Topological Phononic Fiber of Second Spin-Chern Number.

The discovery of quantum spin Hall effect characterized by the first spin-Chern numbers in 2D systems has significantly advanced topological materials. To explore its 4D counterpart is of fundamental importance, but so far remains elusive in experiments. Here, we realize a topological phononic fiber protected by the second spin-Chern number in a 4D manifold, using a 3D geometric structure combined with a 1D rotational parameter space.

Coexistence of All-Order Topological States in a Three-Dimensional Phononic Topological Crystalline Insulator.

Classical-wave topological materials lacking intrinsic half-integer spins are less robust while more tunable. Here, we explore a single 3-dimensional phononic topological crystalline insulator that simultaneously exhibits a whole family of first-order quadratic surface, second-order hinge, and third-order corner states within the same bandgap. Such a topological crystalline insulator hosting all-order phases originates from the different topological nature when hierarchically projected onto different facets and lower dimensions, thus free from trivial cladding crystals.

Ideal acoustic quantum spin Hall phase in a multi-topology platform.

Fermionic time-reversal symmetry ([Formula: see text])-protected quantum spin Hall (QSH) materials feature gapless helical edge states when adjacent to arbitrary trivial cladding materials. However, due to symmetry reduction at the boundary, bosonic counterparts usually exhibit gaps and thus require additional cladding crystals to maintain robustness, limiting their applications. In this study, we demonstrate an ideal acoustic QSH with gapless behaviour by constructing a global T on both the bulk and the boundary based on bilayer structures.

Experimental Demonstration of Bulk-Hinge Correspondence in a Three-Dimensional Topological Dirac Acoustic Crystal.

Three-dimensional topological Dirac semimetal (DSM) is a vital state to explore topological phases and phase transitions. However, its bulk-boundary correspondence is elusive. Here, we experimentally investigate the higher-order hinge states in an acoustic DSM.

Acoustic analogues of three-dimensional topological insulators.

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.