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

Abstract

In this work we theoretically study the interface acoustic states of resonators on a thin plate with topologically protected and conventional designs. Topologically protected interface state is first analyzed by employing the conception of breaking inversion symmetry within the unit cell of a honeycomb lattice for cylindrical and spherical resonators; we further demonstrate the robustness of the wave propagation along a zig-zag path containing sharp corners, defect and disorder. The wave propagation ceases to be preserved if we increase the degree of disorder along the zig-zag path. In parallel, the conventional interface state is also designed and compared to the same situations. We found that the conventional interface state suffers back scattering in the zig-zag path while it can show a more confined wave transport in some cases. The presence of a defect along the propagation path scatters the conventional interface wave and in particular can prohibit a full propagation in presence of a localized state at the defect. If the zig-zag path is made disordered, the propagation of the conventional interface mode can be conserved at given frequencies for a low random degree and disappears for higher random degree as the interface bands become flat in dispersion and turn to localized states. Finally, we show that the immunity of the topologically protected design needs the interface to be surrounded by at least two hexagons of the phononic crystals on both sides, especially at the sharp corners in the zig-zag path, while the conventional design only needs one hexagon bulk media with the advantage of compact wave transport. This work puts a step forward for the interface states in micro-/nano-scale characterization and figures out the behaviors for both topologically protected and conventional interface states.

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Cited by in corpus (12)

• Actively controllable topological phase transition in phononic beam systems
• Gradient index phononic crystals and metamaterials
• Experimental demonstration of topological waveguiding in elastic plates with local resonators
• Geometrically navigating topological platonic modes around gentle and sharp bends
• Valley and pseudospin-valley topologically protected edge states in symmetric pillared phononic crystals
• System size dependent topological zero modes in coupled topolectrical chains
• Elastic Temporal Waveguiding
• Observations of symmetry induced topological mode steering in a reconfigurable elastic plate
• Polarization-dependent and Valley-protected Lamb Waves in Asymmetric Pillared Phononic Crystals
• Theoretical band-gap bounds and coupling sensitivity for a periodic medium with branching resonators
• Dispersion relations of generalized one-dimensional phononic crystals
• Edge modes for flexural waves in quasi-periodic linear arrays of scatterers