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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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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
Principles of Condensed Matter Physics
Chaikin, P. M., & Lubensky, T. C. (1995) · Cambridge University Press eBooks · doi:10.1017/cbo9780511813467 · Cited by 3,571
Read, N., & Green, D. (2000) · Physical review. B, Condensed matter · doi:10.1103/physrevb.61.10267 · Cited by 3,542
Photonic Floquet topological insulators
Rechtsman, M. C., Zeuner, J. M., Plotnik, Y., Lumer, Y., Podolsky, D., Dreisow, F., Nolte, S., Segev, M., & Szameit, A. (2013) · Nature · doi:10.1038/nature12066 · Cited by 3,332
Classification of topological insulators and superconductors in three spatial dimensions
Schnyder, A. P., Ryu, S., Furusaki, A., & Ludwig, A. W. W. (2008) · Physical Review B · doi:10.1103/physrevb.78.195125 · Cited by 3,322
Observation of unidirectional backscattering-immune topological electromagnetic states
Wang, Z., Chong, Y., Joannopoulos, J. D., & Soljačić, M. (2009) · Nature · doi:10.1038/nature08293 · Cited by 3,123
Haldane, F. D. M., & Raghu, S. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.013904 · Cited by 2,787
Non-Hermitian physics and PT symmetry
El‐Ganainy, R., Makris, K. G., Khajavikhan, M., Musslimani, Z. H., Rotter, S., & Christodoulides, D. N. (2018) · Nature Physics · doi:10.1038/nphys4323 · Cited by 2,767
Classification of topological quantum matter with symmetries
Chiu, C.-K., Teo, J. C. Y., Schnyder, A. P., & Ryu, S. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.035005 · Cited by 2,736
Exceptional points in optics and photonics
Miri, M., & Alù, A. (2019) · Science · doi:10.1126/science.aar7709 · Cited by 2,270
Edge States and Topological Invariants of Non-Hermitian Systems
Yao, S., & Wang, Z. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.086803 · Cited by 2,250
Controlling sound with acoustic metamaterials
Cummer, S. A., Christensen, J., & Alù, A. (2016) · Nature Reviews Materials · doi:10.1038/natrevmats.2016.1 · Cited by 2,216
Self-citationThe topological theory of defects in ordered media
Mermin, N. D. (1979) · Reviews of Modern Physics · doi:10.1103/revmodphys.51.591 · Cited by 2,205
Topological Crystalline Insulators
Fu, L. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.106802 · Cited by 2,095
Ashida, Y., Gong, Z., & Ueda, M. (2020) · Advances In Physics · doi:10.1080/00018732.2021.1876991 · Cited by 2,048
Quantized electric multipole insulators
Benalcazar, W. A., Bernevig, B. A., & Hughes, T. L. (2017) · Science · doi:10.1126/science.aah6442 · Cited by 2,029
Photonic topological insulators
Khanikaev, A. B., Hossein Mousavi, S., Tse, W.-K., Kargarian, M., MacDonald, A. H., & Shvets, G. (2013) · Nature Materials · doi:10.1038/nmat3520 · Cited by 1,971
Non-Abelian Statistics of Half-Quantum Vortices in p -Wave Superconductors
Ivanov, D. A. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.268 · Cited by 1,933
Parity–time symmetry and exceptional points in photonics
Özdemir, Ş. K., Rotter, S., Nori, F., & Yang, L. (2019) · Nature Materials · doi:10.1038/s41563-019-0304-9 · Cited by 1,764
(2006) · Wiley eBooks · doi:10.1002/0471784192 · Cited by 1,735
Exceptional topology of non-Hermitian systems
Bergholtz, E. J., Budich, J. C., & Kunst, F. K. (2021) · Reviews of Modern Physics · doi:10.1103/revmodphys.93.015005 · Cited by 1,711
Scheme for Achieving a Topological Photonic Crystal by Using Dielectric Material
Wu, L.-H., & Hu, X. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.223901 · Cited by 1,648
Yang, Z., Gao, F., Shi, X., Lin, X., Gao, Z. L., Chong, Y. D., & Zhang, B. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.114301 · Cited by 1,331
Topological insulator laser: Experiments
Bandres, M. A., Wittek, S., Harari, G., Parto, M., Ren, J., Segev, M., Christodoulides, D. N., & Khajavikhan, M. (2018) · Science · doi:10.1126/science.aar4005 · Cited by 1,315
Topological Origin of Non-Hermitian Skin Effects
Ōkuma, N., Kawabata, K., Shiozaki, K., & Sato, M. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.086801 · Cited by 1,234
Acoustic topological insulator and robust one-way sound transport
He, C., Ni, X., Ge, H., Sun, X., Chen, Y., Lu, M., Liu, X.-P., & Chen, Y. (2016) · Nature Physics · doi:10.1038/nphys3867 · Cited by 1,208
Self-citationTopological Band Theory for Non-Hermitian Hamiltonians
Shen, H., Zhen, B., & Fu, L. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.146402 · Cited by 1,171
Experimental observation of Weyl points
Lu, L., Wang, Z., Ye, D., Ran, L., Fu, L., Joannopoulos, J. D., & Soljačić, M. (2015) · Science · doi:10.1126/science.aaa9273 · Cited by 1,067
Sound Isolation and Giant Linear Nonreciprocity in a Compact Acoustic Circulator
Fleury, R., Sounas, D. L., Sieck, C. F., Haberman, M. R., & Alù, A. (2014) · Science · doi:10.1126/science.1246957 · Cited by 1,066
Topolectrical-circuit realization of topological corner modes
Imhof, S., Berger, C., Bayer, F., Brehm, J., Molenkamp, L. W., Kiessling, T., Schindler, F., Lee, C. H., Greiter, M., Neupert, T., et al. (2018) · Nature Physics · doi:10.1038/s41567-018-0246-1 · Cited by 1,034
Vozmediano, M. A. H., Katsnelson, M. I., & Guinea, F. (2010) · Physics Reports · doi:10.1016/j.physrep.2010.07.003 · Cited by 1,017
Observation of topological valley transport of sound in sonic crystals
Lu, J., Qiu, C., Ye, L., Fan, X., Ke, M., Zhang, F., & Liu, Z. (2017) · Nature Physics · doi:10.1038/nphys3999 · Cited by 985
Observation of a phononic quadrupole topological insulator
Serra-Garcia, M., Peri, V., Süsstrunk, R., Bilal, O. R., Larsen, T., Villanueva, L. G., & Huber, S. D. (2018) · Nature · doi:10.1038/nature25156 · Cited by 982
Electronic transport in polycrystalline graphene
Yazyev, O. V., & Louie, S. G. (2010) · Nature Materials · doi:10.1038/nmat2830 · Cited by 940
Lasing in topological edge states of a one-dimensional lattice
St-Jean, P., Goblot, V., Galopin, E., Lemaître, A., Ozawa, T., Le Gratiet, L., Sagnes, I., Bloch, J., & Amo, A. (2017) · Nature Photonics · doi:10.1038/s41566-017-0006-2 · Cited by 892
Topologically protected bound states in photonic parity–time-symmetric crystals
Weimann, S., Kremer, M., Plotnik, Y., Lumer, Y., Nolte, S., Makris, K. G., Segev, M., Rechtsman, M. C., & Szameit, A. (2016) · Nature Materials · doi:10.1038/nmat4811 · Cited by 864
Higher-Order Topological Insulators and Semimetals on the Breathing Kagome and Pyrochlore Lattices
Ezawa, M. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.026801 · Cited by 862
Acoustic higher-order topological insulator on a kagome lattice
Xue, H., Yang, Y., Gao, F., Chong, Y. D., & Zhang, B. (2018) · Nature Materials · doi:10.1038/s41563-018-0251-x · Cited by 853
Topological insulator laser: Theory
Harari, G., Bandres, M. A., Lumer, Y., Rechtsman, M. C., Chong, Y. D., Khajavikhan, M., Christodoulides, D. N., & Segev, M. (2018) · Science · doi:10.1126/science.aar4003 · Cited by 848
Topological phases in acoustic and mechanical systems
Ma, G., Xiao, M., & Chan, C. T. (2019) · Nature Reviews Physics · doi:10.1038/s42254-019-0030-x · Cited by 834
Topological defects and gapless modes in insulators and superconductors
Teo, J. C. Y., & Kane, C. L. (2010) · Physical Review B · doi:10.1103/physrevb.82.115120 · Cited by 820
Topological funneling of light
Weidemann, S., Kremer, M., Helbig, T., Hofmann, T., Stegmaier, A., Greiter, M., Thomale, R., & Szameit, A. (2020) · Science · doi:10.1126/science.aaz8727 · Cited by 808
A quantized microwave quadrupole insulator with topologically protected corner states
Peterson, C. W., Benalcazar, W. A., Hughes, T. L., & Bahl, G. (2018) · Nature · doi:10.1038/nature25777 · Cited by 797
Topologically protected elastic waves in phononic metamaterials
Mousavi, S. H., Khanikaev, A. B., & Wang, Z. (2015) · Nature Communications · doi:10.1038/ncomms9682 · Cited by 785
Nonreciprocal lasing in topological cavities of arbitrary geometries
Bahari, B., Ndao, A., Vallini, F., El Amili, A., Fainman, Y., & Kanté, B. (2017) · Science · doi:10.1126/science.aao4551 · Cited by 770
Observation of higher-order topological acoustic states protected by generalized chiral symmetry
Ni, X., Weiner, M., Alù, A., & Khanikaev, A. B. (2018) · Nature Materials · doi:10.1038/s41563-018-0252-9 · Cited by 744
Observation of a Topological Transition in the Bulk of a Non-Hermitian System
Zeuner, J. M., Rechtsman, M. C., Plotnik, Y., Lumer, Y., Nolte, S., Rudner, M. S., Segev, M., & Szameit, A. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.040402 · Cited by 730
Valley photonic crystals for control of spin and topology
Dong, J.-W., Chen, X.-D., Zhu, H., Wang, Y., & Zhang, X. (2017) · Nature Materials · doi:10.1038/nmat4807 · Cited by 730
Self-citationWeyl points and line nodes in gyroid photonic crystals
Lü, L., Fu, L., Joannopoulos, J. D., & Marin Soljacic, A. (2013) · Nature Photonics · doi:10.1038/nphoton.2013.42 · Cited by 681
Lee, C. H., Imhof, S., Berger, C., Bayer, F., Brehm, J., Molenkamp, L. W., Kiessling, T., & Thomale, R. (2018) · Communications Physics · doi:10.1038/s42005-018-0035-2 · Cited by 661
Observation of bulk Fermi arc and polarization half charge from paired exceptional points
Zhou, H., Peng, C., Yoon, Y., Hsu, C. W., Nelson, K. A., Fu, L., Joannopoulos, J. D., Marin Soljacic, A., & Zhen, B. (2018) · Science · doi:10.1126/science.aap9859 · Cited by 649
Floquet topological insulators for sound
Fleury, R., Khanikaev, A. B., & Alù, A. (2016) · Nature Communications · doi:10.1038/ncomms11744 · Cited by 628
Nonlinear topological photonics
Smirnova, D. A., Leykam, D., Chong, Y. D., & Kivshar, Y. S. (2020) · Applied Physics Reviews · doi:10.1063/1.5142397 · Cited by 615
Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice
Khanikaev, A. B., Fleury, R., Mousavi, S. H., & Alù, A. (2015) · Nature Communications · doi:10.1038/ncomms9260 · Cited by 607
Zero modes of the vortex-fermion system
Jackiw, R., & Rossi, P. (1981) · Nuclear Physics B · doi:10.1016/0550-3213(81)90044-4 · Cited by 605
Xie, B.-Y., Su, G., Wang, H., Su, H. L., Shen, X., Zhan, P., Lu, M., Wang, Z., & Chen, Y. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.233903 · Cited by 597
Self-citationTopologically protected refraction of robust kink states in valley photonic crystals
Gao, F., Xue, H., Yang, Z., Lai, K., Yu, Y., Lin, X., Chong, Y., Shvets, G., & Zhang, B. (2018) · Nature Physics · doi:10.1038/nphys4304 · Cited by 576
Direct Observation of Corner States in Second-Order Topological Photonic Crystal Slabs
Chen, X., Deng, W., Shi, F., Zhao, F.-L., Chen, M., & Dong, J. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.233902 · Cited by 563
Xie, B., Wang, H.-X., Zhang, X., Zhan, P., Jiang, J.-H., Lu, M., & Chen, Y. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00323-4 · Cited by 562
Self-citationSelective enhancement of topologically induced interface states in a dielectric resonator chain
Poli, C., Bellec, M., Kuhl, U., Mortessagne, F., & Schomerus, H. (2015) · Nature Communications · doi:10.1038/ncomms7710 · Cited by 544
Edge-Mode Lasing in 1D Topological Active Arrays
Parto, M., Wittek, S., Hodaei, H., Harari, G., Bandres, M. A., Ren, J., Rechtsman, M. C., Segev, M., Christodoulides, D. N., & Khajavikhan, M. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.113901 · Cited by 533
Bzdušek, T., Wu, Q., Rüegg, A., Sigrist, M., & Soluyanov, A. A. (2016) · Nature · doi:10.1038/nature19099 · Cited by 528
Non-Hermitian topological light steering
Zhao, H. X., Qiao, X., Wu, T., Midya, B., Longhi, S., & Feng, L. H. (2019) · Science · doi:10.1126/science.aay1064 · Cited by 473
Electron Fractionalization in Two-Dimensional Graphenelike Structures
Hou, C.-Y., Chamon, C., & Mudry, C. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.186809 · Cited by 471
Second-order topology and multidimensional topological transitions in sonic crystals
Zhang, X., Wang, H., Lin, Z., Tian, Y., Xie, B., Lu, M., Chen, Y., & Jiang, J. (2019) · Nature Physics · doi:10.1038/s41567-019-0472-1 · Cited by 457
Self-citationStrain-induced pseudomagnetic field and photonic Landau levels in dielectric structures
Rechtsman, M. C., Zeuner, J. M., Tünnermann, A., Nolte, S., Segev, M., & Szameit, A. (2013) · Nature Photonics · doi:10.1038/nphoton.2012.302 · Cited by 453
Valley Vortex States in Sonic Crystals
Lu, J., Qiu, C., Ke, M., & Liu, Z. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.093901 · Cited by 448
Universal non-Hermitian skin effect in two and higher dimensions
Zhang, K., Yang, Z., & Fang, C. (2022) · Nature Communications · doi:10.1038/s41467-022-30161-6 · Cited by 437
Topological hybrid silicon microlasers
Zhao, H., Miao, P., Teimourpour, M. H., Malzard, S., El-Ganainy, R., Schomerus, H., & Feng, L. (2018) · Nature Communications · doi:10.1038/s41467-018-03434-2 · Cited by 429
One-dimensional topologically protected modes in topological insulators with lattice dislocations
Ran, Y., Zhang, Y., & Vishwanath, A. (2009) · Nature Physics · doi:10.1038/nphys1220 · Cited by 421
Synthetic gauge flux and Weyl points in acoustic systems
Xiao, M., Chen, W.-J., He, W.-Y., & Chan, C. T. (2015) · Nature Physics · doi:10.1038/nphys3458 · Cited by 408
Classification of Exceptional Points and Non-Hermitian Topological Semimetals
Kawabata, K., Bessho, T., & Sato, M. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.066405 · Cited by 407
Ma, T., Khanikaev, A. B., Mousavi, S. H., & Shvets, G. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.127401 · Cited by 393
Topologically protected midgap states in complex photonic lattices
Schomerus, H. (2013) · Optics Letters · doi:10.1364/ol.38.001912 · Cited by 384
Experimental realization of a Weyl exceptional ring
Cerjan, A., Huang, S., Wang, M., Chen, K. P., Chong, Y. D., & Rechtsman, M. C. (2019) · Nature Photonics · doi:10.1038/s41566-019-0453-z · Cited by 374
Zhang, X., Xiao, M., Cheng, Y., Lu, M., & Christensen, J. (2018) · Communications Physics · doi:10.1038/s42005-018-0094-4 · Cited by 367
Self-citationAcoustic non-Hermitian skin effect from twisted winding topology
Zhang, L., Yang, Y., Ge, Y., Guan, Y., Chen, Q., Yan, Q., Chen, F., Xi, R., Li, Y., Jia, D., et al. (2021) · Nature Communications · doi:10.1038/s41467-021-26619-8 · Cited by 364
Edge Solitons in Nonlinear-Photonic Topological Insulators
Leykam, D., & Chong, Y. D. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.143901 · Cited by 355
Weyl points and Fermi arcs in a chiral phononic crystal
Li, F., Huang, X., Lu, J., Ma, J., & Liu, Z. (2017) · Nature Physics · doi:10.1038/nphys4275 · Cited by 340
Topological complex-energy braiding of non-Hermitian bands
Wang, K., Dutt, A., Wojcik, C. C., & Fan, S. (2021) · Nature · doi:10.1038/s41586-021-03848-x · Cited by 335
Observation of Floquet solitons in a topological bandgap
Mukherjee, S., & Rechtsman, M. C. (2020) · Science · doi:10.1126/science.aba8725 · Cited by 331
Nonlinear tuning of PT symmetry and non-Hermitian topological states
Xia, S., Kaltsas, D., Song, D., Komis, I., Xu, J., Szameit, A., Buljan, H., Makris, K. G., & Chen, Z. (2021) · Science · doi:10.1126/science.abf6873 · Cited by 317
Self-citationBulk–disclination correspondence in topological crystalline insulators
Liu, Y., Leung, S., Li, F., Lin, Z., Tao, X., Poo, Y., & Jiang, J. (2021) · Nature · doi:10.1038/s41586-020-03125-3 · Cited by 312
Observation of bulk Fermi arc and polarization half charge from paired exceptional pointsPreprint
Yoon, Y., Hsu, C. W., Nelson, K. A., Zhou, H., Peng, C., Fu, L., Joannopoulos, J. D., Marin Soljacic, A., & Zhen, B. (2017) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 307
Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)
Machida, T., Sun, Y., Pyon, S., Takeda, S., Kohsaka, Y., Hanaguri, T., Sasagawa, T., & Tamegai, T. (2019) · Nature Materials · doi:10.1038/s41563-019-0397-1 · Cited by 290
Ni, X., He, C., Sun, X., Liu, X.-P., Lu, M., Feng, L., & Chen, Y. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/5/053016 · Cited by 281
Self-citationNonlinearity-induced photonic topological insulator
Maczewsky, L. J., Heinrich, M., Kremer, M., Ivanov, S. K., Ehrhardt, M., Martinez, F., Kartashov, Y. V., Konotop, V. V., Torner, L., Bauer, D., et al. (2020) · Science · doi:10.1126/science.abd2033 · Cited by 268
Non-Abelian band topology in noninteracting metals
Wu, Q., Soluyanov, A. A., & Bzdušek, T. (2019) · Science · doi:10.1126/science.aau8740 · Cited by 260
Photonic topological insulator with broken time-reversal symmetry
He, C., Sun, X., Liu, X., Lu, M., Chen, Y., Feng, L., & Chen, Y. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1525502113 · Cited by 260
Self-citationZero-energy Vortex Bound State in the Superconducting Topological Surface State of Fe(Se,Te)
Machida, T., Sun, Y., Pyon, S., Pyon, S., 駿, 竹., Takeda, S., 祐生, 幸., Kohsaka, Y., 哲郎, 花., Hanaguri, T., et al. (2020) · Tokyo Tech Research Repository (Tokyo Institute of Technology) · Cited by 252
Nonlinear second-order photonic topological insulators
Kirsch, M. S., Zhang, Y., Kremer, M., Maczewsky, L. J., Ivanov, S. K., Kartashov, Y. V., Torner, L., Bauer, D., Szameit, A., & Heinrich, M. (2021) · Nature Physics · doi:10.1038/s41567-021-01275-3 · Cited by 243
Non-Hermitian Sonic Second-Order Topological Insulator
Zhang, Z., López, M. R., Cheng, Y., Liu, X., & Christensen, J. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.195501 · Cited by 232
Self-citationTopological-cavity surface-emitting laser
Yang, L., Li, G., Gao, X., & Lü, L. (2022) · Nature Photonics · doi:10.1038/s41566-022-00972-6 · Cited by 232
Kremer, M., Petrides, I., Meyer, E., Heinrich, M., Zilberberg, O., & Szameit, A. (2020) · Nature Communications · doi:10.1038/s41467-020-14692-4 · Cited by 226
Dirac-vortex topological cavities
Gao, X., Yang, L., Lin, H., Zhang, L., Li, J., Bo, F., Wang, Z., & Lü, L. (2020) · Nature Nanotechnology · doi:10.1038/s41565-020-0773-7 · Cited by 223
Non-Abelian reciprocal braiding of Weyl points and its manifestation in ZrTe
Bouhon, A., Wu, Q., Slager, R.-J., Weng, H., Yazyev, O. V., & Bzdušek, T. (2020) · Nature Physics · doi:10.1038/s41567-020-0967-9 · Cited by 218
Topological triple phase transition in non-Hermitian Floquet quasicrystals
Weidemann, S., Kremer, M., Longhi, S., & Szameit, A. (2022) · Nature · doi:10.1038/s41586-021-04253-0 · Cited by 217
Nonlinear Second-Order Topological Insulators
Zangeneh‐Nejad, F., & Fleury, R. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.053902 · Cited by 185
Self-citationKnots and Non-Hermitian Bloch Bands
Hu, H., & Zhao, E. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.010401 · Cited by 185
Non-Hermitian topological whispering gallery
Hu, B., Zhang, Z., Zhang, H., Zheng, L., Xiong, W., Yue, Z., Wang, X., Xu, J., Cheng, Y., Liu, X., et al. (2021) · Nature · doi:10.1038/s41586-021-03833-4 · Cited by 179
Self-citationNon-Hermitian Hopf-link exceptional line semimetals
Yang, Z., & Hu, J. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.99.081102 · Cited by 177
Teo, J. C. Y., & Hughes, T. L. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.047006 · Cited by 174
Trapped fractional charges at bulk defects in topological insulators
Peterson, C. W., Li, T., Jiang, W., Hughes, T. L., & Bahl, G. (2021) · Nature · doi:10.1038/s41586-020-03117-3 · Cited by 173
Experimental observation of non-Abelian topological acoustic semimetals and their phase transitions
Jiang, B., Bouhon, A., Lin, Z.-K., Zhou, X., Hou, B., Li, F., Slager, R.-J., & Jiang, J. (2021) · Nature Physics · doi:10.1038/s41567-021-01340-x · Cited by 166
Deep‐Subwavelength Holey Acoustic Second‐Order Topological Insulators
Zhang, Z., Long, H., Liu, C., Shao, C., Cheng, Y., Liu, X., & Christensen, J. (2019) · Advanced Materials · doi:10.1002/adma.201904682 · Cited by 166
Self-citationTopological insulator vertical-cavity laser array
Dikopoltsev, A., Harder, T. H., Lustig, E., Egorov, O. A., Beierlein, J., Wolf, A., Lumer, Y., Emmerling, M., Schneider, C., Höfling, S., et al. (2021) · Science · doi:10.1126/science.abj2232 · Cited by 164
Fractional disclination charge in two-dimensional Cn -symmetric topological crystalline insulators
Li, T., Zhu, P., Benalcazar, W. A., & Hughes, T. L. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.115115 · Cited by 163
Experimental observation of non-Abelian topological charges and edge states
Guo, Q., Jiang, T., Zhang, R.-Y., Zhang, L., Zhang, Z.-Q., Yang, B., Zhang, S., & Chan, C. T. (2021) · Nature · doi:10.1038/s41586-021-03521-3 · Cited by 162
Homotopy characterization of non-Hermitian Hamiltonians
Wojcik, C. C., Sun, X.-Q., Bzdušek, T., & Fan, S. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.205417 · Cited by 160
Topological Euler Class as a Dynamical Observable in Optical Lattices
Ünal, F. N., Bouhon, A., & Slager, R.-J. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.053601 · Cited by 160
Non-Abelian Thouless pumping in photonic waveguides
Sun, Y., Zhang, X., Yu, F., Tian, Z., Chen, Q., & Sun, H. (2022) · Nature Physics · doi:10.1038/s41567-022-01669-x · Cited by 150
Self-citationTopoelectrical circuit octupole insulator with topologically protected corner states
Bao, J., Zou, D., Zhang, W., He, W., Sun, H., & Zhang, X. (2019) · Physical Review B · doi:10.1103/physrevb.100.201406 · Cited by 149
Self-citationPhotonic Floquet topological insulators in a fractal lattice
Yang, Z., Lustig, E., Lumer, Y., & Segev, M. (2020) · Light Science & Applications · doi:10.1038/s41377-020-00354-z · Cited by 145
Xie, B.-Y., Wang, H., Zhu, X.-Y., Lu, M., Wang, Z., & Chen, Y. (2018) · Optics Express · doi:10.1364/oe.26.024531 · Cited by 135
Self-citationObservation of Acoustic Non-Hermitian Bloch Braids and Associated Topological Phase Transitions
Zhang, Q., Li, Y., Sun, H., Liu, X., Zhao, L., Feng, X., Fan, X., & Qiu, C. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.017201 · Cited by 133
Synthesis and observation of non-Abelian gauge fields in real space
Yang, Y., Peng, C., Zhu, D., Buljan, H., Joannopoulos, J. D., Zhen, B., & Marin Soljacic, A. (2019) · Science · doi:10.1126/science.aay3183 · Cited by 132
Fractal photonic topological insulators
Biesenthal, T., Maczewsky, L. J., Yang, Z., Kremer, M., Segev, M., Szameit, A., & Heinrich, M. (2022) · Science · doi:10.1126/science.abm2842 · Cited by 130
Measuring the knot of non-Hermitian degeneracies and non-commuting braids
Patil, Y. S., Hoeller, J., Henry, P. A., Guria, C., Zhang, Y., Jiang, L., Kralj, N., Read, N., & Harris, J. (2022) · Nature · doi:10.1038/s41586-022-04796-w · Cited by 130
Slager, R.-J., Mesaroš, A., Juričić, V., & Zaanen, J. (2014) · Physical Review B · doi:10.1103/physrevb.90.241403 · Cited by 125
Experimental observation of photonic nodal line degeneracies in metacrystals
Gao, W., Yang, B., Tremain, B., Liu, H., Guo, Q., Xia, L., Hibbins, A. P., & Zhang, S. (2018) · Nature Communications · doi:10.1038/s41467-018-03407-5 · Cited by 112
Nodal rings and drumhead surface states in phononic crystals
Deng, W., Lu, J., Li, F., Huang, X., Yan, M., Ma, J., & Liu, Z. (2019) · Nature Communications · doi:10.1038/s41467-019-09820-8 · Cited by 112
Realization of the Square-Root Higher-Order Topological Insulator in Electric Circuits
Song, L., Yang, H., Cao, Y., & Yan, P. (2020) · Nano Letters · doi:10.1021/acs.nanolett.0c03049 · Cited by 111
Observation of Protected Photonic Edge States Induced by Real-Space Topological Lattice Defects
Wang, Q., Xue, H., Zhang, B., & Chong, Y. D. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.243602 · Cited by 105
Braiding photonic topological zero modes
Noh, J., Schuster, T., Iadecola, T., Huang, S., Wang, M., Chen, K. P., Chamon, C., & Rechtsman, M. C. (2020) · Nature Physics · doi:10.1038/s41567-020-1007-5 · Cited by 103
Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
Peng, B., Bouhon, A., Monserrat, B., & Slager, R.-J. (2022) · Nature Communications · doi:10.1038/s41467-022-28046-9 · Cited by 96
Topological modes in a laser cavity through exceptional state transfer
Schumer, A., Liu, Y. G. N., Leshin, J., Ding, L., Alahmadi, Y., Hassan, A. U., Nasari, H., Rotter, S., Christodoulides, D. N., LiKamWa, P., et al. (2022) · Science · doi:10.1126/science.abl6571 · Cited by 95
Photonic topological insulator induced by a dislocation in three dimensions
Lustig, E., Maczewsky, L. J., Beck, J., Biesenthal, T., Heinrich, M., Yang, Z., Plotnik, Y., Szameit, A., & Segev, M. (2022) · Nature · doi:10.1038/s41586-022-05129-7 · Cited by 94
Majorana-like Zero Modes in Kekulé Distorted Sonic Lattices
Gao, P., Torrent, D., Cervera, F., San-José, P., Sánchez‐Dehesa, J., & Christensen, J. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.196601 · Cited by 92
Self-citationHomotopical characterization of non-Hermitian band structures
Li, Z., & Mong, R. S. K. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.103.155129 · Cited by 92
Classical non-Abelian braiding of acoustic modes
Chen, Z., Zhang, R.-Y., Chan, C. T., & Ma, G. (2021) · Nature Physics · doi:10.1038/s41567-021-01431-9 · Cited by 92
Self-citationExperimental demonstration of acoustic semimetal with topologically charged nodal surface
Xiao, M., Ye, L., Qiu, C., He, H., Liu, Z., & Fan, S. (2020) · Science Advances · doi:10.1126/sciadv.aav2360 · Cited by 91
Non-Abelian gauge field optics
Chen, Y., Zhang, R.-Y., Xiong, Z., Hang, Z. H., Li, J., Shen, J. Q., & Chan, C. T. (2019) · Nature Communications · doi:10.1038/s41467-019-10974-8 · Cited by 88
Yang, Y., Xia, J., Sun, H.-X., Ge, Y., Jia, D., Yuan, S.-Q., Yang, S. A., Chong, Y. D., & Zhang, B. (2019) · Nature Communications · doi:10.1038/s41467-019-13258-3 · Cited by 88
Dualities and non-Abelian mechanics
Fruchart, M., Zhou, Y., & Vitelli, V. (2020) · Nature · doi:10.1038/s41586-020-1932-6 · Cited by 87
Non-Abelian topology of nodal-line rings in PT -symmetric systems
Tiwari, A., & Bzdušek, T. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.195130 · Cited by 86
Observation of Non-Abelian Thouless Pump
You, O., Liang, S., Xie, B., Gao, W., Ye, W., Zhu, J., & Zhang, S. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.244302 · Cited by 86
Topological dislocation modes in three-dimensional acoustic topological insulators
Ye, L., Qiu, C., Xiao, M., Li, T., Du, J., Ke, M., & Liu, Z. (2022) · Nature Communications · doi:10.1038/s41467-022-28182-2 · Cited by 83
Non-Abelian band topology in noninteracting metals
Wu, Q., Soluyanov, A. A., & Bzdušek, T. (2019) · Zurich Open Repository and Archive (University of Zurich) · doi:10.5167/uzh-181242 · Cited by 77
Observation of quadratic Weyl points and double-helicoid arcs
He, H., Qiu, C., Cai, X., Xiao, M., Ke, M., Zhang, F., & Liu, Z. (2020) · Nature Communications · doi:10.1038/s41467-020-15825-5 · Cited by 77
Anomalous Topological Edge States in Non-Hermitian Piezophononic Media
Gao, P., Willatzen, M., & Christensen, J. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.206402 · Cited by 71
Self-citationXue, H., Jia, D., Ge, Y., Guan, Y., Wang, Q., Yuan, S.-Q., Sun, H.-X., Chong, Y. D., & Zhang, B. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.214301 · Cited by 69
Gain-induced topological response via tailored long-range interactions
Liu, Y. G. N., Jung, P. S., Parto, M., Christodoulides, D. N., & Khajavikhan, M. (2021) · Nature Physics · doi:10.1038/s41567-021-01185-4 · Cited by 68
Observation of Degenerate Zero-Energy Topological States at Disclinations in an Acoustic Lattice
Deng, Y., Benalcazar, W. A., Chen, Z., Oudich, M., Ma, G., & Jing, Y. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.174301 · Cited by 68
Self-citationNanomechanical topological insulators with an auxiliary orbital degree of freedom
Ma, J., Xi, X., Li, Y., & Sun, X. (2021) · Nature Nanotechnology · doi:10.1038/s41565-021-00868-6 · Cited by 65
Non-Abelian Thouless pumping in a photonic lattice
Brosco, V., Pilozzi, L., Fazio, R., & Conti, C. (2021) · Physical Review A · doi:10.1103/physreva.103.063518 · Cited by 61
Self-induced topological transition in phononic crystals by nonlinearity management
Chaunsali, R., & Theocharis, G. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.100.014302 · Cited by 60
Mechanical Analogue of a Majorana Bound State
Chen, C., Lera, N., Chaunsali, R., Torrent, D., Alvarez, J. V., Yang, J., San-José, P., & Christensen, J. (2019) · Advanced Materials · doi:10.1002/adma.201904386 · Cited by 58
Self-citationPhotonic Topological Mode Bound to a Vortex
Menssen, A. J., Guan, J., Felce, D., Booth, M. J., & Walmsley, I. A. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.117401 · Cited by 58
Fermionic time-reversal symmetry in a photonic topological insulator
Maczewsky, L. J., Höckendorf, B., Kremer, M., Biesenthal, T., Heinrich, M., Alvermann, A., Fehske, H., & Szameit, A. (2020) · Nature Materials · doi:10.1038/s41563-020-0641-8 · Cited by 57
Poor man's topological quantum gate based on the Su-Schrieffer-Heeger model
Boross, P., Asbóth, J. K., Széchenyi, G., Oroszlány, L., & Pályi, A. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.100.045414 · Cited by 57
Symmetry-enforced three-dimensional Dirac phononic crystals
Cai, X., Ye, L., Qiu, C., Xiao, M., Yu, R., Ke, M., & Liu, Z. (2020) · Light Science & Applications · doi:10.1038/s41377-020-0273-4 · Cited by 55
Four-band non-Abelian topological insulator and its experimental realization
Jiang, T., Guo, Q., Zhang, R.-Y., Zhang, Z.-Q., Yang, B., & Chan, C. T. (2021) · Nature Communications · doi:10.1038/s41467-021-26763-1 · Cited by 51
Non-Hermitian higher-order Dirac semimetals
Ghorashi, S. A. A., Li, T., Sato, M., & Hughes, T. L. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.l161116 · Cited by 49
Experimental realization of non-Abelian permutations in a three-state non-Hermitian system
Tang, W., Ding, K., & Ma, G. (2022) · National Science Review · doi:10.1093/nsr/nwac010 · Cited by 48
Tunable Nonlinear Topological Insulator for Acoustic Waves
Darabi, A., & Leamy, M. J. (2019) · Physical Review Applied · doi:10.1103/physrevapplied.12.044030 · Cited by 48
Synthesis and observation of non-Abelian gauge fields in real spacePreprint
Yang, Y., Peng, C., Zhu, D., Buljan, H., Joannopoulos, J. D., Zhen, B., & Marin Soljacic, A. (2019) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 45
Experimental Observation of Non-Abelian Earring Nodal Links in Phononic Crystals
Wang, M., Liu, S., Ma, Q., Zhang, R.-Y., Wang, D., Guo, Q., Yang, B., Ke, M., Liu, Z., & Chan, C. T. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.246601 · Cited by 43
Pseudospin induced topological corner state at intersecting sonic lattices
Zhang, Z., Hu, B., Liu, F., Cheng, Y., Liu, X., & Christensen, J. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.220102 · Cited by 36
Self-citationTopologically valley-polarized edge states in elastic phononic plates yielded by lattice defects
Xia, B., Zhang, J., Tong, L., Zheng, S., & Man, X. (2022) · International Journal of Solids and Structures · doi:10.1016/j.ijsolstr.2021.111413 · Cited by 36
Three-dimensional non-Abelian quantum holonomy
Neef, V., Pinske, J., Klauck, F., Teuber, L., Kremer, M., Ehrhardt, M., Heinrich, M., Scheel, S., & Szameit, A. (2022) · Nature Physics · doi:10.1038/s41567-022-01807-5 · Cited by 35
Dualities and non-Abelian mechanics
Fruchart, M., Zhou, Y., & Vitelli, V. (2020) · Leiden Repository (Leiden University) · doi:10.5281/zenodo.3417425 · Cited by 33
Topological Euler insulators and their electric circuit realization
Ezawa, M. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.103.205303 · Cited by 30
Non-Hermitian Weyl semimetals: Non-Hermitian skin effect and non-Bloch bulk–boundary correspondence
Yang, X., Cao, Y., & Zhai, Y. (2021) · Chinese Physics B · doi:10.1088/1674-1056/ac3738 · Cited by 28
Straight nodal lines and waterslide surface states observed in acoustic metacrystals
Qiu, H., Qiu, C., Yu, R., Xiao, M., He, H., Ye, L., Ke, M., & Liu, Z. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.100.041303 · Cited by 21
Floquet Edge Multicolor Solitons
Ivanov, S. K., Kartashov, Y. V., Szameit, A., Torner, L., & Konotop, V. V. (2021) · Laser & Photonics Review · doi:10.1002/lpor.202100398 · Cited by 21
Topological Sound Pumping of Zero‐Dimensional Bound States
Gao, P., & Christensen, J. (2020) · Advanced Quantum Technologies · doi:10.1002/qute.202000065 · Cited by 19
Self-citationBound vortex light in an emulated topological defect in photonic lattices
Sheng, C., Wang, Y., Chang, Y., Wang, H., Lu, Y., Yang, Y., Zhu, S. N., Jin, X., & Liu, H. (2022) · Light Science & Applications · doi:10.1038/s41377-022-00931-4 · Cited by 18
Topological vortices for sound and light
Gao, P., & Christensen, J. (2021) · Nature Nanotechnology · doi:10.1038/s41565-021-00853-z · Cited by 14
Self-citationElectrons broken into pieces at crystal defects
Ortix, C. (2021) · Nature · doi:10.1038/d41586-021-00079-y · Cited by 6
Zhang, R.-Y., Cui, X., & Chan, C. T. (2023) · doi:10.14711/dataset/kkrjpl · Cited by 5
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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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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