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This study investigates the occurrence of acoustic topological edge states ina 2D phononic elastic waveguide due to a phenomenon that is the acousticanalogue of the quantum valley Hall effect. We show that a topologicaltransition takes place between two lattices having broken space inversionsymmetry due to the application of a tunable strain field. This condition leadsto the formation of gapless edge states at the domain walls, as furtherillustrated by the analysis of the bulk-edge correspondence and of theassociated topological invariants. Although time reversal symmetry is stillintact in these systems, the edge states are topologically protected wheninter-valley mixing is either weak or negligible. Interestingly, topologicaledge states can also be triggered at the boundary of a single domain ifboundary conditions are properly selected. We also show that the staticmodulation of the strain field allows tuning the response of the materialbetween the different supported edge states.

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