Topological valley states at the domain wall between two artificial crystals with opposite valley Chern numbers offer a feasible way to realize robust wave transport since only broken spatial symmetry is required. In addition to the valley, spin and crystal dimension are two other important degrees of freedom, particularly in realizing spin-related topological phenomena. Here we experimentally demonstrate that it is possible to construct two-dimensional acoustic topological pseudospin-valley coupled saddle surface states, designed from glide symmetry in a three-dimensional system. By taking advantage of such two-dimensional surface states, a full set of acoustic pseudospins can be realized, exhibiting pseudospin-valley dependent transport. Furthermore, due to the hyperbolic character of the dispersion of saddle surface states, multi-directional anisotropic controllable robust sound transport with little backscattering is observed. Our findings may open research frontiers for acoustic pseudospins and provide a satisfactory platform for exploring unique acoustic topological properties in three-dimensional structures.
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