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

TL;DR

This paper investigates the robustness of topological corner modes in a 2D higher-order topological insulator model, demonstrating their stability against disorder and implementing the concept in acoustic networks.

Contribution

It analytically describes corner states in a 2D SSH model, analyzes their robustness under disorder, and experimentally demonstrates these effects in acoustic networks.

Findings

Corner modes are robust against certain types of disorder.

Disorder preserving chiral symmetry maintains corner mode localization.

Experimental acoustic networks confirm theoretical predictions.

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.