Feedback-based Mechanical Haldane Model


  Lea Beilkin  ,  Yair Shokef  ,  Roni Ilan  ,  Yoav Lahini  
Tel Aviv University

We demonstrate an analogy of the Quantum Hall Effect that is based on the exact Haldane model in a mechanical metamaterial. As the Haldane model employs complex valued hopping to break time reversal symmetry in a quantum system, generating analogous directional interactions in a mechanical lattice is a challenge. An even greater challenge, however, is to generate the interactions and the associated chiral modes in the most basic two- band system, which implies out-of-plane degrees of freedom only, without any actual in-plane rotation. We employ a feedback-based design by subjecting a conventional spring-mass lattice to external mechanical forces, operated in closed loop. The forces depend on the lattice response that is measured in real-time and processed through an electronic controller. The feedback mechanism shapes the dynamical response of the system and generates, via the control program alone, the interactions defining the Haldane model. The resulting metamaterial supports a topologically protected, strictly unidirectional, mechanical wave propagation along its edges. This feedback-based approach opens a new direction of programmed metamaterials that can generate physical properties upon request, in particular those initially considered unachievable in classical mechanical systems.