[1] 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, 45, 494(1980).

[2] 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).

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

[4] Kane C L, Mele E J. Quantum spin Hall effect in graphene[J]. Physical Review Letters, 95, 226801(2005).

[5] Bernevig B A, Hughes T L, Zhang S C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells[J]. Science, 314, 1757-1761(2006).

[6] König M, Wiedmann S, Brüne C et al. Quantum spin Hall insulator state in HgTe quantum wells[J]. Science, 318, 766-770(2007).

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

[8] Qi X L, Zhang S C. Topological insulators and superconductors[J]. Reviews of Modern Physics, 83, 1057(2011).

[9] Weng H M, Yu R, Hu X et al. Quantum anomalous Hall effect and related topological electronic states[J]. Advances in Physics, 64, 227-282(2015).

[10] Chen J F, Liang W Y, Li Z Y. Progress of topological photonic state in magneto-optical photonic crystal[J]. Acta Optica Sinica, 41, 0823015(2021).

[11] Liu C, Guo X W, Li S R et al. Theory and application of edge states in topological photonic crystals[J]. Laser & Optoelectronics Progress, 59, 0100001(2022).

[12] Li X M, Zhang M D, Zhu X D et al. Unidirectional wave guide based on valley Hall effect in optical communication band[J]. Acta Optica Sinica, 41, 1913001(2021).

[13] Haldane F D M, Raghu S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry[J]. Physical Review Letters, 100, 013904(2008).

[14] Wang Z, Chong Y D, Joannopoulos J D et al. Observation of unidirectional backscattering-immune topological electromagnetic states[J]. Nature, 461, 772-775(2009).

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

[16] 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, 120, 217401(2018).

[17] He C, Ni X, Ge H et al. Acoustic topological insulator and robust one-way sound transport[J]. Nature Physics, 12, 1124-1129(2016).

[18] Zhang Z W, Wei Q, Cheng Y et al. Topological creation of acoustic pseudospin multipoles in a flow-free symmetry-broken metamaterial lattice[J]. Physical Review Letters, 118, 084303(2017).

[19] Yu S Y, He C, Wang Z et al. Elastic pseudospin transport for integratable topological phononic circuits[J]. Nature Communications, 9, 3072(2018).

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