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

TL;DR

This paper explores an acoustic analogue of the 2D Su-Schrieffer-Heeger model, revealing perfect reflection of edge waves at corners and the emergence of localized corner modes in finite networks.

Contribution

It introduces a scattering theory for topological acoustic edge waves and demonstrates perfect reflection at corners, leading to new methods for creating and understanding corner modes.

Findings

Edge waves undergo perfect reflection at corners.

High reflection occurs for various edge defects.

Localized edge and corner modes are identified in finite networks.

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.