Topological phases have recently been realised in bosonic systems. The associated boundary modes between regions of distinct topology have been used to demonstrate robust waveguiding, protected from defects by the topology of the surrounding bulk. A related type of topologically protected state that is not propagating but is bound to a defect has not been demonstrated to date in a bosonic setting. Here we demonstrate numerically and experimentally that an acoustic mode can be topologically bound to a vortex fabricated in a two-dimensional, Kekulé-distorted triangular acoustic lattice. Such lattice realises an acoustic analogue of the Jackiw-Rossi mechanism that topologically binds a bound state in a p-wave superconductor vortex. The acoustic bound state is thus a bosonic analogue of Majorana bound state, where the two valleys replace particle and hole components. We numerically show that it is topologically protected against arbitrary symmetrypreserving local perturbations, and remains pinned to the Dirac frequency of the unperturbed lattice regardless of parameter variations. We demonstrate our prediction experimentally by 3D printing the vortex pattern in a plastic matrix and measuring the spectrum of the acoustic response of the device. Despite viscothermal losses, the measured topological resonance remains robust, with its frequency closely matching our simulations. arXiv:1910.01956v1 [cond-mat.mes-hall]
heavy masses, the work reported here provides a simple approach to construct low-cost structures with potential applications in aeronautic and astronautic industries for broadband vibration suppression at low frequencies.
A multiple scattering theory is applied to study the properties of flexural waves propagating in a plate with periodically structured N -beam resonators. Each resonator consists of a circular hole containing an inner disk connected to background plate with N rectangular beams. The Bloch theorem is employed to obtain the band structure of a two-dimensional lattice containing a single resonator per unit cell. Also, a numerical algorithm has been developed to get the transmittance through resonators slabs infinitely long in the direction perpendicular to the incident wave. For the numerical
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