Tunable topological bandgaps and frequencies in a pre-stressed soft phononic crystal

Abstract

Topological insulators (TIs) have recently received significant attention due to the promise of lossless transport of various types of energy. Despite this interest, one outstanding issue is that the topological bandgap and the frequencies that are topologically permitted are typically fixed once the topological structure has been designed and fabricated. Therefore, an open and unresolved question concerns the ability to actively tune both the bandgap magnitude, as well as the frequencies, for which the energy is topologically protected. In this work, we report a mechanically tunable phononic TI using an acoustic analog of the quantum valley Hall effect. We propose a phononic crystal comprised of a soft, hyperelastic material where the phononic band structure is modulated through large deformation of the structure. In doing so, space-inversion symmetry can be broken, which leads to a phase transition between two topologically-contrasted states and the emergence of topologically-protected interface modes according to bulk-edge correspondence. We further demonstrate the robustness of this topological protection of the edge state along the interface, which demonstrates that mechanical deformation can be used to effectively tailor and tune the topological properties of elastic structures.