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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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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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Wang, W., Huang, L., Wan, X., & Tang, F. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.205141 · Cited by 4
Yao, J., Tang, S., Lü, C., Zhang, J., Song, J., & Jiang, Y. (2024) · Physical Review Applied · doi:10.1103/physrevapplied.22.044009 · Cited by 4
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Fractal polariton topological insulator
Sabour, K., & Kartashov, Y. V. (2025) · Optics Letters · doi:10.1364/ol.574475
Experimental demonstration of tunable spectral flow of elastic localized modes
Kuchibhatla, S. A. R., Gupta, A., Miniaci, M., & Leamy, M. J. (2025) · Applied Physics Letters · doi:10.1063/5.0293535
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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