Quadrature skyrmions in two-dimensionally arrayed parametric resonators

Skyrmions are topological solitons in two-dimensional systems and have been observed in various physical systems. Generating and controlling skyrmions in artificial resonator arrays lead to novel acoustic, photonic, and electric devices, but it is a challenge to implement a vector variable with the chiral exchange interaction. Here, we propose to use quadrature variables, where their parametric coupling enables skyrmions to be stabilized. A finite-element simulation indicates that a acoustic skyrmion would exist in a realistic structure consisting of a piezoelectric membrane array.