Topological transmission in Suzuki phase sonic crystals

Abstract: This work reports topological extraordinary properties of sound transmission through topological states in sonic crystals denominated Suzuki phase, consisting of a rectangular lattice of vacancies created in a triangular lattice. These low-symmetry crystals exhibit unique properties due to the embedded lattice of vacancies. A generalized folding method explains the band structure and the quasi-type-II Dirac point in the Suzuki phase, which is related to the underlying triangular lattice. In analogy to the acoustic valley Hall effect, the Suzuki phase contains three types of topological edge states on the four possible interfaces separating two Suzuki phase crystals with distinct topological phases. The edge states have defined symmetries with inherent directionality, which affect the topological sound transmission and are different from chirality, valley vorticity or helicity. Particularly, the existence of topological deaf bands is here reported. The propagation of topological eigenmodes on the same interface is also different, which is quantified using the acoustic Shannon entropy, making the topological transport dependent on the frequency of the edge states. Based on the abundant topological edge states of Suzuki phase crystals, a multifunctional device with acoustic diodes, multi-channel transmission, and selective acoustic transmission can be designed. Numerical simulations and measurements demonstrate the topological transmission. Our work extends the research platform of acoustic topological states to lattices with low symmetry, which opens new avenues for enriching topological states with broad engineering applications.