The interface state in two-dimensional (2D) sonic crystals (SCs) was obtained based on trying or cutting approach, which greatly limits its practical applications. In this paper, we theoretically demonstrate that one category of interface states can deterministically exist at the boundary of two square-lattice SCs due to the geometric phase transitions of bulk bands. First, we derive a tight-binding formalism for acoustic waves and introduce it into the 2D case. Furthermore, the extended 2D Zak phase is employed to characterize the topological phase transitions of bulk bands. Moreover, the topological interface states can be deterministically found in the nontrivial bandgap. Finally, two kinds of SCs with the [Formula: see text] symmetry closely resembling the 2D Su–Schrieffer–Heeger (SSH) model are proposed to realize the deterministic interface states. We find that tuning the strength of intermolecular coupling by contacting or expanding the scatterers can effectively induce the bulk band inversion between the trivial and nontrivial crystals. The presence of acoustic interface states for both cases is further demonstrated. These deterministic interface states in 2D acoustic systems will be a great candidate for future waveguide applications.

中文翻译：

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二维声学系统中的确定性界面模式

二维（2D）声波晶体（SCs）的界面态是基于尝试或切割方法获得的，这极大地限制了其实际应用。在本文中，我们从理论上证明，由于体带的几何相变，一类界面态可以确定性地存在于两个方形晶格 SC 的边界。首先，我们推导出声波的紧束缚形式，并将其引入二维情况。此外，扩展的 2D Zak 相用于表征体带的拓扑相变。此外，拓扑界面态可以确定地在非平凡带隙中找到。最后，两种带有 [公式：见文本] 提出了与 2D Su-Schrieffer-Heeger (SSH) 模型非常相似的对称性来实现确定性界面状态。我们发现通过接触或扩展散射体来调整分子间耦合的强度可以有效地诱导平凡晶体和非平凡晶体之间的体带反转。进一步证明了两种情况下声学界面态的存在。二维声学系统中的这些确定性界面态将成为未来波导应用的理想选择。