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Unlike Topological edge states where bulk-boundary distinction is achieved by insulating the bulk state acoustic, topological phenomena could be explored inside the Bulk exploiting the acoustic spin angular momentum. Here is this presentation we show that despite acoustic phonons are boson like spin zero particles, a topological bulk state is emerged at a specific Dirac state due to intrinsic acoustic spin quantized by +1/2 and -1/2. Time resolved analysis show that the spin vector essentially pass through a manifold causing an accumulation of geometric phase and prevail the topological energy sink.
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Sourav Banerjee, Mustahseen M. Indaleeb, "Acoustic spin and topological bulk state in metamaterials," Proc. SPIE 12951, Health Monitoring of Structural and Biological Systems XVIII, 129510R (10 May 2024); https://doi.org/10.1117/12.3016464