Non-Newtonian Topological Mechanical Metamaterials Using Feedback Control.

We introduce a method to design topological mechanical metamaterials that are not constrained by Newtonian dynamics. Here, each unit cell in a mechanical lattice is subjected to active feedback forces that are processed through autonomous closed-loop controllers, pre-programmed to generate the desired local response in real-time. This approach enables the realization of topological mechanical systems that are hard or impossible to achieve otherwise. As an example, we focus on the quantum Haldane model, in which time reversal symmetry is broken in a two-band system via complex coupling terms. Using our method, we describe an active medium for acoustic waves, which implements the non-Newtonian response required to obtain the Haldane topological phase in a mechanical system. Our feedback-based approach is general and could be used to realize arbitrary lattice parameters, such as non-local or nonlinear couplings, time dependent potentials, non-Hermitian dynamics, and more. The application of this method could open a route to the study and discovery of new topological phases on a single, reprogrammable platform.