Tunable Acoustic Valley-Hall Edge States in Reconfigurable Phononic Elastic Waveguides

Abstract: This study investigates the occurrence of acoustic topological edge states in a 2D phononic elastic waveguide due to a phenomenon that is the acoustic analogue of the quantum valley Hall effect. We show that a topological transition takes place between two lattices having broken space inversion symmetry due to the application of a tunable strain field. This condition leads to the formation of gapless edge states at the domain walls, as further illustrated by the analysis of the bulk-edge correspondence and of the associated topological invariants. Although time reversal symmetry is still intact in these systems, the edge states are topologically protected when inter-valley mixing is either weak or negligible. Interestingly, topological edge states can also be triggered at the boundary of a single domain if boundary conditions are properly selected. We also show that the static modulation of the strain field allows tuning the response of the material between the different supported edge states.