Topological band theory strongly relies on prototypical lattice models with particular symmetries. We report here on a theoretical and experimental work on acoustic waveguides that are directly mapped to the one-dimensional Su-Schrieffer-Heeger model. Starting from the continuous two-dimensional wave equation, we use a combination of monomode approximation and the condition of equal-length tube segments to arrive at the wanted chiral symmetric discrete equations. It is shown that open or closed boundary conditions lead automatically to the existence of topological edge modes. We illustrate by graphical construction how the edge modes appear naturally owing to a quarter-wavelength condition and the conservation of flux. Furthermore, the transparent chirality of our system, which is ensured by simple geometrical constraints allows us to study chiral disorder numerically and experimentally. Our experimental results in the audible regime demonstrate the predicted robustness of the topological edge modes.

中文翻译：

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声学 Su-Schrieffer-Heeger 点阵：将声波导管直接映射到 Su-Schrieffer-Heeger 模型

拓扑带理论强烈依赖于具有特定对称性的原型晶格模型。我们在此报告直接映射到一维 Su-Schrieffer-Heeger 模型的声波导管的理论和实验工作。从连续二维波动方程开始，我们结合使用单模近似和等长管段条件来得到所需的手征对称离散方程。结果表明，开放或封闭边界条件自动导致拓扑边缘模式的存在。我们通过图形构造说明边缘模式如何由于四分之一波长条件和通量守恒而自然出现。此外，我们系统的透明手性，这是由简单的几何约束确保的，这使我们能够通过数值和实验来研究手性无序。我们在可听范围内的实验结果证明了拓扑边缘模式的预测鲁棒性。