Journals Articles Conferences News About CLP
Submit a paper Email Alert
Search
Search
Articles
Journals
News
Advanced Search
Top Searches
2D MaterialsTransformation opticsQuantum PhotonicsSmall lasersSemiconductor UV PhotonicsSupersymmetric microring laser arrays

Photonics Insights, Volume. 1, Issue 1, R02(2022)

Topological photonics in metamaterials Story Video

Shaojie Ma1, Biao Yang2, and Shuang Zhang1,3、*
Author Affiliations
  • 1Department of Physics, University of Hong Kong, Hong Kong, China
  • 2College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, China
  • 3Department of Electrical & Electronic Engineering, University of Hong Kong, Hong Kong, China
    • show less
    Full TextGet PDF
    Figures&Tables (6)
    Equations (24)
    References (178)
    Tools
    Paper Information
    Topics
    References(178)

    [1] A. Hatcher. Algebraic Topology(2002).

    [2] K. V. Klitzing, G. Dorda, M. Pepper. New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance. Phys. Rev. Lett., 45, 494(1980).

    [3] R. B. Laughlin. Quantized Hall conductivity in two dimensions. Phys. Rev. B, 23, 5632(1981).

    [4] D. J. Thouless et al. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett., 49, 405(1982).

    [5] K. S. Novoselov et al. Room-temperature quantum Hall effect in graphene. Science, 315, 1379(2007).

    [6] M. E. Cage et al. The Quantum Hall Effect(2012).

    [7] D. C. Tsui, H. L. Stormer, A. C. Gossard. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett., 48, 1559(1982).

    [8] G. Moore, N. Read. Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B, 360, 362(1991).

    [9] C. L. Kane, E. J. Mele. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett., 95, 146802(2005).

    [10] C. L. Kane, E. J. Mele. Quantum spin Hall effect in grapheme. Phys. Rev. Lett., 95, 226801(2005).

    [11] B. A. Bernevig, T. L. Hughes, S.-C. Zhang. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science, 314, 1757(2006).

    [12] B. A. Bernevig, S.-C. Zhang. Quantum spin Hall effect. Phys. Rev. Lett., 96, 106802(2006).

    [13] C.-X. Liu et al. Quantum anomalous Hall effect in Hg1–yMnyTe quantum wells. Phys. Rev. Lett., 101, 146802(2008).

    [14] C.-Z. Chang et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science, 340, 167(2013).

    [15] Y. Deng et al. Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4. Science, 367, 895(2020).

    [16] M. Stone. Quantum Hall Effect(1992).

    [17] H. L. Stormer, D. C. Tsui, A. C. Gossard. The fractional quantum Hall effect. Rev. Mod. Phys., 71, S298(1999).

    [18] J. Sinova et al. Spin Hall effects. Rev. Mod. Phys., 87, 1213(2015).

    [19] F. D. M. Haldane, S. Raghu. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett., 100, 013904(2008).

    [20] S. Raghu, F. D. M. Haldane. Analogs of quantum-Hall-effect edge states in photonic crystals. Phys. Rev. A, 78, 033834(2008).

    [21] Z. Wang et al. Reflection-free one-way edge modes in a gyromagnetic photonic crystal. Phys. Rev. Lett., 100, 013905(2008).

    [22] Z. Wang et al. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature, 461, 772(2009).

    [23] L. Lu et al. Weyl points and line nodes in gyroid photonic crystals. Nat. Photonics, 7, 294(2013).

    [24] M. C. Rechtsman et al. Photonic Floquet topological insulators. Nature, 496, 196(2013).

    [25] L. Lu, J. D. Joannopoulos, M. Soljačić. Topological photonics. Nat. Photonics, 8, 821(2014).

    [26] L. Lu et al. Experimental observation of Weyl points. Science, 349, 622(2015).

    [27] L. Lu et al. Symmetry-protected topological photonic crystal in three dimensions. Nat. Phys., 12, 337(2016).

    [28] L. Lu, J. D. Joannopoulos, M. Soljačić. Topological states in photonic systems. Nat. Phys., 12, 626(2016).

    [29] A. B. Khanikaev, G. Shvets. Two-dimensional topological photonics. Nat. Photonics, 11, 763(2017).

    [30] H. He et al. Topological negative refraction of surface acoustic waves in a Weyl phononic crystal. Nature, 560, 61(2018).

    [31] S. Stutzer et al. Photonic topological Anderson insulators. Nature, 560, 461(2018).

    [32] O. Zilberberg et al. Photonic topological boundary pumping as a probe of 4D quantum Hall physics. Nature, 553, 59(2018).

    [33] J. Noh et al. Topological protection of photonic mid-gap defect modes. Nat. Photonics, 12, 408(2018).

    [34] M. Li et al. Higher-order topological states in photonic kagome crystals with long-range interactions. Nat. Photonics, 14, 89(2019).

    [35] Z. Yang et al. Topological acoustics. Phys. Rev. Lett., 114, 114301(2015).

    [36] S. D. Huber. Topological mechanics. Nat. Phys., 12, 621(2016).

    [37] G. Ma, M. Xiao, C. T. Chan. Topological phases in acoustic and mechanical systems. Nat. Rev. Phys., 1, 281(2019).

    [38] N. P. Armitage, E. J. Mele, A. Vishwanath. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys., 90, 015001(2018).

    [39] T. Ozawa et al. Topological photonics. Rev. Mod. Phys., 91, 015006(2019).

    [40] B. Q. Lv, T. Qian, H. Ding. Experimental perspective on three-dimensional topological semimetals. Rev. Mod. Phys., 93, 025002(2021).

    [41] C. Simovski. Spectroscopy, material parameters of metamaterials (a review). Opt. Spectrosc., 107, 726(2009).

    [42] O. Sakai, K. Tachibana. Technology, plasmas as metamaterials: a review. Plasma Sources Sci. Technol., 21, 013001(2012).

    [43] S. Sun et al. Electromagnetic metasurfaces: physics and applications. Adv. Opt. Photonics, 11, 380(2019).

    [44] X. Yang et al. Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws. Nat. Photonics, 6, 450(2012).

    [45] A. Poddubny et al. Hyperbolic metamaterials. Nat. Photonics, 7, 948(2013).

    [46] Z. Liu et al. Far-field optical hyperlens magnifying sub-diffraction-limited objects. Science, 315, 1686(2007).

    [47] P. Shekhar, J. Atkinson, Z. Jacob. Hyperbolic metamaterials: fundamentals and applications. Nano Converg., 1, 14(2014).

    [48] J. K. Gansel et al. Gold helix photonic metamaterial as broadband circular polarizer. Science, 325, 1513(2009).

    [49] S. Zhang et al. Negative refractive index in chiral metamaterials. Phys. Rev. Lett., 102, 023901(2009).

    [50] V. S. Asadchy, A. Díaz-Rubio, S. Tretyakov. Bianisotropic metasurfaces: physics and applications. Nanophotonics, 7, 1069(2018).

    [51] L. Peng et al. Transverse photon spin of bulk electromagnetic waves in bianisotropic media. Nat. Photonics, 13, 878(2019).

    [52] S. Sun et al. Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves. Nat. Mater., 11, 426(2012).

    [53] F. Ding, A. Pors, S. Bozhevolnyi. Gradient metasurfaces: a review of fundamentals and applications. Rep. Prog. Phys., 81, 026401(2017).

    [54] H. Jia et al. Observation of chiral zero mode in inhomogeneous three-dimensional Weyl metamaterials. Science, 363, 148(2019).

    [55] L. Zhou, S. T. Chui. Eigenmodes of metallic ring systems: a rigorous approach. Phys. Rev. B, 74, 035419(2006).

    [56] R. K. Zhao, T. Koschny, C. M. Soukoulis. Chiral metamaterials: retrieval of the effective parameters with and without substrate. Opt. Express, 18, 14553(2010).

    [57] A. Raman, S. Fan. Photonic band structure of dispersive metamaterials formulated as a Hermitian eigenvalue problem. Phys. Rev. Lett., 104, 087401(2010).

    [58] Y. Liu, G. P. Wang, S. Zhang. A nonlocal effective medium description of topological Weyl metamaterials. Laser Photonics Rev., 15, 2100129(2021).

    [59] T. Van Mechelen, Z. Jacob. Photonic Dirac monopoles and skyrmions: spin-1 quantization [Invited]. Opt. Mater. Express, 9, 95(2018).

    [60] K. Y. Bliokh, D. Smirnova, F. Nori. Quantum spin Hall effect of light. Science, 348, 1448(2015).

    [61] Y. Yang et al. Topological triply degenerate point with double Fermi arcs. Nat. Phys., 15, 645(2019).

    [62] B. Bradlyn et al. Beyond Dirac and Weyl fermions: unconventional quasiparticles in conventional crystals. Science, 353, aaf5037(2016).

    [63] W. Gao et al. Topological photonic phase in chiral hyperbolic metamaterials. Phys. Rev. Lett., 114, 037402(2015).

    [64] B. Yang et al. Direct observation of topological surface-state arcs in photonic metamaterials. Nat. Commun., 8, 97(2017).

    [65] M. Xiao, Q. Lin, S. Fan. Hyperbolic Weyl point in reciprocal chiral metamaterials. Phys. Rev. Lett., 117, 057401(2016).

    [66] C. Zhang et al. Cycling Fermi arc electrons with Weyl orbits. Nat. Rev. Phys., 3, 660(2021).

    [67] B. Yan, C. Felser. Topological materials: Weyl semimetals. Annu. Rev. Condens. Matter Phys., 8, 337(2017).

    [68] B. Q. Lv et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X, 5, 031013(2015).

    [69] S. Jia, S. Y. Xu, M. Z. Hasan. Weyl semimetals, Fermi arcs and chiral anomalies. Nat. Mater., 15, 1140(2016).

    [70] A. A. Soluyanov et al. Type-II Weyl semimetals. Nature, 527, 495(2015).

    [71] H. B. Nielsen, M. Ninomiya. A no-go theorem for regularizing chiral fermions. Phys. Lett. B, 105, 219(1981).

    [72] H. B. Nielsen, M. Ninomiya. Absence of neutrinos on a lattice: (I). proof by homotopy theory. Nucl. Phys. B, 185, 20(1981).

    [73] H. B. Nielsen, M. Ninomiya. Absence of neutrinos on a lattice: (II). intuitive topological proof. Nucl. Phys. B, 193, 173(1981).

    [74] D. Friedan. A proof of the Nielsen-Ninomiya theorem. Commun. Math. Phys., 85, 481(1982).

    [75] X. Wan et al. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B, 83, 205101(2011).

    [76] B. Yang et al. Ideal Weyl points and helicoid surface states in artificial photonic crystal structures. Science, 359, 1013(2018).

    [77] Ş. K. Özdemir. Fermi arcs connect topological degeneracies. Science, 359, 995(2018).

    [78] W. Gao et al. Photonic Weyl degeneracies in magnetized plasma. Nat. Commun., 7, 12435(2016).

    [79] Y. Yang et al. Ideal unconventional Weyl point in a chiral photonic metamaterial. Phys. Rev. Lett., 125, 143001(2020).

    [80] A. A. Soluyanov et al. Type-II Weyl semimetals. Nature, 527, 495(2015).

    [81] Z.-M. Yu, Y. Yao, S. Yang. Predicted unusual magnetoresponse in type-II Weyl semimetals. Phys. Rev. Lett., 117, 077202(2016).

    [82] J. Ma et al. Nonlinear photoresponse of type-II Weyl semimetals. Nat. Mater., 18, 476(2019).

    [83] T. Dubcek et al. Weyl points in three-dimensional optical lattices: synthetic magnetic monopoles in momentum space. Phys. Rev. Lett., 114, 225301(2015).

    [84] M. Xiao et al. Synthetic gauge flux and Weyl points in acoustic systems. Nat. Phys., 11, 920(2015).

    [85] Q. Wang et al. Optical interface states protected by synthetic Weyl points. Phys. Rev. X, 7, 031032(2017).

    [86] C. Fang et al. Topological semimetals with helicoid surface states. Nat. Phys., 12, 936(2016).

    [87] A. Zyuzin, A. Burkov. Topological response in Weyl semimetals and the chiral anomaly. Phys. Rev. B, 86, 115133(2012).

    [88] D. Son, B. Spivak. Chiral anomaly and classical negative magnetoresistance of Weyl metals. Phys. Rev. B, 88, 104412(2013).

    [89] J. Zhou, H.-R. Chang, D. Xiao. Plasmon mode as a detection of the chiral anomaly in Weyl semimetals. Phys. Rev. B, 91, 035114(2015).

    [90] H. Cheng et al. Vortical reflection and spiraling Fermi arcs with Weyl metamaterials. Phys. Rev. Lett., 125, 093904(2020).

    [91] Y. Yang et al. Veselago lensing with Weyl metamaterials. Optica, 8, 249(2021).

    [92] H. Jia et al. Chiral transport of pseudospinors induced by synthetic gravitational field in photonic Weyl metamaterials. Phys. Rev. B, 104, 045132(2021).

    [93] F. Guinea, M. I. Katsnelson, A. K. Geim. Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering. Nat. Phys., 6, 30(2009).

    [94] R. Ilan, A. G. Grushin, D. I. Pikulin. Pseudo-electromagnetic fields in 3D topological semimetals. Nat. Rev. Phys., 2, 29(2020).

    [95] D. Wang et al. Photonic Weyl points due to broken time-reversal symmetry in magnetized semiconductor. Nat. Phys., 15, 1150(2019).

    [96] G.-G. Liu et al. Observation of Weyl point pair annihilation in a gyromagnetic photonic crystal(2021).

    [97] Z.-Y. Wang et al. Realization of an ideal Weyl semimetal band in a quantum gas with 3D spin-orbit coupling. Science, 372, 271(2021).

    [98] S.-M. Huang et al. New type of Weyl semimetal with quadratic double Weyl fermions. Proc. Natl. Acad. Sci. U S A, 113, 1180(2016).

    [99] T. Zhang et al. Double-Weyl phonons in transition-metal monosilicides. Phys. Rev. Lett., 120, 016401(2018).

    [100] H. He et al. Observation of quadratic Weyl points and double-helicoid arcs. Nat. Commun., 11, 1820(2020).

    [101] Q. Yan et al. Unconventional Weyl exceptional contours in non-Hermitian photonic continua. Photonics Res., 9, 2435(2021).

    [102] C. Fang et al. Topological nodal line semimetals. Chin. Phys. B, 25, 117106(2016).

    [103] Q. Xu et al. Topological nodal line semimetals in the CaP3 family of materials. Phys. Rev. B, 95, 045136(2017).

    [104] J.-M. Carter et al. Semimetal and topological insulator in perovskite iridates. Phys. Rev. B, 85, 115105(2012).

    [105] G. van Miert, C. Ortix, C. M. Smith. Topological origin of edge states in two-dimensional inversion-symmetric insulators and semimetals. 2D Mater., 4, 015023(2016).

    [106] G. Bian et al. Drumhead surface states and topological nodal-line fermions in TlTaSe2. Phys. Rev. B, 93, 121113(2016).

    [107] Y.-H. Chan et al. Ca3P2 and other topological semimetals with line nodes and drumhead surface states. Phys. Rev. B, 93, 205132(2016).

    [108] W. Gao et al. Experimental observation of photonic nodal line degeneracies in metacrystals. Nat. Commun., 9, 950(2018).

    [109] L. Xia et al. Observation of hourglass nodal lines in photonics. Phys. Rev. Lett., 122, 103903(2019).

    [110] E. Yang et al. Observation of non-Abelian nodal links in photonics. Phys. Rev. Lett., 125, 033901(2020).

    [111] Q. Guo et al. Experimental observation of non-Abelian topological charges and edge states. Nature, 594, 195(2021).

    [112] A. Demetriadou, J. B. Pendry. Taming spatial dispersion in wire metamaterial. J. Phys. Condens. Matter, 20, 295222(2008).

    [113] B. Zheng et al. Hourglass phonons jointly protected by symmorphic and nonsymmorphic symmetries. Phys. Rev. B, 104, L060301(2021).

    [114] Q. Wu, A. A. Soluyanov, T. Bzdusek. Non-Abelian band topology in noninteracting metals. Science, 365, 1273(2019).

    [115] T. Jiang et al. Four-band non-Abelian topological insulator and its experimental realization. Nat. Commun., 12, 6471(2021).

    [116] S. M. Young et al. Dirac semimetal in three dimensions. Phys. Rev. Lett., 108, 140405(2012).

    [117] Z. Liu et al. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science, 343, 864(2014).

    [118] S. Borisenko et al. Experimental realization of a three-dimensional Dirac semimetal. Phys. Rev. Lett., 113, 027603(2014).

    [119] Q. Guo et al. Three dimensional photonic Dirac points in metamaterials. Phys. Rev. Lett., 119, 213901(2017).

    [120] Q. Guo et al. Observation of three-dimensional photonic Dirac points and spin-polarized surface arcs. Phys. Rev. Lett., 122, 203903(2019).

    [121] S. Ma et al. Linked Weyl surfaces and Weyl arcs in photonic metamaterials. Science, 373, 572(2021).

    [122] A. B. Khanikaev et al. Photonic topological insulators. Nat. Mater., 12, 233(2013).

    [123] K. Hasebe. SO(5) Landau models and nested Nambu matrix geometry. Nucl. Phys. B, 956, 115012(2020).

    [124] C. N. Yang. SU2 monopole harmonics. J. Math. Phys., 19, 2622(1978).

    [125] C. N. Yang. Generalization of Dirac’s monopole to SU2 gauge fields. J. Math. Phys., 19, 320(1978).

    [126] B. Lian, S. C. Zhang. Five-dimensional generalization of the topological Weyl semimetal. Phys. Rev. B, 94, 041105(2016).

    [127] B. Lian, S. C. Zhang. Weyl semimetal and topological phase transition in five dimensions. Phys. Rev. B, 95, 235106(2017).

    [128] J. Y. Chen, B. Lian, S. C. Zhang. Doubling theorem and boundary states of five-dimensional Weyl semimetal. Phys. Rev. B, 100, 075112(2019).

    [129] X. L. Qi, T. L. Hughes, S. C. Zhang. Topological field theory of time-reversal invariant insulators. Phys. Rev. B, 78, 195424(2008).

    [130] Y. Yang et al. Realization of a three-dimensional photonic topological insulator. Nature, 565, 622(2019).

    [131] B. Yang et al. Momentum space toroidal moment in a photonic metamaterial. Nat. Commun., 12, 1784(2021).

    [132] R. S. Mong, J. H. Bardarson, J. E. Moore. Quantum transport and two-parameter scaling at the surface of a weak topological insulator. Phys. Rev. Lett., 108, 076804(2012).

    [133] T. Kaelberer et al. Toroidal dipolar response in a metamaterial. Science, 330, 1510(2010).

    [134] N. Papasimakis et al. Electromagnetic toroidal excitations in matter and free space. Nat. Mater., 15, 263(2016).

    [135] N. A. Spaldin, M. Fiebig, M. Mostovoy. The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect. J. Phys. Condens. Matter., 20, 434203(2008).

    [136] D. Xiao, W. Yao, Q. Niu. Valley-contrasting physics in graphene: magnetic moment and topological transport. Phys. Rev. Lett., 99, 236809(2007).

    [137] S. Roy et al. Tunable axial gauge fields in engineered Weyl semimetals: semiclassical analysis and optical lattice implementations. 2D Mater., 5, 024001(2018).

    [138] T. Dubček et al. Weyl points in three-dimensional optical lattices: synthetic magnetic monopoles in momentum space. Phys. Rev. Lett., 114, 225301(2015).

    [139] J. Bravo-Abad et al. Weyl points in photonic-crystal superlattices. 2D Mater., 2, 034013(2015).

    [140] Q. Wang et al. Optical interface states protected by synthetic Weyl points. Phys. Rev. X, 7, 031032(2017).

    [141] T. Ochiai. Floquet–Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice. J. Phys. Condens. Matter, 28, 425501(2016).

    [142] H. Wang, L. Zhou, Y. D. Chong. Floquet Weyl phases in a three-dimensional network model. Phys. Rev. B, 93, 144114(2016).

    [143] Y. Lu et al. Probing the Berry curvature and Fermi arcs of a Weyl circuit. Phys. Rev. B, 99, 020302(2019).

    [144] K. Luo, R. Yu, H. Weng. Topological nodal states in circuit lattice. Research, 2018, 6793752(2018).

    [145] F. Mei et al. Witnessing topological Weyl semimetal phase in a minimal circuit-QED lattice. Quantum Sci. Technol., 1, 015006(2016).

    [146] Z. Xiong et al. Hidden-symmetry-enforced nexus points of nodal lines in layer-stacked dielectric photonic crystals. Light Sci. Appl., 9, 176(2020).

    [147] T. Kawakami, X. Hu. Symmetry-guaranteed nodal-line semimetals in an FCC lattice. Phys. Rev. B, 96, 235307(2017).

    [148] Q. Yan et al. Experimental discovery of nodal chains. Nat. Phys., 14, 461(2018).

    [149] W. Deng et al. Nodal rings and drumhead surface states in phononic crystals. Nat. Commun., 10, 1769(2019).

    [150] H. Wang et al. Three-dimensional photonic Dirac points stabilized by point group symmetry. Phys. Rev. B, 93, 235155(2016).

    [151] A. Slobozhanyuk et al. Three-dimensional all-dielectric photonic topological insulator. Nat. Photonics, 11, 130(2017).

    [152] H.-X. Wang et al. Type-II Dirac photons. NPJ Quantum Mater., 2, 54(2017).

    [153] A. B. Khanikaev et al. Photonic topological insulators. Nat. Mater., 12, 233(2013).

    [154] X. Cheng et al. Robust reconfigurable electromagnetic pathways within a photonic topological insulator. Nat. Mater., 15, 542(2016).

    [155] T. Ma, G. Shvets. All-Si valley-Hall photonic topological insulator. New J. Phys., 18, 025012(2016).

    [156] C. He et al. Photonic topological insulator with broken time-reversal symmetry. Proc. Natl. Acad. Sci. U S A, 113, 4924(2016).

    [157] A. B. Khanikaev et al. Photonic topological insulators. Nat. Mater., 12, 233(2013).

    [158] N. Shahrubudin, T. C. Lee, R. Ramlan. An overview on 3D printing technology: technological, materials, and applications. Procedia Manuf., 35, 1286(2019).

    [159] C. Liu et al. Disorder-induced topological state transition in photonic metamaterials. Phys. Rev. Lett., 119, 183901(2017).

    [160] C. Liu et al. Disorder-immune photonics based on Mie-resonant dielectric metamaterials. Phys. Rev. Lett., 123, 163901(2019).

    [161] X. N. Liu et al. An elastic metamaterial with simultaneously negative mass density and bulk modulus. Appl. Phys. Lett., 98, 251907(2011).

    [162] X. Zhou, X. Liu, G. Hu. Elastic metamaterials with local resonances: an overview. Theor. Appl. Mech. Lett., 2, 041001(2012).

    [163] L. Lu, H. Gao, Z. Wang. Topological one-way fiber of second Chern number. Nat. Commun., 9, 1(2018).

    [164] L. Wang, S.-K. Jian, H. Yao. Topological photonic crystal with equifrequency Weyl points. Phys. Rev. A, 93, 061801(2016).

    [165] J. Xiong et al. Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science, 350, 413(2015).

    [166] L. Zhang, X.-Y. Song, F. Wang. Quantum oscillation in narrow-gap topological insulators. Phys. Rev. Lett., 116, 046404(2016).

    [167] P. L. Cai et al. Drastic pressure effect on the extremely large magnetoresistance in WTe2: quantum oscillation study. Phys. Rev. Lett., 115, 057202(2015).

    [168] G. Rosenberg, H.-M. Guo, M. Franz. Wormhole effect in a strong topological insulator. Phys. Rev. B, 82, 041104(2010).

    [169] Y. Yang et al. Synthesis and observation of non-Abelian gauge fields in real space. Science, 365, 1021(2019).

    [170] Y. Yang et al. Non-Abelian generalizations of the Hofstadter model: spin-orbit-coupled butterfly pairs. Light Sci. Appl., 9, 177(2020).

    [171] R. El-Ganainy et al. Non-Hermitian physics and PT symmetry. Nat. Phys., 14, 11(2018).

    [172] C. M. Bender. Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys., 70, 947(2007).

    [173] S. Yu, X. Piao, N. Park. Topological hyperbolic lattices. Phys. Rev. Lett., 125, 053901(2020).

    [174] E. Lustig, Y. Sharabi, M. Segev. Topological aspects of photonic time crystals. Optica, 5, 1390(2018).

    [175] G. G. Liu et al. Topological Anderson insulator in disordered photonic crystals. Phys. Rev. Lett., 125, 133603(2020).

    [176] W. A. Benalcazar, B. A. Bernevig, T. L. Hughes. Quantized electric multipole insulators. Science, 357, 61(2017).

    [177] S. Liu et al. Octupole corner state in a three-dimensional topological circuit. Light Sci. Appl., 9, 145(2020).

    [178] B. Xie et al. Higher-order band topology. Nat. Rev. Phys., 3, 520(2021).

    Tools

    Get Citation

    Copy Citation Text

    Shaojie Ma, Biao Yang, Shuang Zhang, "Topological photonics in metamaterials," Photon. Insights 1, R02 (2022)

    Download Citation

    EndNote(RIS)BibTexPlain Text
    Set citation alerts for article
    Save article for my favorites
    Paper Information

    Category: Review Articles

    Received: Feb. 16, 2022

    Accepted: May. 19, 2022

    Published Online: Aug. 3, 2022

    The Author Email: Shuang Zhang (shuzhang@hku.hk)

    DOI:10.3788/PI.2022.R02

    Topics

    laser devices and laser physics
    Lasers and Laser Optics
    Laser physics
    laser manufacturing
    Instrumentation, Measurement and Metrology