Obstructed atomic limits and boundary states in a mikado of SSH chains

In this presentation, I consider a two-dimensional amorphous system made of randomly distributed intertwined SSH chains coupled to each other. We show that, similarly to isolated SSH chains, it has two topologically distinct electronic configurations, that when interfaced with each other, result in edge modes at the interface. By using our recently developed local symmetry indicators for amorphous systems we determine which symmetries protect the boundary states.

We generalize this model to three dimensions and discuss experimental realizations on realistic platforms.