Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal
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 associ...
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Nature Portfolio
2023-07-01
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| Series: | Nature Communications |
| Online Access: | https://doi.org/10.1038/s41467-023-40252-7 |
| _version_ | 1797769443788455936 |
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| author | Haoran Xue Z. Y. Chen Zheyu Cheng J. X. Dai Yang Long Y. X. Zhao Baile Zhang |
| author_facet | Haoran Xue Z. Y. Chen Zheyu Cheng J. X. Dai Yang Long Y. X. Zhao Baile Zhang |
| author_sort | Haoran Xue |
| collection | DOAJ |
| description | 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 experimentally validate the two Stiefel-Whitney topological charges and demonstrate their unique bulk-boundary correspondence in a physical system. |
| first_indexed | 2024-03-12T21:08:06Z |
| format | Article |
| id | doaj.art-7c105be2346244fca8de4b606fa775db |
| institution | Directory Open Access Journal |
| issn | 2041-1723 |
| language | English |
| last_indexed | 2024-03-12T21:08:06Z |
| publishDate | 2023-07-01 |
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| spelling | doaj.art-7c105be2346244fca8de4b606fa775db2023-07-30T11:20:04ZengNature PortfolioNature Communications2041-17232023-07-011411810.1038/s41467-023-40252-7Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystalHaoran Xue0Z. Y. Chen1Zheyu Cheng2J. X. Dai3Yang Long4Y. X. Zhao5Baile Zhang6Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological UniversityNational Laboratory of Solid State Microstructures and Department of Physics, Nanjing UniversityDivision of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological UniversityNational Laboratory of Solid State Microstructures and Department of Physics, Nanjing UniversityDivision of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological UniversityDepartment of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong KongDivision of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological UniversityAbstract 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.https://doi.org/10.1038/s41467-023-40252-7 |
| spellingShingle | Haoran Xue Z. Y. Chen Zheyu Cheng J. X. Dai Yang Long Y. X. Zhao Baile Zhang Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal Nature Communications |
| title | Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal |
| title_full | Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal |
| title_fullStr | Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal |
| title_full_unstemmed | Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal |
| title_short | Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal |
| title_sort | stiefel whitney topological charges in a three dimensional acoustic nodal line crystal |
| url | https://doi.org/10.1038/s41467-023-40252-7 |
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