Non-singular and singular flat bands in tunable phononic metamaterials
Non-singular and singular flat bands in tunable phononic metamaterials
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DOI：
10.1103/physrevresearch.5.023036
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发表时间：
2022-11
影响因子：
4.2
通讯作者：
Pragalv Karki;J. Paulose
中科院分区：
文献类型：
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作者：
Pragalv Karki;J. Paulose
无色散平坦带可以分为两种类型：（1）非奇异平坦带，其本征模完全由紧凑的局域态表征;（2）奇异平坦带，其布洛赫本征函数在与相邻色散带的带接触点处具有不连续性，从而需要额外的扩展态来跨越其本征模空间。在这项研究中，我们设计和数值演示了二维薄板声学超材料，其中可以实现这两种可调的平坦频带。非奇异的平带是通过微调三角形和蜂窝晶格的平板谐振器的整体张力和弯曲刚度的比率来实现的。在可果美晶格中，由于晶格的几何结构，出现了一个奇异的平带，通过调节板的张力，可以使它退化为两个额外的平带。连续薄板系统的离散模型揭示了确定两种类型的平坦带存在的几何和力学因素的相互作用。kagome晶格平带的奇异性是通过一个称为希尔伯特-施密特距离的度量建立的，该距离是在无限接近二次带接触点的一对本征态之间计算的。我们还模拟了一个强大的边界模式所产生的奇异平坦带和保护的有限系统中的实空间拓扑结构的声学表现。我们的理论和计算研究建立了一个框架，探索平带物理在一个可调的经典系统，并设计具有潜在有用的声音操纵能力的声学超材料。
Dispersionless flat bands can be classified into two types: (1) non-singular flat bands whose eigenmodes are completely characterized by compact localized states; and (2) singular flat bands that have a discontinuity in their Bloch eigenfunctions at a band touching point with an adjacent dispersive band, thereby requiring additional extended states to span their eigenmode space. In this study, we design and numerically demonstrate two-dimensional thin-plate acoustic metamaterials in which tunable flat bands of both kinds can be achieved. Non-singular flat bands are achieved by fine-tuning the ratio of the global tension and the bending stiffness in triangular and honeycomb lattices of plate resonators. A singular flat band arises in a kagome lattice due to the underlying lattice geometry, which can be made degenerate with two additional flat bands by tuning the plate tension. A discrete model of the continuum thin-plate system reveals the interplay of geometric and mechanical factors in determining the existence of flat bands of both types. The singular nature of the kagome lattice flat band is established via a metric called the Hilbert-Schmidt distance calculated between a pair of eigenstates infinitesimally close to the quadratic band touching point. We also simulate an acoustic manifestation of a robust boundary mode arising from the singular flat band and protected by real-space topology in a finite system. Our theoretical and computational study establishes a framework for exploring flat-band physics in a tunable classical system, and for designing acoustic metamaterials with potentially useful sound manipulation capabilities.