Experimental observation of multiple edge and corner states in photonic slabs heterostructures

Mingxing Li; Yueke Wang; Tian Sang; Hongchen Chu; Yun Lai; Guofeng Yang

doi:10.1364/PRJ.440640

[1] D. J. Thouless, M. Kohmoto, M. P. Nightingale, M. den Nijs. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett., 49, 405-408(1982).

[2] 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).

[3] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, M. Z. Hasan. A topological Dirac insulator in a quantum spin Hall phase. Nature, 452, 970-974(2008).

[4] X. L. Qi, S. C. Zhang. Topological insulators and superconductors. Rev. Mod. Phys., 83, 1057-1110(2011).

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

[6] B. Y. Xie, G. X. Su, H. F. Wang, H. Su, X. P. Shen, P. Zhan, M. H. Lu, Z. L. Wang, Y. F. Chen. Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals. Phys. Rev. Lett., 122, 233903(2019).

[7] X. D. Chen, W. M. Deng, F. L. Shi, F. L. Zhao, M. Chen, J. W. Dong. Direct observation of corner states in second-order topological photonic crystal slabs. Phys. Rev. Lett., 122, 233902(2019).

[8] A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, G. Shvets. Photonic topological insulators. Nat. Mater., 12, 233-239(2013).

[9] J. Noh, W. A. Benalcazar, S. Huang, M. J. Collins, K. P. Chen, T. L. Hughes, M. C. Rechtsman. Topological protection of photonic mid-gap defect modes. Nat. Photonics, 12, 408-415(2018).

[10] X. Huang, Y. Lai, Z. H. Hang, H. Zheng, C. T. Chan. Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials. Nat. Mater., 10, 582-586(2011).

[11] L. H. Wu, X. Hu. Scheme for achieving a topological photonic crystal by using dielectric material. Phys. Rev. Lett., 114, 223901(2015).

[12] C. He, X. Ni, H. Ge, X. C. Sun, Y. B. Chen, M. H. Lu, X. P. Liu, Y. F. Chen. Acoustic topological insulator and robust one-way sound transport. Nat. Phys., 12, 1124-1129(2016).

[13] X. Ni, M. Weiner, A. Alù, A. B. Khanikaev. Observation of higher-order topological acoustic states protected by generalized chiral symmetry. Nat. Mater., 18, 113-120(2019).

[14] Z. J. Yang, F. Gao, X. Lin, B. L. Zhang. Topological acoustics. Phys. Rev. Lett., 114, 114301(2015).

[15] M. Xiao, G. C. Ma, Z. Y. Yang, P. Sheng, Z. Q. Zhang, C. T. Chan. Geometric phase and band inversion in periodic acoustic systems. Nat. Phys., 11, 240-244(2015).

[16] H. L. He, C. Y. Qiu, L. P. Ye, X. Y. Fan, M. Z. Ke, Z. Y. Liu. Topological negative refraction of surface acoustic waves in a Weyl phononic crystal. Nature, 560, 61-64(2018).

[17] Y. T. Yang, Y. F. Xu, T. Xu, X. Hu, Z. H. Hang. Visualization of a unidirectional electromagnetic waveguide using topological photonic crystals made of dielectric materials. Phys. Rev. Lett., 120, 217401(2018).

[18] Y. Poo, R. X. Wu, Z. Lin, Y. Yang, C. T. Chan. Experimental realization of self-guiding unidirectional electromagnetic edge states. Phys. Rev. Lett., 106, 093903(2011).

[19] X. Ni, C. He, X. C. Sun, X. P. Liu, M. H. Lu, L. Feng, Y. F. Chen. Topologically protected one-way edge mode in networks of acoustic resonators with circulating air flow. New J. Phys., 17, 053016(2015).

[20] G. C. Wei, Z. Z. Liu, Y. C. Liu, D. S. Zhang, J. J. Xiao. Frequency selective topological edge wave routing in meta-structures made of cylinders. Opt. Lett., 45, 5608-5611(2020).

[21] J. F. Chen, W. Y. Liang, Z. Y. Li. Broadband dispersionless topological slow light. Opt. Lett., 45, 4964-4967(2020).

[22] H. Y. Zhang, L. Qian, C. Y. Wang, C. C. Lu. Topological rainbow based on graded topological photonic crystals. Opt. Lett., 46, 1237-1240(2021).

[23] W. A. Benalcazar, B. A. Bernevig, T. L. Hughes. Quantized electric multipole insulators. Science, 357, 61-66(2017).

[24] C. W. Peterson, W. A. Benalcazar, T. L. Hughes, G. Bahl. A quantized microwave quadrupole insulator with topologically protected corner states. Nature, 555, 346-350(2018).

[25] Z. D. Song, Z. Fang, C. Fang. (D−2)-dimensional edge states of rotation symmetry protected topological states. Phys. Rev. Lett., 119, 246402(2017).

[26] M. Geier, L. Trifunovic, M. Hoskam, P. W. Brouwer. Second-order topological insulators and superconductors with an order-two crystalline symmetry. Phys. Rev. B, 97, 205135(2018).

[27] H. D. Xue, Y. H. Yang, F. Gao, Y. D. Chong, B. L. Zhang. Acoustic higher-order topological insulator on a Kagome lattice. Nat. Mater., 18, 108-112(2019).

[28] X. J. Zhang, H. X. Wang, Z. K. Lin, Y. Tian, B. Y. Xie, M. H. Lu, Y. F. Chen, J. H. Jiang. Second-order topology and multidimensional topological transitions in sonic crystals. Nat. Phys., 15, 582-588(2019).

[29] D. Xiao, M. C. Chang, Q. Niu. Berry phase effects on electronic properties. Rev. Mod. Phys., 82, 1959-2007(2010).

[30] T. L. Hughes, R. G. Leigh, O. Parrikar. Torsional anomalies, Hall viscosity, and bulk-boundary correspondence in topological states. Phys. Rev. D, 88, 025040(2013).

[31] C. Han, M. Kang, H. Jeon. Lasing at multidimensional topological states in a two-dimensional photonic crystal structure. ACS Photon., 7, 2027-2036(2020).

[32] X. T. He, M. Y. Li, H. Y. Qiu, F. L. Zhao, J. W. Dong. In-plane excitation of a topological nanophotonic corner state at telecom wavelengths in a cross-coupled cavity. Photon. Res., 9, 1423-1431(2019).

[33] C. Schmidt, A. Palatnik, M. Sudzius, K. Leo. Coupled topological interface states. Phys. Rev. B, 103, 085412(2021).

[34] M. D. Wang, W. Y. Zhou, L. Y. Bi, C. Y. Qiu, M. Z. Ke, Z. Y. Liu. Valley-locked waveguide transport in acoustic heterostructures. Nat. Commun., 11, 3000(2020).

[35] Q. L. Chen, L. Zhang, F. J. Chen, H. S. Chen, Y. H. Yang. Photonic topological valley-locked waveguides. ACS Photon., 8, 1400-1406(2021).

[36] M. L. N. Chen, L. J. Jiang, Z. Lan, W. E. I. Sha. Pseudospin-polarized topological line defects in dielectric photonic crystals. IEEE Trans. Antennas Propag., 68, 609-613(2020).

[37] Y. F. Gao, Z. Jiang, L. L. Zhang, L. He, J. Zhao. Unidirectional propagation of coupled edge states in sandwich topological photonic crystals. J. Appl. Phys., 124, 213107(2018).

[38] Z. Jiang, Y. F. Gao, L. He, H. Song, J. Zhou, R. J. Zhu. Helical edge states of topological photonic crystals with line defects. Appl. Opt., 58, 2294-2299(2019).

[39] W. P. Su, J. R. Schrieffer, A. J. Heeger. Solitons in polyacetylene. Phys. Rev. Lett., 42, 1698-1701(1979).

[40] F. Liu, K. Wakabayashi. Novel topological phase with a zero Berry curvature. Phys. Rev. Lett., 118, 076803(2017).

[41] F. Liu, H. Y. Deng, K. Wakabayashi. Topological photonic crystals with zero Berry curvature. Phys. Rev. B, 97, 035442(2018).

[42] C. Poli, M. Bellec, U. Kuhl, F. Mortessagne, H. Schomerus. Selective enhancement of topologically induced interface states in a dielectric resonator chain. Nat. Commun., 6, 6710(2015).

[43] W. A. Benalcazar, T. Li, T. L. Hughes. Quantization of fractional corner charge in CN-symmetric higher-order topological crystalline insulators. Phys. Rev. B, 99, 245151(2019).

[44] X. D. Yang, J. Yao, X. Zhang. Experimental realization of three-dimensional indefinite cavities at the nanoscale with anomalous scaling laws. Nat. Photonics, 6, 450-454(2012).

[45] M. Yoshida, M. De Zoysa, K. Ishizaki, Y. Tanaka, M. Kawasaki, R. Hatsuda, B. Song, J. Gelleta, S. Noda. Double-lattice photonic-crystal resonators enabling high-brightness semiconductor lasers with symmetric narrow divergence beams. Nat. Mater., 18, 121-128(2019).

[46] F. Alpeggiani, L. Kuipers. Topological edge states in bichromatic photonic crystals. Optica, 6, 96-103(2019).

[47] M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, A. J. Turberfield. Fabrication of photonic crystals for the visible spectrum by holographic lithography. Nature, 404, 53-56(2000).