Spin resolved topological bulk state in acoustics

TL;DR

This paper introduces a new topological acoustic phenomenon where energy is trapped in the bulk of a material, unlike typical edge-based topological effects.

Contribution

The paper presents a novel topological acoustic conductor with energy trapped in the bulk, not explained by existing quantum Hall effects.

Findings

Accidental triple degeneracies in phononic crystals produce a Dirac-like cone at the Γ point.

Spin angular momentum causes a geometric phase switch from 0 to 2π in a cyclic pattern.

Wave energy remains trapped in the bulk without preferential transport direction.

Abstract

Extremely rare topologically protected acoustic energy sink is presented in this article. Acoustic topological phenomena are generally described using quantum anomalous hall effects (QAHE), quantum valley hall effects (QVHE), and quantum spin hall effects (QSHE) where spin orbit coupling is predominant. Topological edge states are demonstrated by bulk-boundary distinction when the bulk is insulated. In this article topological acoustic conductor and its phenomena are theoretically demonstrated where the boundaries are insulated. This is exactly opposite to the behavior of a topological acoustic insulator. Phenomena presented in this article could not be explained by any of the trio Quantum Hall effects. To explain the phenomenon phononic crystals or PnCs were designed to obtain accidental triple degeneracies, resulting a Dirac-like cone at the Γ point (\documentclass[12pt]{minimal}
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\begin{document}$$\overrightarrow{k}=0$$\end{document}k→=0). The phenomenon is microarchitecture and microrotation field independent. Here time reversal symmetry or the space inversion symmetry is not broken, and the degenerated ‘Deaf band’ dominates the local dispersion with a syncline top band. This scenario results in continuously changing ‘up spin’ and ‘down spin’ of the wave energy in the media and remain trapped without specific preferential direction of wave transport. The spin was found to generate the spin angular momentum, causing the switching in geometric phase from \documentclass[12pt]{minimal}
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\begin{document}$$0-2\pi$$\end{document}0-2π in cyclic pattern, keeping the energy trapped inside the bulk media.

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