Topological sound has enriched the way of implementing the sound manipulation, which can effectively suppress the backscattering due to topological protection. As an inherent longitudinal wave, sound wave has no " spin” and only supports longitudinal vibration. Creating the " pseudospin” degree of freedom is crucial to topological state for acoustic wave. In previous studies, a circulating fluid flow in the background field is introduced to break the reciprocity of wave propagation in an acoustic system, which still faces technically a challenge. On the other hand, acoustic analogues of quantum spin Hall state and valley Hall state are realized by relying on the Kramers doublet in the lattices with
C
6symmetry and the broken mirror symmetry or inversion symmetry, respectively. In these cases, the distributions of acoustic energy flux in the unit cells emulate the pseudospins. Based on the band inversion, the topological sound carrying pseudospin is implemented at the interface between topologically trivial and non-trivial sonic crystal. Because of the close relevance to the lattice symmetry, these pseudospin-based topological state in the time-reversal invariant system is sensitive to structural defects.
In this work, we investigate the topological sound in chiral sonic crystal consisting of resonant air tubes. The counterclockwise and clockwise length variation of air tube correspond to different topological phases. A defect meta-molecule is created at the symmetric interface, which supports resonant state in the band gap. The interface state occurs at the boundary between two opposite chiral sonic crystals. Owing to the resonant structure, we realize subwavelength topological sound transport with a subwavelength-transverse confinement. For the state carrying monopolar-mode symmetry, it is expected to preserve the mode symmetry under randomly introduced defects. As anticipated, the numerical results show that the topological sound has very strong robustness against various defects, such as the variation of positions and length of air tube. Finally, we utilize the field symmetry of topological sound in chiral sonic crystal to realize robust edge transport along soft or rigid boundary. Through the mirror symmetry operation of soft or rigid boundary, we construct an interface between the real lattice and its virtual image. The approach greatly reduces the dimension of sonic crystal device. Our work may conduce to the advances in topological acoustics, since the subwavelength-scale topological state promotes the applications of miniaturized acoustic devices.
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