Topological insulators (TIs) can host an insulating gapped bulk with conducting gapless boundary states in lower dimensions than the bulk. To date, various kinds of classical wave TIs with gapless symmetry-protected boundary states have been discovered, promising for the efficient confinement and robust guiding of waves. However, for airborne sound, an acoustic analogue of a three-dimensional TI has not been achieved due to its spinless nature. Here, we experimentally demonstrate a three-dimensional topological acoustic crystal with pseudospins using bilayer chiral structures, in which multi-order topological bandgaps are generated step by step via elaborately manipulating the corresponding spatial symmetries. We observe acoustic analogues of 1st-order (two-dimensional gapless surface Dirac cones) and 2nd-order (one-dimensional gapless hinge Dirac dispersion) TIs in three dimensions, supporting robust surface or hinge sound transport. Based solely on spatial symmetry, our work provides a route to engineer the hierarchies of TIs and explore topological devices for three-dimensional spinless systems.

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Topological design for band structures of artificial materials such as acoustic crystals provides a powerful tool to manipulate wave propagating in a robust and symmetry-protected way. In this paper, based on the band folding and breaking mechanism by building blocks with acoustic atoms, we construct a three-dimensional topological acoustic crystal with a large complete bandgap. At a mirror-symmetry domain wall, two gapped symmetry and anti-symmetry surface states can be found in the bandgap, originated from two opposite Su-Schrieffer-Heeger chains. Remarkably, by enforcing a glide symmetry on the domain wall, we can tune the original gapped surface states in a gapless fashion at the boundaries of surface Brillouin zone, acting as omnidirectional acoustic quantum spin Hall effect. Our tunable yet straightforward acoustic crystals offer promising potentials in realizing future topological acoustic devices.