Robustness of topological corner modes against disorder and application to acoustic networks

Abstract

We study the two-dimensional extension of the Su-Schrieffer-Heeger model in its higher order topological insulator phase, which is known to host corner states. Using the separability of the model into a product of one-dimensional Su-Schrieffer-Heeger chains, we analytically describe the eigen-modes, and specifically the zero-energy level, which includes states localized in corners. We then consider networks with disordered hopping coefficients that preserve the chiral (sublattice) symmetry of the model. We show that the corner mode and its localization properties are robust against disorder if the hopping coefficients have a vanishing flux on appropriately defined super plaquettes. We then show how this model with disorder can be realised using an acoustic network of air channels, and confirm the presence and robustness of corner modes.

arXiv comment18 pages, 13 figures. V2: small clarifications added, subsections of section III re-ordered, color scales added on figures, new appendix B-2

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Cited by in corpus (14)

• Fast and robust quantum state transfer via a topological chain
• Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to Su-Schrieffer-Heeger model
• Quantized Topological Anderson-Thouless Pump
• Optimization and robustness of topological corner state in second-order topological photonic crystal
• Hidden symmetries in acoustic wave systems
• Arbitrary synthetic dimensions via multi-boson dynamics on a one-dimensional lattice
• Topological two-dimensional Su-Schrieffer-Heeger analogue acoustic networks: Total reflection at corners and corner induced modes
• Subwavelength Su-Schrieffer-Heeger topological modes in acoustic waveguides
• Topologically invisible defects in chiral mirror lattices
• Topological phase transition in disordered elastic quantum spin Hall system
• Remote control of spin polarization of topological corner states
• Edge States with Hidden Topology in Spinner Lattices
• Characterization of the 2D Su-Schrieffer-Heeger Model with Second-Nearest-Neighbor Interactions
• Single $\pi$-flux hosting topological defect modes in bilayer acoustic metamaterials