Acoustic Topological Metamaterials of Large Winding Number

Long-range couplings beyond the nearest neighbors can trigger exotic topological phases in metamaterials but have been overlooked in many topological models. The authors study the effect of the long-range couplings on the topological properties, and demonstrate that a Su-Schrieffer-Heeger model including the third nearest coupling, implemented by acoustic metamaterials, can lead to topological phases of large winding numbers. The experimental results show additional topological end states and rotonlike dispersions for sound waves, highlighting the potential of these long-range metamaterials in creating rich topological features.