[1] Thouless D J, Kohmoto M, Nightingale M P et al. Quantized Hall conductance in a two-dimensional periodic potential[J]. Physical Review Letters, 49, 405-408(1982).

[2] Haldane F D. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “parity anomaly”[J]. Physical Review Letters, 61, 2015-2018(1988).

[3] Hasan M Z, Kane C L. Colloquium: topological insulators[J]. Reviews of Modern Physics, 82, 3045-3067(2010).

[4] Lu L, Joannopoulos J D, Soljačić M. Topological photonics[J]. Nature Photonics, 8, 821-829(2014).

[5] Hui Z F, Xie J B, He X D et al. Multichannel diffuse correlation spectroscopy topography system[J]. Chinese Journal of Lasers, 46, 0907002(2019).

[6] Fang Y T, He H Q, Hu J X. Transforming unidirectional edge waveguide into unidirectional air waveguide[J]. IEEE Journal of Selected Topics in Quantum Electronics, 22, 293-301(2016).

[7] Wang M J, Lin N N. Propagation characteristics of Laguerre-Gaussian beams in periodic films with topological insulators[J]. Chinese Journal of Lasers, 47, 0105003(2020).

[8] Wu Y H, Li X X, Fang Y T. Evolution and reversal of topological edge states at optical frequencies from a two-dimensional photonic crystal[J]. Journal of Optics, 22, 105102(2020).

[9] Qi X L, Zhang S C. The quantum spin Hall effect and topological insulators[J]. Physics Today, 63, 33-38(2010).

[10] Chen X D, Zhao F L, Chen M et al. Valley-contrasting physics in all-dielectric photonic crystals: orbital angular momentum and topological propagation[J]. Physical Review B, 96, 020202(2017).

[11] Lu J Y, Qiu C Y, Ye L P et al. Observation of topological valley transport of sound in sonic crystals[J]. Nature Physics, 13, 369-374(2017).

[12] Xu L, Wang H X, Xu Y D et al. Accidental degeneracy in photonic bands and topological phase transitions in two-dimensional core-shell dielectric photonic crystals[J]. Optics Express, 24, 018059(2016).

[13] Fang Y T, Wang Z X, Fan E P et al. Topological phase transition based on structure reversal of two-dimensional photonic crystals and construction of topological edge states[J]. Acta Physica Sinica, 69, 184101(2020).

[14] Wu L H, Hu X. Scheme for achieving a topological photonic crystal by using dielectric material[J]. Physical Review Letters, 114, 223901(2015).

[15] Shalaev M I, Desnavi S, Walasik W et al. Reconfigurable topological photonic crystal[J]. New Journal of Physics, 20, 023040(2018).

[16] Geng H, Ji Q S, Zhang C X et al. Time-reversal-symmetry broken quantum spin Hall in Lieb lattice[J]. Acta Physica Sinica, 66, 127303(2017).

[17] Gao Y F, Jiang Z, Zhang L L et al. Unidirectional propagation of coupled edge states in sandwich topological photonic crystals[J]. Journal of Applied Physics, 124, 213107(2018).

[18] Zhu X, Wang H X, Xu C Q et al. Topological transitions in continuously deformed photonic crystals[J]. Physical Review B, 97, 085148(2018).

[19] Barik S, Miyake H, DeGottardi W et al. Two-dimensionally confined topological edge states in photonic crystals[J]. New Journal of Physics, 18, 113013(2016).

[20] Chen Z G, Mei J, Sun X C et al. Multiple topological phase transitions in a gyromagnetic photonic crystal[J]. Physical Review A, 95, 043827(2017).

[21] Wang Y L, Li Y. Pseudospin states and topological phase transitions in twodimensional photonic crystals made of dielectric materials[J]. Acta Physica Sinica, 69, 094206(2020).

[22] Wang H X, Xu L, Jiang J H. Dirac photonic crystal[J]. Acta Physica Sinica, 66, 220302(2017).

[23] Jiang Z, Gao Y F, He L et al. Manipulation of pseudo-spin guiding and flat bands for topological edge states[J]. Physical Chemistry Chemical Physics: PCCP, 21, 11367-11375(2019).

[24] Wu X, Meng Y, Tian J et al. Direct observation of valley-polarized topological edge states in designer surface plasmon crystals[J]. Nature Communications, 8, 1304(2017).

[25] Pei D L, Yang T, Chen M et al. Broadband periodic and aperiodic acoustic topological insulator based on composite honeycomb structure[J]. Acta Physica Sinica, 69, 024302(2020).

[26] Mei J, Chen Z, Wu Y. Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals[J]. Scientific Reports, 6, 32752(2016).

[27] Huang X Q, Yang Y T, Hang Z H et al. Geometric phase induced interface states in mutually inverted two-dimensional photonic crystals[J]. Physical Review B, 93, 085415(2016).