Topological phononic states of underwater sound based on coupled ring resonators

We report a design of topological phononic states for underwater sound using arrays of acoustic coupled ring resonators. In each individual ring resonator, two degenerate acoustic modes, corresponding to clockwise and counter-clockwise propagation, are treated as opposite pseudospins. The gapless edge states arise in the bandgap resulting in protected pseudospin-dependent sound transportation, which is a phononic analogue of the quantum spin Hall effect. We also investigate the robustness of the topological sound state, suggesting that the observed pseudospin-dependent sound transportation remains unless the introduced defects facilitate coupling between the clockwise and counter-clockwise modes (in other words, the original mode degeneracy is broken). The topological engineering of sound transportation will certainly promise unique design for next generation of acoustic devices in sound guiding and switching, especially for underwater acoustic devices.