Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal

Band topology of materials describes the extent Bloch wavefunctions are twisted in momentum space. Such descriptions rely on a set of topological invariants, generally referred to as topological charges, which form a characteristic class in the mathematical structure of fiber bundles associated with the Bloch wavefunctions. For example, the celebrated Chern number and its variants belong to the Chern class, characterizing topological charges for complex Bloch wavefunctions. Nevertheless, under the space-time inversion symmetry, Bloch wavefunctions can be purely real in the entire momentum space; consequently, their topological classification does not fall into the Chern class, but requires another characteristic class known as the Stiefel-Whitney class. Here, in a three-dimensional acoustic crystal, we demonstrate a topological nodal-line semimetal that is characterized by a doublet of topological charges, the first and second Stiefel-Whitney numbers, simultaneously. Such a doubly charged nodal line gives rise to a doubled bulk-boundary correspondence-while the first Stiefel-Whitney number induces ordinary drumhead states of the nodal line, the second Stiefel-Whitney number supports hinge Fermi arc states at odd inversion-related pairs of hinges. These results experimentally validate the two Stiefel-Whitney topological charges and demonstrate their unique bulk-boundary correspondence in a physical system. Symmetry plays a crucial role in defining the band topology. Here, the authors experimentally demonstrate that spacetime inversion symmetry can lead to Stiefel-Whitney topological charges and protect hinge states in an acoustic nodal-line semimetal.

Automated summary

The band topology of materials relies on topological invariants called topological charges, which describe the twisted nature of Bloch wavefunctions in momentum space. Under space-time inversion symmetry, a different characteristic class called the Stiefel-Whitney class is required for the topological classification of real Bloch wavefunctions. In this study, the authors experimentally demonstrate the presence of two Stiefel-Whitney topological charges in a three-dimensional acoustic crystal, leading to a doubled bulk-boundary correspondence.