The DOI matches its Crossref record; 179 of the 186 references it cites were found in a registry or an index.
A second wave of topological phenomena in photonics and acoustics
Abstract
Light and sound are the most ubiquitous forms of waves, associated with a variety of phenomena and physical effects such as rainbows and echoes. Light and sound, both categorized as classical waves, have lately been brought into unexpected connections with exotic topological phases of matter. We are currently witnessing the onset of a second wave of active research into this topic. The past decade has been marked by fundamental advances comprising two-dimensional quantum Hall insulators and quantum spin and valley Hall insulators, whose topological properties are characterized using linear band topology. Here, going beyond these conventional topological systems, we focus on the latest frontiers, including non-Hermitian, nonlinear and non-Abelian topology as well as topological defects, for which the characterization of the topological features goes beyond the standard band-topology language. In addition to an overview of the current state of the art, we also survey future research directions for valuable applications.
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“The lattice Hamiltonian of Eq. ( 1) can be written in the reciprocal space as”
From Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions (2025) · cites this paper as [26]
Citations
Cites
Colloquium : Topological insulators
Hasan, M. Z., & Kane, C. L. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.3045 · Cited by 19,930
Topological insulators and superconductors
Qi, X.-L., & Zhang, S.-C. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1057 · Cited by 14,394
Quantum Spin Hall Effect in Graphene
Kane, C. L., & Mele, E. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.226801 · Cited by 8,197
Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
Bernevig, B. A., Hughes, T. L., & Zhang, S.-C. (2006) · Science · doi:10.1126/science.1133734 · Cited by 7,090
Quantized Hall Conductance in a Two-Dimensional Periodic Potential
Thouless, D. J., Kohmoto, M., Nightingale, M. P., & den Nijs, M. (1982) · Physical Review Letters · doi:10.1103/physrevlett.49.405 · Cited by 6,973
Non-Abelian anyons and topological quantum computation
Nayak, C., Simon, S. H., Stern, A., Freedman, M., & Das Sarma, S. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.1083 · Cited by 6,861
Su, W. P., Schrieffer, J. R., & Heeger, A. J. (1979) · Physical Review Letters · doi:10.1103/physrevlett.42.1698 · Cited by 6,783
Z 2 Topological Order and the Quantum Spin Hall Effect
Kane, C. L., & Mele, E. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.146802 · Cited by 6,460
Ozawa, T., Price, H. M., Amo, A., Goldman, N., Hafezi, M., Lu, L., Rechtsman, M. C., Schuster, D., Simon, J., Zilberberg, O., et al. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015006 · Cited by 3,722
Lu, L., Joannopoulos, J. D., & Soljačić, M. (2014) · Nature Photonics · doi:10.1038/nphoton.2014.248 · Cited by 3,655
Research works printed but not linked: 5
- Peano, V., Brendel, C., Schmidt, M. & Marquardt, F. Topological phases of sound and light. Phys. Rev. X 5, 031011 (2015).
- Kawabata, K., Shiozaki, K., Ueda, M. & Sato, M. Symmetry and topology in non-Hermitian physics. Phys. Rev. X 9, 041015 (2019). Theoretical framework for non-Hermitian topological phases.
- Zhang, X., Zhang, T., Lu, M.-H. & Chen, Y.-F. A review on non-Hermitian skin effect. Adv. Phys. X 7, 2109431 (2022).
- Oppenheim, A. V. et al. Signals & Systems (Pearson Educación, 1997).
- Boyd, R. W. Nonlinear Optics (Academic Press, 2020).
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Sorted by citations
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Topological transfer of multidimensional states in phononic crystals
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Han, Y.-H., Li, Y., Yang, K., Xiao, L., Jia, S., & Mei, F. (2026) · Physical review. B./Physical review. B · doi:10.1103/k4gb-14cg
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Photon-mediated non-Markovian dynamics in topological Riemannian nanospheres of B i 2 S e 3
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Composite superlattice radio-frequency surface-acoustic-wave devices
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Coupled-wire construction of non-Abelian higher-order topological phases
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Liu, Y.-F., Ru, Y., Chen, Z., Chen, Z., He, G., Zhang, X.-M., Xiao, M., Lu, M.-H., & Chen, Y.-F. (2026) · Newton · doi:10.1016/j.newton.2026.100555
Self-citationYue, Z., Wang, S., Zhang, Z. D., Liao, D., Zhang, H., Cheng, Y., Liu, X., & Christensen, J. (2026) · National Science Review · doi:10.1093/nsr/nwag346
Self-citationOne-dimensional emulation of high-dimensional disclination topology
Wang, J., Lei, S., Song, D., Tang, L., Xia, S., & Chen, Z. (2026) · Photonics Research · doi:10.1364/prj.599128
Self-citationAnonymous, Zhu, D., Wu, J., Yang, Y., Jia, H., Yan, Z., Deng, W., & Liu, Z. (2026) · Physical Review Letters · doi:10.1103/cpzv-qc5v
Higher-Order Topology Embedded in First-Order Topological Bands
Anonymous, Pu, Z., Lu, J., Deng, W., Ke, M., & Liu, Z. (2026) · Physical Review Letters · doi:10.1103/rlk2-psxm
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Dynamic synchronization of driven self-oscillators: Modeling and experiment
Anonymous, Kuhl, U., & Noiray, N. (2026) · Physical review. E · doi:10.1103/61km-kb4j
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Chen, J., Zheng, Y., Li, Z., & Qiu, C. (2026) · Nature Physics · doi:10.1038/s41567-026-03405-1
Tian, L.-R., Ke, H.-K., Liang, X.-F., Zhao, J.-Z., Liu, J.-F., & Wang, J. (2026) · Chinese Physics Letters · doi:10.1088/0256-307x/43/9/090704
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Nunes, A. W., Valentin, C. B. S., Beli, D., & Arruda, J. R. D. F. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7507198
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Li, H., Jia, P., Wang, Z., Guo, L., Bongiovanni, D., Xia, S., Zhao, X., Zhu, Z., & Hu, Y. (2026) · Optics Letters · doi:10.1364/ol.612040
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Ma, Y., wang, H., Belić, M. R., Li, Y., & Zhang, Y. (2026) · Optics Express · doi:10.1364/oe.616357
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Wu, H., Cheng, W., Chen, R., Zhang, B., Yan, W., & Chen, F. (2026) · Optics Letters · doi:10.1364/ol.611145
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Li, M., Shi, L., Zhao, J.-X., Chen, Z., & Shen, Y. (2026) · Applied Physics Letters · doi:10.1063/5.0355924
Self-citationZheng, Y., Chen, J., Ji, Z., Chen, Y., Wan, W., Qiu, C., & Li, Z. (2026) · Applied Physics Reviews · doi:10.1063/5.0316726
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Li, M., & Khanikaev, A. B. (2026) · Elsevier eBooks · doi:10.1016/b978-0-443-13447-0.00008-8
Metadata
- Authors
- Zhang, X., Zangeneh-Nejad, F., Chen, Z.-G., Lu, M.-H., & Christensen, J.
- Affiliations
- National Laboratory of Solid State Microstructures (CN)
- Nanjing University (CN)
- Madrid Institute for Advanced Studies (ES)
- Corresponding author
- Lu, Ming-Hui
- Christensen, Johan
- Venue
- Nature
- Published
- 2023-06-21
- Volume
- 618
- Issue
- 7966
- Pages
- 687-697
- ISSN
- 0028-0836 (ISSN-L)
- 1476-4687
- OpenAlex
- W4381480946
- Cited by
- 240
- References
- 186
- Citations by year
- 2026: 55 · 2025: 96 · 2024: 76 · 2023: 13
- FWCI
- 5.14
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- Nature (publishedVersion)
- PubMed (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Acoustics and Ultrasonics › Acoustic Wave Phenomena Research
- Keywords
- topological photonics, topological acoustics, topological phases, non-Hermitian topology, non-linear topology, topological defects, quantum Hall insulator, waveguide arrays
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