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This work reports topological extraordinary properties of sound transmissionthrough topological states in sonic crystals denominated Suzuki phase,consisting of a rectangular lattice of vacancies created in a triangularlattice. These low-symmetry crystals exhibit unique properties due to theembedded lattice of vacancies. A generalized folding method explains the bandstructure and the quasi-type-II Dirac point in the Suzuki phase, which isrelated to the underlying triangular lattice. In analogy to the acoustic valleyHall effect, the Suzuki phase contains three types of topological edge stateson the four possible interfaces separating two Suzuki phase crystals withdistinct topological phases. The edge states have defined symmetries withinherent directionality, which affect the topological sound transmission andare different from chirality, valley vorticity or helicity. Particularly, theexistence of topological deaf bands is here reported. The propagation oftopological eigenmodes on the same interface is also different, which isquantified using the acoustic Shannon entropy, making the topological transportdependent on the frequency of the edge states. Based on the abundanttopological edge states of Suzuki phase crystals, a multifunctional device withacoustic diodes, multi-channel transmission, and selective acoustictransmission can be designed. Numerical simulations and measurementsdemonstrate the topological transmission. Our work extends the researchplatform of acoustic topological states to lattices with low symmetry, whichopens new avenues for enriching topological states with broad engineeringapplications.

Topological transmission in Suzuki phase sonic crystals