Origin and tuning of bandgap in chiral phononic crystals

The wave equation revealing the wave propagation in chiral phononic crystals, established through force equilibrium law, conceals the underlying physical information, such as the essence of the motion coupling and the inertial amplification effect. This has led to a controversy over the bandgap mechanism. In this article, we theoretically unveil the reason for this controversy, and put forward an alternative approach from wave behavior to formulate the wave equation, offering an alternative pathway to articulate the bandgap physics directly. Based on the physics revealed by our theory method, we identify the obstacles in coupled acoustic and optic branches to widen and lower the bandgap. Then we introduce an approach based on spherical hinges to decrease the barriers, for customizing the bandgap frequency and width. Finally, we validate our proposal through numerical simulation and experimental demonstration.