owing to the mathematical equivalence between their governing equations, and we expect our framework to benefit other types of elastic media that respond to non-mechanical stimuli.