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

Abstract

Topological physics strongly relies on prototypical lattice model with particular symmetries. We report here on a theoretical and experimental work on acoustic waveguides that is directly mapped to the one-dimensional Su-Schrieffer-Heeger chiral model. Starting from the continuous two dimensional wave equation we use a combination of monomadal approximation and the condition of equal length tube segments to arrive at the wanted discrete equations. It is shown that open or closed boundary conditions topological leads automatically to the existence of 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 the 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.

arXiv comment10 pages, 11 figures. Slight modification of title, minor additions to the text

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Cited by in corpus (13)

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• Topological Phases of Tight-Binding Trimer Lattice in the BDI Symmetry Class
• Topologically invisible defects in chiral mirror lattices
• Ferromagnetism in armchair graphene nanoribbon heterostructures
• Exact mobility edges in quasiperiodic network models with slowly varying potentials
• Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend
• Coupled electric dipole model for a Su-Schrieffer-Heeger chain of optically resonant coreshell nanoparticles
• Topological edge states of the hexagonal linear chain
• Chiral solitary waves in a nonlinear topological insulator model
• Single $\pi$-flux hosting topological defect modes in bilayer acoustic metamaterials
• Embedding 1D BDI topological dynamics into continuous elastic plates