  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.
