Volume 14 Issue 4
Jul.  2021
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Chinese Optics  > 2021  >  14(4): 935-954.
LIU Hui, WANG Hao-nan, XIE Bo-yang, CHENG Hua, TIAN Jian-guo, CHEN Shu-qi. Progress of two-dimensional photonic topological insulators[J]. Chinese Optics, 2021, 14(4): 935-954. doi: 10.37188/CO.2021-0076
Citation: LIU Hui, WANG Hao-nan, XIE Bo-yang, CHENG Hua, TIAN Jian-guo, CHEN Shu-qi. Progress of two-dimensional photonic topological insulators[J]. Chinese Optics, 2021, 14(4): 935-954. doi: 10.37188/CO.2021-0076
shu

Progress of two-dimensional photonic topological insulators

  • 1.

    The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, School of Physics and TEDA Institute of Applied Physics, Nankai University, Tianjin 300071, China

  • 2.

    The Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

  • 3.

    Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan 250358, China

Funds:  Supported by the National Key Research and Development Program of China (No. 2016YFA0301102, No. 2017YFA0303800), National Natural Science Fund for Distinguished Young Scholar (No. 11925403), National Natural Science Foundation of China (No. 11974193, No. 91856101, No. 11774186), Natural Science Foundation of Tianjin for Distinguished Young Scientists (No. 18JCJQJC45700)
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    Abstract
  • Inspired by the exciting discovery of topological insulators in condensed-state physics, some topological physics phenomena, such as integer quantum Hall effect, quantum spin Hall effect, topological semimetals and higher order topological insulators, have successively realized in photonic system. Thanks to the clean energy band, simple design and accurate production of samples, the optical system has gradually become an important platform for studying physical topological models and novel topological phenomena. Topological photonics provides new methods to manipulate light fields and photons. The topological protected edge states can realize the propagation of photons which immune to material defects and impurity. Such ideal transport states are unprecedented in traditional optics, which may lead to radical changes in novel integrated optical devices. In this review, based on the two-dimensional optical system, we briefly introduce the exciting developments of topological photonics, such as photonic integer quantum Hall effect, photonic quantum spin Hall effect, photonic Floquet topological insulators, topological Anderson insulators and photonic higher order topological insulators. We focus on the topological insulators mentioned above and its topological model and novel topological phenomena. Finally, we conclude with the novel topological effects in optics and their applications in novel optical device.

     

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  • [1]
    CHEN L, RONG Y W. Digital topological method for computing genus and the Betti numbers[J]. Topology and its Applications, 2010, 157(12): 1931-1936. doi: 10.1016/j.topol.2010.04.006
    [2]
    KLITZING K V, DORDA G, PEPPER M. New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance[J]. Physical Review Letters, 1980, 45(6): 494-497. doi: 10.1103/PhysRevLett.45.494
    [3]
    DEN NIJS M. Quantized Hall conductance in a two dimensional periodic potential[J]. Physica A:Statistical Mechanics and its Applications, 1984, 124(1-3): 199-210. doi: 10.1016/0378-4371(84)90239-5
    [4]
    HALDANE F D M, RAGHU S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry[J]. Physical Review Letters, 2008, 100(1): 013904. doi: 10.1103/PhysRevLett.100.013904
    [5]
    RAGHU S, HALDANE F D M. Analogs of quantum-Hall-effect edge states in photonic crystals[J]. Physical Review A, 2008, 78(3): 033834. doi: 10.1103/PhysRevA.78.033834
    [6]
    WANG ZH, CHONG Y D, JOANNOPOULOS J D, et al. Reflection-free one-way edge modes in a gyromagnetic photonic crystal[J]. Physical Review Letters, 2008, 100(1): 013905. doi: 10.1103/PhysRevLett.100.013905
    [7]
    WANG ZH, CHONG Y D, JOANNOPOULOS J D, et al. Observation of unidirectional backscattering-immune topological electromagnetic states[J]. Nature, 2009, 461(7265): 772-775. doi: 10.1038/nature08293
    [8]
    LIU SH Y, LU W L, LIN ZH F, et al. Magnetically controllable unidirectional electromagnetic waveguiding devices designed with metamaterials[J]. Applied Physics Letters, 2010, 97(20): 201113. doi: 10.1063/1.3520141
    [9]
    HE CH, CHEN X L, LU M H, et al. Left-handed and right-handed one-way edge modes in a gyromagnetic photonic crystal[J]. Journal of Applied Physics, 2010, 107(12): 123117. doi: 10.1063/1.3374470
    [10]
    QIU W J, WANG ZH, SOLJAČIĆ M. Broadband circulators based on directional coupling of one-way waveguides[J]. Optics Express, 2011, 19(22): 22248-22257. doi: 10.1364/OE.19.022248
    [11]
    WANG ZH Y, SHEN L F, YU Z H, et al. Highly efficient photonic-crystal splitters based on one-way waveguiding[J]. Journal of the Optical Society of America B, 2013, 30(1): 173-176. doi: 10.1364/JOSAB.30.000173
    [12]
    BAHARI B, TELLEZ-LIMON R, KANTÉ B. Topological terahertz circuits using semiconductors[J]. Applied Physics Letters, 2016, 109(14): 143501. doi: 10.1063/1.4963789
    [13]
    WU Y, LI CH, HU X Y, et al. Applications of topological photonics in integrated photonic devices[J]. Advanced Optical Materials, 2017, 5(18): 1700357. doi: 10.1002/adom.201700357
    [14]
    NI X, HE CH, SUN X CH, et al. Topologically protected one-way edge mode in networks of acoustic resonators with circulating air flow[J]. New Journal of Physics, 2015, 17(5): 053016. doi: 10.1088/1367-2630/17/5/053016
    [15]
    DING Y J, PENG Y G, ZHU Y F, et al. Experimental demonstration of acoustic chern insulators[J]. Physical Review Letters, 2019, 122(1): 014302. doi: 10.1103/PhysRevLett.122.014302
    [16]
    JO G B, GUZMAN J, THOMAS C K, et al. Ultracold atoms in a tunable optical kagome lattice[J]. Physical Review Letters, 2012, 108(4): 045305. doi: 10.1103/PhysRevLett.108.045305
    [17]
    SOLTAN-PANAHI P, STRUCK J, HAUKE P, et al. Multi-component quantum gases in spin-dependent hexagonal lattices[J]. Nature Physics, 2011, 7(5): 434-440. doi: 10.1038/nphys1916
    [18]
    NAKAJIMA S, TOMITA T, TAIE S, et al. Topological thouless pumping of ultracold fermions[J]. Nature Physics, 2016, 12(4): 296-300. doi: 10.1038/nphys3622
    [19]
    HUBER S D. Topological mechanics[J]. Nature Physics, 2016, 12(7): 621-623. doi: 10.1038/nphys3801
    [20]
    WANG P, LU L, BERTOLDI K. Topological phononic crystals with one-way elastic edge waves[J]. Physical Review Letters, 2015, 115(10): 104302. doi: 10.1103/PhysRevLett.115.104302
    [21]
    SÜSSTRUNK R, HUBER S D. Observation of phononic helical edge states in a mechanical topological insulator[J]. Science, 2015, 349(6243): 47-50. doi: 10.1126/science.aab0239
    [22]
    KANE C L, MELE E J. Z2 topological order and the quantum spin hall effect[J]. Physical Review Letters, 2005, 95(14): 146802. doi: 10.1103/PhysRevLett.95.146802
    [23]
    KANE C L, MELE E J. Quantum Spin hall effect in graphene[J]. Physical Review Letters, 2005, 95(22): 226801. doi: 10.1103/PhysRevLett.95.226801
    [24]
    BERNEVIG B A, HUGHES T L, ZHANG SH CH. Quantum spin hall effect and topological phase transition in HgTe quantum wells[J]. Science, 2006, 314(5806): 1757-1761. doi: 10.1126/science.1133734
    [25]
    KÖNIG M, WIEDMANN S, BRÜNE C, et al. Quantum Spin Hall Insulator State in HgTe Quantum Wells[J]. Science, 2007, 318(5851): 766-770. doi: 10.1126/science.1148047
    [26]
    HAFEZI M, DEMLER E A, LUKIN M D, et al. Robust optical delay lines with topological protection[J]. Nature Physics, 2011, 7(11): 907-912. doi: 10.1038/nphys2063
    [27]
    HAFEZI M, MITTAL S, FAN J, et al. Imaging topological edge states in silicon photonics[J]. Nature Photonics, 2013, 7(12): 1001-1005. doi: 10.1038/nphoton.2013.274
    [28]
    WU L H, HU X. Scheme for achieving a topological photonic crystal by using dielectric material[J]. Physical Review Letters, 2015, 114(22): 223901. doi: 10.1103/PhysRevLett.114.223901
    [29]
    YANG Y T, XU Y F, XU T, et al. Visualization of a unidirectional electromagnetic waveguide using topological photonic crystals made of dielectric materials[J]. Physical Review Letters, 2018, 120(21): 217401. doi: 10.1103/PhysRevLett.120.217401
    [30]
    ZHU X, WANG H X, XU CH Q, et al. Topological transitions in continuously deformed photonic crystals[J]. Physical Review B, 2018, 97(8): 085148. doi: 10.1103/PhysRevB.97.085148
    [31]
    JIA N Y, OWENS C, SOMMER A, et al. Time- and site-resolved dynamics in a topological circuit[J]. Physical Review X, 2015, 5(2): 021031. doi: 10.1103/PhysRevX.5.021031
    [32]
    KITAGAWA T, BERG E, RUDNER M, et al. Topological characterization of periodically driven quantum systems[J]. Physical Review B, 2010, 82(23): 235114. doi: 10.1103/PhysRevB.82.235114
    [33]
    LINDNER N H, REFAEL G, GALITSKI V. Floquet topological insulator in semiconductor quantum wells[J]. Nature Physics, 2011, 7(6): 490-495. doi: 10.1038/nphys1926
    [34]
    RECHTSMAN M C, ZEUNER J M, PLOTNIK Y, et al. Photonic Floquet topological insulators[J]. Nature, 2013, 496(7444): 196-200. doi: 10.1038/nature12066
    [35]
    RUDNER M S, LINDNER N H, BERG E, et al. Anomalous edge states and the bulk-edge correspondence for periodically driven two-dimensional systems[J]. Physical Review X, 2013, 3(3): 031005. doi: 10.1103/PhysRevX.3.031005
    [36]
    NATHAN F, RUDNER M S. Topological singularities and the general classification of Floquet-Bloch systems[J]. New Journal of Physics, 2015, 17(12): 125014. doi: 10.1088/1367-2630/17/12/125014
    [37]
    MUKHERJEE S, SPRACKLEN A, VALIENTE M, et al. Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice[J]. Nature Communications, 2017, 8(1): 3918.
    [38]
    MACZEWSKY L J, ZEUNER J M, NOLTE S, et al. Observation of photonic anomalous Floquet topological insulators[J]. Nature Communications, 2017, 8(1): 13756. doi: 10.1038/ncomms13756
    [39]
    LUMER Y, PLOTNIK Y, RECHTSMAN M C, et al. Self-localized states in photonic topological insulators[J]. Physical Review Letters, 2013, 111(24): 243905. doi: 10.1103/PhysRevLett.111.243905
    [40]
    LEYKAM D, RECHTSMAN M C, CHONG Y D. Anomalous topological phases and unpaired dirac cones in photonic floquet topological insulators[J]. Physical Review Letters, 2016, 117(1): 013902. doi: 10.1103/PhysRevLett.117.013902
    [41]
    KRAUS Y E, LAHINI Y, RINGEL Z, et al. Topological states and adiabatic pumping in quasicrystals[J]. Physical Review Letters, 2012, 109(10): 106402. doi: 10.1103/PhysRevLett.109.106402
    [42]
    ZILBERBERG O, HUANG SH, GUGLIELMON J, et al. Photonic topological boundary pumping as a probe of 4D quantum Hall physics[J]. Nature, 2018, 553(7686): 59-62. doi: 10.1038/nature25011
    [43]
    VERBIN M, ZILBERBERG O, LAHINI Y, et al. Topological pumping over a photonic Fibonacci quasicrystal[J]. Physical Review B, 2015, 91(6): 064201. doi: 10.1103/PhysRevB.91.064201
    [44]
    KE Y G, QIN X ZH, MEI F, et al. Topological phase transitions and thouless pumping of light in photonic waveguide arrays[J]. Laser &Photonics Reviews, 2016, 10(6): 995-1001.
    [45]
    BENALCAZAR W A, BERNEVIG B A, HUGHES T L. Quantized electric multipole insulators[J]. Science, 2017, 357(6346): 61-66. doi: 10.1126/science.aah6442
    [46]
    BENALCAZAR W A, BERNEVIG B A, HUGHES T L. Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators[J]. Physical Review B, 2017, 96(24): 245115. doi: 10.1103/PhysRevB.96.245115
    [47]
    PETERSON C W, BENALCAZAR W A, HUGHES T L, et al. A quantized microwave quadrupole insulator with topologically protected corner states[J]. Nature, 2018, 555(7696): 346-350. doi: 10.1038/nature25777
    [48]
    LI M Y, ZHIRIHIN D, GORLACH M, et al. Higher-order topological states in photonic kagome crystals with long-range interactions[J]. Nature Photonics, 2020, 14(2): 89-94. doi: 10.1038/s41566-019-0561-9
    [49]
    EZAWA M. Higher-order topological insulators and semimetals on the breathing kagome and pyrochlore lattices[J]. Physical Review Letters, 2018, 120(2): 026801. doi: 10.1103/PhysRevLett.120.026801
    [50]
    BENALCAZAR W A, LI T H, HUGHES T L. Quantization of fractional corner charge in Cn-symmetric higher-order topological crystalline insulators[J]. Physical Review B, 2019, 99(24): 245151. doi: 10.1103/PhysRevB.99.245151
    [51]
    ZHANG X J, XIAO M, CHENG Y, et al. Topological sound[J]. Communications Physics, 2018, 1(1): 97. doi: 10.1038/s42005-018-0094-4
    [52]
    YANG ZH J, GAO F, SHI X H, et al. Topological acoustics[J]. Physical Review Letters, 2015, 114(11): 114301. doi: 10.1103/PhysRevLett.114.114301
    [53]
    HE CH, NI X, GE H, et al. Acoustic topological insulator and robust one-way sound transport[J]. Nature Physics, 2016, 12(12): 1124-1129. doi: 10.1038/nphys3867
    [54]
    XIAO M, CHEN W J, HE W Y, et al. Synthetic gauge flux and Weyl points in acoustic systems[J]. Nature Physics, 2015, 11(11): 920-924. doi: 10.1038/nphys3458
    [55]
    XIE B Y, LIU H, CHENG H, et al. Experimental realization of type-II weyl points and fermi arcs in phononic crystal[J]. Physical Review Letters, 2019, 122(10): 104302. doi: 10.1103/PhysRevLett.122.104302
    [56]
    XIE B Y, LIU H, CHENG H, et al. Acoustic topological transport and refraction in a Kekulé Lattice[J]. Physical Review Applied, 2019, 11(4): 044086. doi: 10.1103/PhysRevApplied.11.044086
    [57]
    ROCKLIN D Z, ZHOU SH N, SUN K, et al. Transformable topological mechanical metamaterials[J]. Nature Communications, 2017, 8(1): 14201. doi: 10.1038/ncomms14201
    [58]
    LU L, GAO H ZH, WANG ZH. Topological one-way fiber of second Chern number[J]. Nature Communications, 2018, 9(1): 5384. doi: 10.1038/s41467-018-07817-3
    [59]
    YANG Y H, GAO ZH, XUE H R, et al. Realization of a three-dimensional photonic topological insulator[J]. Nature, 2019, 565(7741): 622-626. doi: 10.1038/s41586-018-0829-0
    [60]
    SLOBOZHANYUK A, MOUSAVI S H, NI X, et al. Three-dimensional all-dielectric photonic topological insulator[J]. Nature Photonics, 2017, 11(2): 130-136. doi: 10.1038/nphoton.2016.253
    [61]
    LU L, FANG CH, FU L, et al. Symmetry-protected topological photonic crystal in three dimensions[J]. Nature Physics, 2016, 12(4): 337-340. doi: 10.1038/nphys3611
    [62]
    YOUNG S M, ZAHEER S, TEO J C Y, et al. Dirac Semimetal in Three Dimensions[J]. Physical Review Letters, 2012, 108(14): 140405. doi: 10.1103/PhysRevLett.108.140405
    [63]
    LU L, FU L, JOANNOPOULOS J D, et al. Weyl points and line nodes in gyroid photonic crystals[J]. Nature Photonics, 2013, 7(4): 294-299. doi: 10.1038/nphoton.2013.42
    [64]
    GUO Q H, YOU O B, YANG B, et al. Observation of three-dimensional photonic dirac points and spin-polarized surface arcs[J]. Physical Review Letters, 2019, 122(20): 203903. doi: 10.1103/PhysRevLett.122.203903
    [65]
    CHENG H, GAO W L, BI Y G, et al. Vortical reflection and spiraling fermi arcs with weyl metamaterials[J]. Physical Review Letters, 2020, 125(9): 093904. doi: 10.1103/PhysRevLett.125.093904
    [66]
    OZAWA T, PRICE H M, GOLDMAN N, et al. Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics[J]. Physical Review A, 2016, 93(4): 043827. doi: 10.1103/PhysRevA.93.043827
    [67]
    LIN Q, SUN X Q, XIAO M, et al. A three-dimensional photonic topological insulator using a two-dimensional ring resonator lattice with a synthetic frequency dimension[J]. Science Advances, 2018, 4(10): eaat2774. doi: 10.1126/sciadv.aat2774
    [68]
    YUAN L Q, LIN Q, XIAO M, et al. Synthetic dimension in photonics[J]. Optica, 2018, 5(11): 1396-1405. doi: 10.1364/OPTICA.5.001396
    [69]
    LUSTIG E, WEIMANN S, PLOTNIK Y, et al. Photonic topological insulator in synthetic dimensions[J]. Nature, 2019, 567(7748): 356-360. doi: 10.1038/s41586-019-0943-7
    [70]
    CHEN Y, ZHANG Y L, SHEN ZH, et al. Synthetic gauge fields in a single optomechanical resonator[J]. Physical Review Letters, 2021, 126(12): 123603. doi: 10.1103/PhysRevLett.126.123603
    [71]
    LI G ZH, ZHENG Y L, DUTT A, et al. Dynamic band structure measurement in the synthetic space[J]. Science Advances, 2021, 7(2): eabe4335. doi: 10.1126/sciadv.abe4335
    [72]
    WANG Q, XIAO M, LIU H, et al. Optical interface states protected by synthetic weyl points[J]. Physical Review X, 2017, 7(3): 031032. doi: 10.1103/PhysRevX.7.031032
    [73]
    LIN Q, XIAO M, YUAN L Q, et al. Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension[J]. Nature Communications, 2016, 7(1): 13731. doi: 10.1038/ncomms13731
    [74]
    SUN B Y, LUO X W, GONG M, et al. Weyl semimetal phases and implementation in degenerate optical cavities[J]. Physical Review A, 2017, 96(1): 013857. doi: 10.1103/PhysRevA.96.013857
    [75]
    ZHANG Y, ZHU Y Y. Generation of Weyl points in coupled optical microdisk-resonator arrays via external modulation[J]. Physical Review A, 2017, 96(1): 013811. doi: 10.1103/PhysRevA.96.013811
    [76]
    LIU ZH ZH, ZHANG Q, QIN F F, et al. Surface states ensured by a synthetic Weyl point in one-dimensional plasmonic dielectric crystals with broken inversion symmetry[J]. Physical Review B, 2019, 99(8): 085441. doi: 10.1103/PhysRevB.99.085441
    [77]
    LEYKAM D, CHONG Y D. Edge solitons in nonlinear-photonic topological insulators[J]. Physical Review Letters, 2016, 117(14): 143901. doi: 10.1103/PhysRevLett.117.143901
    [78]
    PODDUBNY A N, SMIRNOVA D A. Ring Dirac solitons in nonlinear topological systems[J]. Physical Review A, 2018, 98(1): 013827. doi: 10.1103/PhysRevA.98.013827
    [79]
    HADAD Y, KHANIKAEV A B, ALÙ A. Self-induced topological transitions and edge states supported by nonlinear staggered potentials[J]. Physical Review B, 2016, 93(15): 155112. doi: 10.1103/PhysRevB.93.155112
    [80]
    GREENTREE A D, TAHAN C, COLE J H, et al. Quantum phase transitions of light[J]. Nature Physics, 2006, 2(12): 856-861. doi: 10.1038/nphys466
    [81]
    HARTMANN M J, BRANDÃO F G S L, PLENIO M B. Strongly interacting polaritons in coupled arrays of cavities[J]. Nature Physics, 2006, 2(12): 849-855. doi: 10.1038/nphys462
    [82]
    ANGELAKIS D G, SANTOS M F, BOSE S. Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays[J]. Physical Review A, 2007, 76(3): 031805(R). doi: 10.1103/PhysRevA.76.031805
    [83]
    ZHAO H, QIAO X D, WU T W, et al. Non-Hermitian topological light steering[J]. Science, 2019, 365(6458): 1163-1166. doi: 10.1126/science.aay1064
    [84]
    ZHEN B, HSU C W, IGARASHI Y, et al. Spawning rings of exceptional points out of Dirac cones[J]. Nature, 2015, 525(7569): 354-358. doi: 10.1038/nature14889
    [85]
    LEE T E. Anomalous edge state in a non-hermitian lattice[J]. Physical Review Letters, 2016, 116(13): 133903. doi: 10.1103/PhysRevLett.116.133903
    [86]
    SEPKHANOV R A, NILSSON J, BEENAKKER C W J. Proposed method for detection of the pseudospin- Berry phase in a photonic crystal with a Dirac spectrum[J]. Physical Review B, 2008, 78(4): 045122. doi: 10.1103/PhysRevB.78.045122
    [87]
    XIAO D, CHANG M C, NIU Q. Berry phase effects on electronic properties[J]. Reviews of Modern Physics, 2010, 82(3): 1959-2007. doi: 10.1103/RevModPhys.82.1959
    [88]
    THOULESS D J, KOHMOTO M, NIGHTINGALE M P, et al. Quantized hall conductance in a two-dimensional periodic potential[J]. Physical Review Letters, 1982, 49(6): 405-408. doi: 10.1103/PhysRevLett.49.405
    [89]
    SKIRLO S A, LU L, SOLJAČIĆ M. Multimode one-way waveguides of large chern numbers[J]. Physical Review Letters, 2014, 113(11): 113904. doi: 10.1103/PhysRevLett.113.113904
    [90]
    SKIRLO S A, LU L, IGARASHI Y, et al. Experimental observation of large chern numbers in photonic crystals[J]. Physical Review Letters, 2015, 115(25): 253901. doi: 10.1103/PhysRevLett.115.253901
    [91]
    YANG Y, POO Y, WU R X, et al. Experimental demonstration of one-way slow wave in waveguide involving gyromagnetic photonic crystals[J]. Applied Physics Letters, 2013, 102(23): 231113. doi: 10.1063/1.4809956
    [92]
    FU J X, LIU R J, LI Z Y. Robust one-way modes in gyromagnetic photonic crystal waveguides with different interfaces[J]. Applied Physics Letters, 2010, 97(4): 041112. doi: 10.1063/1.3470873
    [93]
    WANG D L, QIU CH W, RAKICH P T, et al.. Guide-wave photonic pulling force using one-way photonic chiral edge states[C]. CLEO: QELS_Fundamental Science 2015, OSA, 2015: FM2D. 7.
    [94]
    RYCERZ A, TWORZYDŁO J, BEENAKKER C W J. Valley filter and valley valve in graphene[J]. Nature Physics, 2007, 3(3): 172-175. doi: 10.1038/nphys547
    [95]
    JU L, SHI ZH W, NAIR N, et al. Topological valley transport at bilayer graphene domain walls[J]. Nature, 2015, 520(7549): 650-655. doi: 10.1038/nature14364
    [96]
    DONG J W, CHEN X D, ZHU H Y, et al. Valley photonic crystals for control of spin and topology[J]. Nature Materials, 2017, 16(3): 298-302. doi: 10.1038/nmat4807
    [97]
    WU X X, MENG Y, TIAN J X, et al. Direct observation of valley-polarized topological edge states in designer surface plasmon crystals[J]. Nature Communications, 2017, 8(1): 1304. doi: 10.1038/s41467-017-01515-2
    [98]
    NOH J, HUANG SH, CHEN K P, et al. Observation of photonic topological valley hall edge states[J]. Physical Review Letters, 2018, 120(6): 063902. doi: 10.1103/PhysRevLett.120.063902
    [99]
    CHEN Q L, ZHANG L, HE M J, et al. Valley-hall photonic topological insulators with dual-band kink states[J]. Advanced Optical Materials, 2019, 7(15): 1900036. doi: 10.1002/adom.201900036
    [100]
    HE X T, LIANG E T, YUAN J J, et al. A silicon-on-insulator slab for topological valley transport[J]. Nature Communications, 2019, 10(1): 872. doi: 10.1038/s41467-019-08881-z
    [101]
    LU J Y, QIU CH Y, YE L P, et al. Observation of topological valley transport of sound in sonic crystals[J]. Nature Physics, 2017, 13(4): 369-374. doi: 10.1038/nphys3999
    [102]
    LU J Y, QIU CH Y, DENG W Y, et al. Valley topological phases in bilayer sonic crystals[J]. Physical Review Letters, 2018, 120(11): 116802. doi: 10.1103/PhysRevLett.120.116802
    [103]
    ZHANG X J, LIU L, LU M H, et al. Valley-selective topological corner states in sonic crystals[J]. Physical Review Letters, 2021, 126(15): 156401. doi: 10.1103/PhysRevLett.126.156401
    [104]
    CHEN W J, JIANG SH J, CHEN X D, et al. Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide[J]. Nature Communications, 2014, 5(1): 5782. doi: 10.1038/ncomms6782
    [105]
    LAI K, MA T, BO X, et al. Experimental realization of a reflections-free compact delay line based on a photonic topological insulator[J]. Scientific Reports, 2016, 6(1): 28453. doi: 10.1038/srep28453
    [106]
    XIAO B, LAI K, YU Y, et al. Exciting reflectionless unidirectional edge modes in a reciprocal photonic topological insulator medium[J]. Physical Review B, 2016, 94(19): 195427. doi: 10.1103/PhysRevB.94.195427
    [107]
    CHENG X J, JOUVAUD C, NI X, et al. Robust reconfigurable electromagnetic pathways within a photonic topological insulator[J]. Nature Materials, 2016, 15(5): 542-548. doi: 10.1038/nmat4573
    [108]
    MA T, KHANIKAEV A B, MOUSAVI S H, et al. Guiding electromagnetic waves around sharp corners: topologically protected photonic transport in metawaveguides[J]. Physical Review Letters, 2015, 114(12): 127401. doi: 10.1103/PhysRevLett.114.127401
    [109]
    YVES S, FLEURY R, LEMOULT F, et al. Topological acoustic polaritons: Robust sound manipulation at the subwavelength scale[J]. New Journal of Physics, 2017, 19(7): 075003. doi: 10.1088/1367-2630/aa66f8
    [110]
    GORLACH M A, NI X, SMIRNOVA D A, et al. Far-field probing of leaky topological states in all-dielectric metasurfaces[J]. Nature Communications, 2018, 9(1): 909. doi: 10.1038/s41467-018-03330-9
    [111]
    BARIK S, KARASAHIN A, FLOWER C, et al. A topological quantum optics interface[J]. Science, 2018, 359(6376): 666-668. doi: 10.1126/science.aaq0327
    [112]
    IMHOF S, BERGER C, BAYER F, et al. Topolectrical-circuit realization of topological corner modes[J]. Nature Physics, 2018, 14(9): 925-929. doi: 10.1038/s41567-018-0246-1
    [113]
    LEE C H, IMHOF S, BERGER C, et al. Topolectrical circuits[J]. Communications Physics, 2018, 1(1): 39. doi: 10.1038/s42005-018-0035-2
    [114]
    LU Y H, JIA N Y, SU L, et al. Probing the Berry curvature and Fermi arcs of a Weyl circuit[J]. Physical Review B, 2019, 99(2): 020302(R). doi: 10.1103/PhysRevB.99.020302
    [115]
    WALLRAFF A, SCHUSTER D I, BLAIS A, et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics[J]. Nature, 2004, 431(7005): 162-167. doi: 10.1038/nature02851
    [116]
    SALA V G, SOLNYSHKOV D D, CARUSOTTO I, et al. Spin-orbit coupling for photons and polaritons in microstructures[J]. Physical Review X, 2015, 5(1): 011034. doi: 10.1103/PhysRevX.5.011034
    [117]
    CAYSSOL J, DÓRA B, SIMON F, et al. Floquet topological insulators[J]. Physica Status Solidi, 2013, 7(1-2): 101-108. doi: 10.1002/pssr.201206451
    [118]
    FANG K J, YU Z F, FAN SH H. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation[J]. Nature Photonics, 2012, 6(11): 782-787. doi: 10.1038/nphoton.2012.236
    [119]
    OZAWA T, PRICE H M, AMO A, et al. Topological photonics[J]. Reviews of Modern Physics, 2019, 91(1): 015006. doi: 10.1103/RevModPhys.91.015006
    [120]
    PASEK M, CHONG Y D. Network models of photonic Floquet topological insulators[J]. Physical Review B, 2014, 89(7): 075113. doi: 10.1103/PhysRevB.89.075113
    [121]
    GAO F, GAO ZH, SHI X H, et al. Probing topological protection using a designer surface plasmon structure[J]. Nature Communications, 2016, 7(48): 11619.
    [122]
    YANG ZH J, LUSTIG E, LUMER Y, et al. Photonic Floquet topological insulators in a fractal lattice[J]. Light:Science &Applications, 2020, 9(1): 128.
    [123]
    LI J, CHU R L, JAIN J K, et al. Topological anderson insulator[J]. Physical Review Letters, 2009, 102(13): 136806. doi: 10.1103/PhysRevLett.102.136806
    [124]
    GROTH C W, WIMMER M, AKHMEROV A R, et al. Theory of the topological anderson insulator[J]. Physical Review Letters, 2009, 103(19): 196805. doi: 10.1103/PhysRevLett.103.196805
    [125]
    TITUM P, LINDNER N H, RECHTSMAN M C, et al. Disorder-induced Floquet topological insulators[J]. Physical Review Letters, 2015, 114(5): 056801. doi: 10.1103/PhysRevLett.114.056801
    [126]
    TITUM P, LINDNER N H, REFAEL G. Disorder-induced transitions in resonantly driven Floquet topological insulators[J]. Physical Review B, 2017, 96(5): 054207. doi: 10.1103/PhysRevB.96.054207
    [127]
    STÜTZER S, PLOTNIK Y, LUMER Y, et al. Photonic topological Anderson insulators[J]. Nature, 2018, 560(7719): 461-465. doi: 10.1038/s41586-018-0418-2
    [128]
    LIU G G, YANG Y H, REN X, et al. Topological anderson insulator in disordered photonic crystals[J]. Physical Review Letters, 2020, 125(13): 133603. doi: 10.1103/PhysRevLett.125.133603
    [129]
    HUANG H Q, LIU F. Theory of spin Bott index for quantum spin Hall states in nonperiodic systems[J]. Physical Review B, 2018, 98(12): 125130. doi: 10.1103/PhysRevB.98.125130
    [130]
    HUANG H Q, LIU F. Quantum Spin hall effect and spin bott index in a quasicrystal lattice[J]. Physical Review Letters, 2018, 121(12): 126401. doi: 10.1103/PhysRevLett.121.126401
    [131]
    SHINDOU R, MURAKAMI S. Effects of disorder in three-dimensional Z2 quantum spin Hall systems[J]. Physical Review B, 2009, 79(4): 045321. doi: 10.1103/PhysRevB.79.045321
    [132]
    HUANG X Q, LU J Y, YAN Z B, et al.. Acoustic corner states in topological insulators with built-in Zeeman-like fields[J]. arXiv: 2008.06272, 2020.
    [133]
    LORING T A, HASTINGS M B. Disordered topological insulators via C*-algebras[J]. EPL (Europhysics Letters), 2011, 92(6): 67004.
    [134]
    HASTINGS M B, LORING T A. Topological insulators and C*-algebras: theory and numerical practice[J]. Annals of Physics, 2011, 326(7): 1699-1759. doi: 10.1016/j.aop.2010.12.013
    [135]
    LORING T A. A guide to the bott index and localizer index[J]. arXiv: 1907.11791, 2019.
    [136]
    TONIOLO D. On the equivalence of the Bott index and the Chern number on a torus, and the quantization of the Hall conductivity with a real space Kubo formula[J]. arXiv: 1708.05912, 2017.
    [137]
    MEIER E J, AN F A, DAUPHIN A, et al. Observation of the topological Anderson insulator in disordered atomic wires[J]. Science, 2018, 362(6417): 929-933. doi: 10.1126/science.aat3406
    [138]
    GUO H M, ROSENBERG G, REFAEL G, et al. Topological Anderson insulator in three dimensions[J]. Physical Review Letters, 2010, 105(21): 216601. doi: 10.1103/PhysRevLett.105.216601
    [139]
    SMIRNOVA D, LEYKAM D, CHONG Y D, et al. Nonlinear topological photonics[J]. Applied Physics Reviews, 2020, 7(2): 021306. doi: 10.1063/1.5142397
    [140]
    DU Z Z, WANG C M, LI SH, et al. Disorder-induced nonlinear Hall effect with time-reversal symmetry[J]. Nature Communications, 2019, 10(1): 3047. doi: 10.1038/s41467-019-10941-3
    [141]
    ZENG Y Q, CHATTOPADHYAY U, ZHU B F, et al. Electrically pumped topological laser with valley edge modes[J]. Nature, 2020, 578(7794): 246-250. doi: 10.1038/s41586-020-1981-x
    [142]
    BANDRES M A, WITTEK S, HARARI G, et al. Topological insulator laser: Experiments[J]. Science, 2018, 359(6381): eaar4005. doi: 10.1126/science.aar4005
    [143]
    TANG L ZH, ZHANG L F, ZHANG G Q, et al. Topological Anderson insulators in two-dimensional non-Hermitian disordered systems[J]. Physical Review A, 2020, 101(6): 063612. doi: 10.1103/PhysRevA.101.063612
    [144]
    LUO X W, ZHANG CH W. Non-hermitian disorder-induced topological insulators[J]. arXiv: 1912.10652, 2019.
    [145]
    SILVEIRINHA M G. Proof of the bulk-edge correspondence through a link between topological photonics and fluctuation-electrodynamics[J]. Physical Review X, 2019, 9(1): 011037. doi: 10.1103/PhysRevX.9.011037
    [146]
    LU L, JOANNOPOULOS J D, SOLJAČIĆ M. Topological photonics[J]. Nature Photonics, 2014, 8(11): 821-829. doi: 10.1038/nphoton.2014.248
    [147]
    PARAMESWARAN S A, WAN Y. Topological insulators turn a corner[J]. Physics, 2017, 10: 132. doi: 10.1103/Physics.10.132
    [148]
    SCHINDLER F, COOK A M, VERGNIORY M G, et al. Higher-order topological insulators[J]. Science Advances, 2018, 4(6): eaat0346. doi: 10.1126/sciadv.aat0346
    [149]
    SERRA-GARCIA M, PERI V, SÜSSTRUNK R, et al. Observation of a phononic quadrupole topological insulator[J]. Nature, 2018, 555(7696): 342-345. doi: 10.1038/nature25156
    [150]
    MITTAL S, ORRE V V, ZHU G Y, et al. Photonic quadrupole topological phases[J]. Nature Photonics, 2019, 13(10): 692-696. doi: 10.1038/s41566-019-0452-0
    [151]
    HE L, ADDISON Z, MELE E J, et al. Quadrupole topological photonic crystals[J]. Nature Communications, 2020, 11(1): 3119. doi: 10.1038/s41467-020-16916-z
    [152]
    ZHOU X X, LIN Z K, LU W X, et al. Twisted quadrupole topological photonic crystals[J]. Laser &Photonics Reviews, 2020, 14(8): 2000010.
    [153]
    SU W P, SCHRIEFFER J R, HEEGER A J. Solitons in polyacetylene[J]. Physical Review Letters, 1979, 42(25): 1698-1701. doi: 10.1103/PhysRevLett.42.1698
    [154]
    XUE H R, YANG Y H, GAO F, et al. Acoustic higher-order topological insulator on a kagome lattice[J]. Nature Materials, 2019, 18(2): 108-112. doi: 10.1038/s41563-018-0251-x
    [155]
    LIU F, WAKABAYASHI K. Novel topological phase with a zero berry curvature[J]. Physical Review Letters, 2017, 118(7): 076803. doi: 10.1103/PhysRevLett.118.076803
    [156]
    XIE B Y, WANG H F, WANG H X, et al. Second-order photonic topological insulator with corner states[J]. Physical Review B, 2018, 98(20): 205147. doi: 10.1103/PhysRevB.98.205147
    [157]
    CHEN X D, DENG W M, SHI F L, et al. Direct observation of corner states in second-order topological photonic crystal slabs[J]. Physical Review Letters, 2019, 122(23): 233902. doi: 10.1103/PhysRevLett.122.233902
    [158]
    XIE B Y, SU G X, WANG H F, et al. Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals[J]. Physical Review Letters, 2019, 122(23): 233903. doi: 10.1103/PhysRevLett.122.233903
    [159]
    KIM M, RHO J. Topological edge and corner states in a two-dimensional photonic Su-Schrieffer-Heeger lattice[J]. Nanophotonics, 2020, 9(10): 3227-3234. doi: 10.1515/nanoph-2019-0451
    [160]
    OTA Y, LIU F, KATSUMI R, et al. Photonic crystal nanocavity based on a topological corner state[J]. Optica, 2019, 6(6): 786-789. doi: 10.1364/OPTICA.6.000786
    [161]
    NOH J, BENALCAZAR W A, HUANG SH, et al. Topological protection of photonic mid-gap defect modes[J]. Nature Photonics, 2018, 12(7): 408-415. doi: 10.1038/s41566-018-0179-3
    [162]
    EL HASSAN A, KUNST F K, MORITZ A, et al. Corner states of light in photonic waveguides[J]. Nature Photonics, 2019, 13(10): 697-700. doi: 10.1038/s41566-019-0519-y
    [163]
    XIE X, ZHANG W X, HE X W, et al. Cavity quantum electrodynamics with second-order topological corner state[J]. Laser &Photonics Reviews, 2020, 14(8): 1900425.
    [164]
    ZHANG W X, XIE X, HAO H M, et al. Low-threshold topological nanolasers based on the second-order corner state[J]. Light:Science &Applications, 2020, 9(1): 109.
    [165]
    ZHANG L, YANG Y H, LIN Z K, et al. Higher-order topological states in surface-wave photonic crystals[J]. Advsnced Science, 2020, 7(6): 1902724.
    [166]
    LUO X W, ZHANG C W. Higher-order topological corner states induced by gain and loss[J]. Physical Review Letters, 2019, 123(7): 73601. doi: 10.1103/PhysRevLett.123.073601
    [167]
    LIU T, ZHANG Y R, AI Q, et al. Second-order topological phases in non-hermitian systems[J]. Physical Review Letters, 2019, 122(7): 76801. doi: 10.1103/PhysRevLett.122.076801
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