The Berry phase generally plays a key role in characterizing the topological phase for quantum and classic systems. However, topological edge states in a two-dimensional acoustic system are generally characterized by nonzero Berry curvature. Here we achieve the topological phase transition characterized by zero Berry curvature, based on the phononic crystal composed of 8-metaatomic composite metamolecules. We demonstrate that the phase transition can be induced through either modulating the intervals between the adjacent metaatoms or changing their sizes. The nontrivial Zak phase ensures the existence of the acoustic topological edge states, confining sound waves along the boundaries of finite sonic crystal rather than transmitting along the interface between the two structures possessing opposite topological phases. Furthermore, the multiple topological phase transitions are simply realized thanks to the two limbic metaatoms introduced. Although the eigenfrequencies of topological edge states, which appear in the partial band gap, overlap with the bulk states, we still numerically observe the topological edge states selectively through modulating the wavenumber in real space. The proposed acoustic topological insulator may have potential applications in acoustic waveguiding and isolating.

中文翻译：

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蜂窝晶格上Zak相启发的声学拓扑边缘状态

Berry相通常在表征量子和经典系统的拓扑相中起关键作用。然而，二维声学系统中的拓扑边缘状态通常以非零贝里曲率为特征。在此，我们基于由8元原子复合超分子组成的声子晶体，实现了零贝里曲率为特征的拓扑相变。我们证明相变可以通过调节相邻的原子之间的间隔或改变它们的大小来诱导。非平凡的Zak相确保存在声拓扑边缘状态，将声波限制在有限的声波晶体边界上，而不是沿着具有相反拓扑相的两个结构之间的界面传输。此外，由于引入了两个边缘隐喻，多个拓扑相变得以简单实现。尽管出现在局部带隙中的拓扑边缘态的特征频率与体态重叠，但我们仍然通过调制实际空间中的波数来选择性地观察拓扑边缘态的数值。所提出的声学拓扑绝缘体在声学波导和隔离中可能具有潜在的应用。