Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to the Su-Schrieffer-Heeger model

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.