Volume 14 Issue 4
Jul.  2021
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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

Progress of two-dimensional photonic topological insulators

doi: 10.37188/CO.2021-0076
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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  • 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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    HUBER S D. Topological mechanics[J]. Nature Physics, 2016, 12(7): 621-623. doi: 10.1038/nphys3801
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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.
    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
    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
    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
    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
    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
    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
    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.
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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.
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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.
    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.
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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.
    LORING T A, HASTINGS M B. Disordered topological insulators via C*-algebras[J]. EPL (Europhysics Letters), 2011, 92(6): 67004.
    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
    LORING T A. A guide to the bott index and localizer index[J]. arXiv: 1907.11791, 2019.
    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.
    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
    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
    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
    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
    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
    BANDRES M A, WITTEK S, HARARI G, et al. Topological insulator laser: Experiments[J]. Science, 2018, 359(6381): eaar4005. doi: 10.1126/science.aar4005
    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
    LUO X W, ZHANG CH W. Non-hermitian disorder-induced topological insulators[J]. arXiv: 1912.10652, 2019.
    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
    LU L, JOANNOPOULOS J D, SOLJAČIĆ M. Topological photonics[J]. Nature Photonics, 2014, 8(11): 821-829. doi: 10.1038/nphoton.2014.248
    PARAMESWARAN S A, WAN Y. Topological insulators turn a corner[J]. Physics, 2017, 10: 132. doi: 10.1103/Physics.10.132
    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
    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
    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
    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
    ZHOU X X, LIN Z K, LU W X, et al. Twisted quadrupole topological photonic crystals[J]. Laser &Photonics Reviews, 2020, 14(8): 2000010.
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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.
    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.
    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.
    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
    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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