  The Su-Schrieffer-Heeger (SSH) model on a two-dimensional square lattice has
been considered as a significant platform for studying topological multipole
insulators. However, due to the highly-degenerate bulk energy bands protected
by $ C_{4v} $ and chiral symmetry, the discussion of the zero-energy
topological corner states and the corresponding physical realization have been
rarely presented. In this work, by tuning the hopping terms to break $ C_{4v} $
symmetry down to $ C_{2v} $ symmetry but with the topological phase invariant,
we show that the degeneracies can be removed and a complete band gap can be
opened, which provides robust protection for the spectrally isolated
zero-energy corner states. Meanwhile, we propose a rigorous acoustic
crystalline insulator and therefore these states can be observed directly. Our
work reveals the topological properties of the robust zero-energy states, and
provides a new way to explore novel topological phenomena.
