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In this work we theoretically study the interface acoustic states ofresonators on a thin plate with topologically protected and conventionaldesigns. Topologically protected interface state is first analyzed by employingthe conception of breaking inversion symmetry within the unit cell of ahoneycomb lattice for cylindrical and spherical resonators; we furtherdemonstrate the robustness of the wave propagation along a zig-zag pathcontaining sharp corners, defect and disorder. The wave propagation ceases tobe preserved if we increase the degree of disorder along the zig-zag path. Inparallel, the conventional interface state is also designed and compared to thesame situations. We found that the conventional interface state suffers backscattering in the zig-zag path while it can show a more confined wave transportin some cases. The presence of a defect along the propagation path scatters theconventional interface wave and in particular can prohibit a full propagationin presence of a localized state at the defect. If the zig-zag path is madedisordered, the propagation of the conventional interface mode can be conservedat given frequencies for a low random degree and disappears for higher randomdegree as the interface bands become flat in dispersion and turn to localizedstates. Finally, we show that the immunity of the topologically protecteddesign needs the interface to be surrounded by at least two hexagons of thephononic crystals on both sides, especially at the sharp corners in the zig-zagpath, while the conventional design only needs one hexagon bulk media with theadvantage of compact wave transport. This work puts a step forward for theinterface states in micro-/nano-scale characterization and figures out thebehaviors for both topologically protected and conventional interface states.

Analysis of the Robustness of Conventional and Topologically Protected Edge States in Phononic Crystal Plates