A General Method to Design Acoustic Higher-Order Topological Insulators

Abstract

Acoustic systems that are without limitations imposed by the Fermi level have been demonstrated as 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 hopping and onsite 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 provide a general platform to construct desired acoustic topological devices hosting desired topological phenomena for versatile applications.

Robust zero-energy states in two-dimensional Su-Schrieffer-Heeger topological insulators

“…The side length of the cavity is s = 6 cm, and the radius of the tube is r = 0.5 cm. For the bulk lattices, the lengths of the intra-and inter-lattices tubes in the two directions are l w x = 15.8 cm, l w y = 2.7 cm, l v x = 4.7 cm and l v x = 0.3 cm, respectively; for the lattices at the boundaries, all the outermost tubes need a correction length of 0.85r [68]. The mass density of the air and the corresponding sound speed are ρ 0 = 1.29 kg/m 3 and c 0 = 343 m/s, respectively.…”

“…The corresponding hopping terms of the Hamiltonian can be calculated as w x = 2.56 × 10 5 , w y = 1.2 × 10 6 and β = 3, respectively, and the on-site terms can be obtained as ω 2 0 = w x + w y + v x + v y (see detailed derivation in Appendix B). Accordingly, the numerical and theoretical results of the bulk energy bands are shown in Further, we apply soft boundary condition to the outermost tubes of the finite structure [68,69], and the calculated energy band structures of the two ribbon-shaped superlattices consisting of 15 bulk lattices in the x-direction and the y-direction are presented in Figs. 6(a) and 6(b), respectively, which corresponds to the theoretical results shown in Figs.…”

“…We then introduce a Bloch wave function |u = [u 1 , u 2 , u 3 , u 4 ] T into the bulk lattice. Therefore, for the specific site,e.g., the 1-site, the flow of the wave component can be described as [68,69]…”