Abstract
In this work, we study the propagation of sound waves in a honeycomb waveguide network loaded with Helmholtz resonators (HRs). By using a plane wave approximation in each waveguide we obtain a first-principle modeling of the network, which is an exact mapping to the graphene tight-binding Hamiltonian. We show that additional Dirac points appear in the band diagram when HRs are introduced at the network nodes. It allows to break the inversion (sub-lattice) symmetry by tuning the resonators, leading to the appearence of edge modes that reflect the configuration of the zigzag boundaries. Besides, the dimerization of the resonators also permits the formation of interface modes located in the band gap, and these modes are found to be robust against symmetry preserving defects. Our results and the proposed networks reveal the additional degree of freedom bestowed by the local resonance in tuning the properties of not only acoustical graphene-like structures but also of more complex systems.
Highlights
Over the last years, in the context of metamaterials, a plethora of sophisticated acoustic structures exhibiting unusual wave properties have been theoretically proposed and experimentally studied
Our structure allows us to independently tune both the resonance frequency of Helmholtz resonators (HRs) and the Dirac point frequency. We use this flexibility of our design by setting these two frequencies at the same point and we study the combined effect of the resonance and of the symmetry breaking
More branches for edge/interface modes appear in the gaps. As it has been studied in the analogs of quantum valley Hall (QVH) system [5, 7, 23, 31], the interface modes in the full gap appearing by breaking the Dirac cone at the K point are robust in a sense that they can travel through corners of 120◦ with respect to its original direction of propagation
Summary
Li-Yang Zheng , Vassos Achilleos, Ze-Guo Chen, Olivier Richoux, Georgios Theocharis, Ying Wu3, Jun Mei , Simon Felix, Vincent Tournat and Vincent Pagneux.
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