Method to Derive the Hamiltonian of Acoustic Topological Crystalline Insulators

Acoustic systems that are without limitations imposed by the Fermi level have been demonstrated as a significant platform for the exploration of fruitful topological phases. By surrounding the nontrivial domain with trivial "environment," the domain-wall topological states have been theoretically and experimentally demonstrated. In this work, based on the topological crystalline insulator with a kagome lattice, we rigorously derive the corresponding Hamiltonian from the traditional acoustics perspective, and exactly reveal the correspondences of the hoppings and on-site terms within acoustic systems. Crucially, these results directly indicate that instead of applying the trivial domain, the soft-boundary condition precisely corresponds to the theoretical models, which always require generalized chiral symmetry. These results may provide a platform to construct desired acoustic topological devices hosting desired topological phenomena for versatile applications.