Over the past few years, the rapid development in the fields of condensed matter physics, electronic, and photonic systems have inspired the design and experimental demonstration of various acoustic topological insulators (TIs). Among these, the topologically protected one-way propagation is a phenomenon that is gaining increased attention. Pseudospin states, which is the analogue of the quantum spin Hall effect from electronic systems, has been proven to enable topological edge states in acoustics. Similarly, the valley Hall (VH) effect is also observed in acoustic systems and provides a pair of valley vortex states with opposite chirality. These valley vortex states can similarly form topologically protected edge states and, in turn, realize robust one-way propagation. However, the differences in the physics behind these acoustic systems give rise to distinct features such as different angle selections and immunization levels to various types of defects. This article conducts a comparison study between topological states in valley Hall phononic crystals and TIs that reveals the differences and similarities in several aspects. Both of them have topologically protected edge states and thus the robust one-way propagation. For the maximum transmission incident angle and defect immunization, however, VH topological waveguides and TI waveguides show different characteristics.

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