Coexisting valley and pseudo-spin topological edge states in photonic topological insulators made of distorted Kekul&#233; lattices

Guochao Wei; Zhenzhen Liu; Licheng Wang; Jianyuan Song; Jun-Jun Xiao

doi:10.1364/PRJ.453803

[1] 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).

[2] J. Lu, C. Qiu, L. Ye, X. Fan, M. Ke, F. Zhang, Z. Liu. Observation of topological valley transport of sound in sonic crystals. Nat. Phys., 13, 369-374(2016).

[3] L. Zhang, Y. Yang, M. He, H. X. Wang, Z. Yang, E. Li, F. Gao, B. Zhang, R. Singh, J. H. Jiang, H. Chen. Valley kink states and topological channel intersections in substrate-integrated photonic circuitry. Laser Photonics Rev., 13, 1900159(2019).

[4] Q. Guo, B. Yang, L. Xia, W. Gao, H. Liu, J. Chen, Y. Xiang, S. Zhang. Three dimensional photonic Dirac points in metamaterials. Phys. Rev. Lett., 119, 213901(2017).

[5] B. Yang, Q. Guo, B. Tremain, L. E. Barr, W. Gao, H. Liu, B. Beri, Y. Xiang, D. Fan, A. P. Hibbins, S. Zhang. Direct observation of topological surface-state arcs in photonic metamaterials. Nat. Commun., 8, 97(2017).

[6] W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Beri, J. Li, S. Zhang. Topological photonic phase in chiral hyperbolic metamaterials. Phys. Rev. Lett., 114, 037402(2015).

[7] M. Li, Y. Wang, T. Sang, H. Chu, Y. Lai, G. Yang. Experimental observation of multiple edge and corner states in photonic slabs heterostructures. Photon. Res., 10, 197-204(2021).

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

[9] A. B. Khanikaev, G. Shvets. Two-dimensional topological photonics. Nat. Photonics, 11, 763-773(2017).

[10] M. Kim, Z. Jacob, J. Rho. Recent advances in 2D, 3D and higher-order topological photonics. Light Sci. Appl., 9, 130(2020).

[11] S. Iwamoto, Y. Ota, Y. Arakawa. Recent progress in topological waveguides and nanocavities in a semiconductor photonic crystal platform. Opt. Mater. Express, 11, 319-337(2021).

[12] X.-T. He, E.-T. Liang, J.-J. Yuan, H.-Y. Qiu, X.-D. Chen, F.-L. Zhao, J.-W. Dong. A silicon-on-insulator slab for topological valley transport. Nat. Commun., 10, 872(2019).

[13] M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, N. M. Litchinitser. Robust topologically protected transport in photonic crystals at telecommunication wavelengths. Nat. Nanotechnol., 14, 31-34(2019).

[14] L. Wang, R.-Y. Zhang, M. Xiao, D. Han, C. T. Chan, W. Wen. The existence of topological edge states in honeycomb plasmonic lattices. New J. Phys., 18, 103029(2016).

[15] J. Lu, C. Qiu, M. Ke, Z. Liu. Valley vortex states in sonic crystals. Phys. Rev. Lett., 116, 093901(2016).

[16] L. Ye, C. Qiu, J. Lu, X. Wen, Y. Shen, M. Ke, F. Zhang, Z. Liu. Observation of acoustic valley vortex states and valley-chirality locked beam splitting. Phys. Rev. B, 95, 174106(2017).

[17] Y. Yang, H. Jiang, Z. H. Hang. Topological valley transport in two-dimensional honeycomb photonic crystals. Sci. Rep., 8, 1588(2018).

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

[19] J. Ma, X. Xi, X. Sun. Topological photonic integrated circuits based on valley kink states. Laser Photonics Rev., 13, 1900087(2019).

[20] S. Arora, T. Bauer, R. Barczyk, E. Verhagen, L. Kuipers. Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths. Light Sci. Appl., 10, 9(2021).

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

[22] Y. H. Yang, Y. Yamagami, X. B. Yu, P. Pitchappa, J. Webber, B. L. Zhang, M. Fujita, T. Nagatsuma, R. Singh. Terahertz topological photonics for on-chip communication. Nat. Photonics, 14, 446-451(2020).

[23] X. Xi, K. P. Ye, R. X. Wu. Topological photonic crystal of large valley Chern numbers. Photon. Res., 8, B1-B7(2020).

[24] J. Lu, C. Qiu, W. Deng, X. Huang, F. Li, F. Zhang, S. Chen, Z. Liu. Valley topological phases in bilayer sonic crystals. Phys. Rev. Lett., 120, 116802(2018).

[25] L. He, H. Y. Ji, Y. J. Wang, X. D. Zhang. Topologically protected beam splitters and logic gates based on two-dimensional silicon photonic crystal slabs. Opt. Express, 28, 34015-34023(2020).

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

[27] L. H. Wu, X. Hu. Topological properties of electrons in honeycomb lattice with detuned hopping energy. Sci. Rep., 6, 24347(2016).

[28] 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).

[29] H. Kagami, T. Amemiya, S. Okada, N. Nishiyama, X. Hu. Topological converter for high-efficiency coupling between Si wire waveguide and topological waveguide. Opt. Express, 28, 33619-33631(2020).

[30] J. P. Xia, D. Jia, H. X. Sun, S. Q. Yuan, Y. Ge, Q. R. Si, X. J. Liu. Programmable coding acoustic topological insulator. Adv. Mater., 30, 1805002(2018).

[31] D. A. J. Bisharat, D. F. Sievenpiper. Electromagnetic-dual metasurfaces for topological states along a 1D interface. Laser Photonics Rev., 13, 1900126(2019).

[32] L. He, W. X. Zhang, X. D. Zhang. Topological all-optical logic gates based on two-dimensional photonic crystals. Opt. Express, 27, 25841-25859(2019).

[33] Y. Kang, X. Ni, X. Cheng, A. B. Khanikaev, A. Z. Genack. Pseudo-spin-valley coupled edge states in a photonic topological insulator. Nat. Commun., 9, 3029(2018).

[34] Z. Zhang, Y. Tian, Y. Wang, S. Gao, Y. Cheng, X. Liu, J. Christensen. Directional acoustic antennas based on valley-Hall topological insulators. Adv. Mater., 30, 1803229(2018).

[35] Y. Yang, Y. F. Xu, T. Xu, H. X. Wang, J. H. Jiang, 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).

[36] M. L. N. Chen, L. J. Jiang, Z. Lan, W. E. I. Sha. Coexistence of pseudospin- and valley-Hall-like edge states in a photonic crystal with C_3v symmetry. Phys. Rev. Res., 2, 043148(2020).

[37] Y. Liu, C. S. Lian, Y. Li, Y. Xu, W. Duan. Pseudospins and topological effects of phonons in a Kekule lattice. Phys. Rev. Lett., 119, 255901(2017).

[38] T.-W. Liu, F. Semperlotti. Nonconventional topological band properties and gapless helical edge states in elastic phononic waveguides with Kekulé distortion. Phys. Rev. B, 100, 214110(2019).

[39] T. W. Liu, F. Semperlotti. Synthetic Kramers pair in phononic elastic plates and helical edge states on a dislocation interface. Adv. Mater., 33, 2005160(2021).

[40] X. Wu, Y. Meng, Y. Hao, R. Y. Zhang, J. Li, X. Zhang. Topological corner modes induced by Dirac vortices in arbitrary geometry. Phys. Rev. Lett., 126, 226802(2021).

[41] P. A. Pantaleon, R. Carrillo-Bastos, Y. Xian. Topological magnon insulator with a Kekule bond modulation. J. Phys. Condens. Matter, 31, 085802(2019).

[42] Q. Chen, L. Zhang, M. He, Z. Wang, X. Lin, F. Gao, Y. Yang, B. Zhang, H. Chen. Valley-Hall photonic topological insulators with dual-band kink states. Adv. Opt. Mater., 7, 1900036(2019).

[43] G.-J. Tang, X.-D. Chen, F.-L. Shi, J.-W. Liu, M. Chen, J.-W. Dong. Frequency range dependent topological phases and photonic detouring in valley photonic crystals. Phys. Rev. B, 102, 174202(2020).

[44] G.-C. Wei, Z.-Z. Liu, D.-S. Zhang, J.-J. Xiao. Frequency dependent wave routing based on dual-band valley-Hall topological photonic crystal. New J. Phys., 23, 023029(2021).

[45] X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, W. Wen. Direct observation of valley-polarized topological edge states in designer surface plasmon crystals. Nat. Commun., 8, 1304(2017).

[46] Q. Chen, L. Zhang, S. Xu, Z. Wang, E. Li, Y. Yang, H. Chen. Robust waveguiding in substrate-integrated topological photonic crystals. Appl. Phys. Lett., 116, 231106(2020).

[47] https://cn.comsol.com. https://cn.comsol.com

[48] X. Xi, J. Ma, S. Wan, C. H. Dong, X. Sun. Observation of chiral edge states in gapped nanomechanical graphene. Sci. Adv., 7, eabe1398(2021).

[49] M. L. N. Chen, L. Jun Jiang, Z. Lan, W. E. I. Sha. Local orbital-angular-momentum dependent surface states with topological protection. Opt. Express, 28, 14428-14435(2020).

[50] J. Wang, Y. Huang, W. Chen. Tailoring edge and interface states in topological metastructures exhibiting the acoustic valley Hall effect. Sci. China: Phys., Mech. Astron., 63, 224611(2019).

[51] H. B. Huang, Z. H. Tan, S. Y. Huo, L. Y. Feng, J. J. Chen, X. Han. Topologically protected zero refraction of elastic waves in pseudospin-Hall phononic crystals. Commun. Phys., 3, 46(2020).

[52] M. Blanco de Paz, C. Devescovi, G. Giedke, J. J. Saenz, M. G. Vergniory, B. Bradlyn, D. Bercioux, A. García-Etxarri. Tutorial: computing topological invariants in 2D photonic crystals. Adv. Quantum Technol., 3, 1900117(2019).

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