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.
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