Topological two-dimensional Su-Schrieffer-Heeger analogue acoustic networks: Total reflection at corners and corner induced modes

Abstract

In this work, we investigate some aspects of an acoustic analogue of the two-dimensional Su-Schrieffer-Heeger model. The system is composed of alternating cross-section tubes connected in a square network, which in the limit of narrow tubes is described by a discrete model coinciding with the two-dimensional Su-Schrieffer-Heeger model. This model is known to host topological edge waves, and we develop a scattering theory to analyze how these waves scatter on edge structure changes. We show that these edge waves undergo a perfect reflection when scattering on a corner, incidentally leading to a new way of constructing corner modes. It is shown that reflection is high for a broad class of edge changes such as steps or defects. We then study consequences of this high reflectivity on finite networks. Globally, it appears that each straight part of edges, separated by corners or defects, hosts localized edge modes isolated from their neighbourhood.

arXiv comment19+5 pages, 15 figures. V2: small extra remarks added

References in corpus (22)

• Topological Insulators
• Double-slit photoelectron interference in strong-field ionization of the neon dimer
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Photonics
• Topological Crystalline Insulators
• Acoustic topological insulator and robust one-way sound transport
• Floquet Topological Insulators for Sound
• Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems
• The Zak phase and the existence of edge states in graphene
• Second-order photonic topological insulator with corner states
• Novel Topological Phase with Zero Berry Curvature
• Photonic crystal nanocavity based on a topological corner state
• Observation of a higher-order topological bound state in the continuum
• Bound states in the continuum of higher-order topological insulators
• Dimensional Crossover of Topological Edge States in Su-Schrieffer-Heeger Model
• On the spectra of carbon nano-structures
• Topological Properties of Electrons in Honeycomb Lattice with Kekulé Hopping Textures
• Observation of edge waves in a two-dimensional Su-Schrieffer-Heeger acoustic network
• Of Bulk and Boundaries: Generalized Transfer Matrices for Tight-Binding Models
• Large Photonic Band Gaps in Certain Periodic and Quasi-Periodic Networks in two and three dimensions
• Robustness of topological corner modes against disorder and application to acoustic networks
• Slow sound laser in lined flow ducts

Cited by in corpus (9)

• Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to Su-Schrieffer-Heeger model
• Hidden symmetries in acoustic wave systems
• Subwavelength Su-Schrieffer-Heeger topological modes in acoustic waveguides
• Topology of multiple cross-linked Su-Schrieffer-Heeger chains
• Topologically invisible defects in chiral mirror lattices
• Higher-order topology protected by latent crystalline symmetries
• Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend
• Edge States with Hidden Topology in Spinner Lattices
• Single $\pi$-flux hosting topological defect modes in bilayer acoustic metamaterials