Acoustic flatbands in phononic crystal defect lattices

In this paper, we investigate the acoustic flatbands (FBs) in phononic crystal (PnC) defect lattices. The defects are introduced into a PnC composed of periodic rigid rods air background. Since energy is highly confined inside defects, interaction between can be described by tight-binding model. We construct two bipartite lattices, namely, stub and Lieb FBs observed for both Moreover, protected chiral symmetry. That is, preserved even though hopping strengths neighboring perturbed. proposed lattices provide feasible platform study FB systems topological insulators.