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

TL;DR

This paper demonstrates a three-dimensional acoustic crystal exhibiting topological nodal-line semimetal behavior characterized by Stiefel-Whitney topological charges, revealing novel bulk-boundary correspondence beyond traditional topological classifications.

Contribution

It introduces the concept of Stiefel-Whitney topological charges in acoustic materials and shows their role in defining unique boundary states in a 3D topological semimetal.

Findings

Identification of a doubly charged nodal line with two Stiefel-Whitney numbers

Observation of drumhead states induced by the first Stiefel-Whitney number

Detection of hinge Fermi arc states supported by the second Stiefel-Whitney number

Abstract

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 establish the Stiefel-Whitney topological charges as intrinsic topological invariants for topological materials, with their unique bulk-boundary correspondence beyond the conventional framework of topological band theory.