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

In this work, we investigate some aspects of an acoustic analog of the two-dimensional Su-Schrieffer-Heeger model. The system is composed of alternating cross-sectional 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 the consequences of this high reflectivity on finite networks. Globally, it appears that each straight part of the edges, separated by corners or defects, hosts localized edge modes isolated from their neighborhood.