Non-reciprocity and roton dispersion in non-local piezoelectric metamaterials

Abstract

This talk will investigate the behavior of piezoelectric acoustic metamaterials with non-local circuit interactions, demonstrating that unbalanced, directional interactions yield non-reciprocal, roton-type dispersion behavior. The coupling between mechanical and electrical domains introduces additional dispersion branches whose periodicity is determined by the non-local circuit spacing. When these branches intersect the original dispersion curves of the system, non-reciprocal band gaps are opened in the mechanical domain. Furthermore, although the system is non-Hermitian, the appropriate use of local electrical resistance ensures that all dispersion branches are stable. This offers a practical alternative to realize non-reciprocal propagation that does not rely on nonlinearity or time-varying components, but instead on well-established directional electrical circuits. Numerical simulations show that the strength and spacing of the non-local interactions determines the frequency of non-reciprocity, providing a straightforward mechanism to program the dispersion properties of the system. The talk will conclude with preliminary experimental results and a discussion of system stability.