Local topological charges and gapless helical edge states on a dislocation of a 2D phononic elastic plate with Kekule distortion

Ting-Wei Liu; Fabio Semperlotti

doi:10.1117/12.2612349

18 April 2022 Local topological charges and gapless helical edge states on a dislocation of a 2D phononic elastic plate with Kekule distortion

Ting-Wei Liu, Fabio Semperlotti

Author Affiliations +

Proceedings Volume PC12048, Health Monitoring of Structural and Biological Systems XVI; PC120480D (2022) https://doi.org/10.1117/12.2612349
Event: SPIE Smart Structures + Nondestructive Evaluation, 2022, Long Beach, California, United States

Abstract

The Z2 invariant associated with quantum spin Hall topological insulators is connected to the unique property of fermionic systems whose wavefunction acquires a negative sign upon two consecutive applications of the time-reversal operator. However, this property is not acquired by the classical-wave systems. Instead, a combination of spatial and temporal symmetry is required to synthesize the Kramers degeneracy. In this study, we propose an elastic phononic plate engraved with a honeycomb lattice whose depth varies according to a Kekule pattern. The “local topological charge” can be defined based on the difference of integrated pseudospin-resolved Berry curvature profiles, as an alternative to the Z2 invariant. Such “local topological charge” is not a topological invariant in a rigorous sense, since it depends on the position of the reference frame. This condition also leads to the result that the same phononic structure can be in different topological phases based on different reference frames. It follows that edge states can exist on a dislocation interface connecting two pieces of the same phononic structure with relative shifting. Two pseudospin-polarized edge-state bands crossing at zero-k point (synthetic Kramers pair) are achieved without repulsion, hence indicating decoupling and robustness of the counter-propagating states.

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Ting-Wei Liu and Fabio Semperlotti "Local topological charges and gapless helical edge states on a dislocation of a 2D phononic elastic plate with Kekule distortion", Proc. SPIE PC12048, Health Monitoring of Structural and Biological Systems XVI, PC120480D (18 April 2022); https://doi.org/10.1117/12.2612349

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KEYWORDS

Dielectrics

Distortion

Acoustics

Interfaces

Magnetism

Quantum electronics

Wave propagation

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