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Dual-band valley-protected topological edge states in graphene-like phononic crystals with waveguide

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Abstract

Since valley was introduced into phononic crystals, it has promoted far-reaching developments in topologically protected acoustic transmission. However, in the novel research field of valley-Hall phononic topological insulators, most researchers only focus on valley-protected edge state with a single working frequency band. Here, we demonstrate dual-band valley-protected topological edge states in a graphene-like two-dimensional phononic crystal, which consists of columnar air cavities and rigid scatters. It is demonstrated that energy band inversion happens and a gap can be opened at the two Dirac cones at the K (K') symmetry points of the Brillouin zone by tuning the radius differences between adjacent columnar air cavities. In addition, we demonstrate the presence of dual-band topologically protected edge states with properties like suppressed back-scattering, one-way transmission, and sharp bend resistance. In these contexts, beam splitting with dual-band is achieved by combining valley vortex states with opposite chirality. Our work may provide a practical method for solving high-efficiency and high-capacity multi-channel acoustic communication in fluid media.

Graphical Abstract

The dual-band valley-protected topological edge states have been demonstrated in a graphenelike two-dimensional phononic crystal, which consists of columnar air cavities and rigid scatters. The energy band inversion happens and a gap can be opened at the two Dirac cones at the K (K’) symmetry points of the Brillouin zone by tuning the radius differences between adjacent columnar air cavities. Based on these, beam splitting with dual-band can be achieved by combining valley vortex states with opposite chirality

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Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. K. Vonklitzing, G. Dorda, M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45(6), 494 (1980)

    ADS  Google Scholar 

  2. R.B. Laughlin, Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50(18), 1395 (1983)

    ADS  Google Scholar 

  3. K. Guo, J. Wu, F. Chen, K. Zhou, S. Liu, Z. Guo, Second harmonic generation enhancement and directional emission from topological corner state based on quantum spin Hall effect. Opt. Express. 29(17), 26841–26850 (2021)

    ADS  Google Scholar 

  4. B.A. Bernevig, T.L. Hughes, S.C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314(5806), 1757–1761 (2006)

    ADS  Google Scholar 

  5. M.Z. Hasan, C.L. Kane, Colloquium: Topological insulators. Rev. Mod. Phys. 82(4), 3045 (2010)

    ADS  Google Scholar 

  6. Z. Yin, F. Chen, K. Guo, F. Shen, K. Zhou, J. Gao, S. Liu, Z. Guo, Tunable THz Generalized Weyl Points. Opt. Express. 27(2), 512–522 (2019)

    ADS  Google Scholar 

  7. R. Yu, W. Zhang, H.J. Zhang, S.C. Zhang, X. Dai, Z. Fang, Quantized anomalous Hall effect in magnetic topological insulators. Science 329(5987), 61–64 (2010)

    ADS  Google Scholar 

  8. J. Ma, K. Guo, F. Chen, K. Zhou, S. Liu, Z. Guo, Manipulating second harmonic generation (SHG) in high-order topological photonic crystals (TPCs). Ann Phys-Berlin 533(10), 2100191 (2021)

    ADS  Google Scholar 

  9. M. Jung, Z.Y. Fan, G. Shvets, Midinfrared plasmonic valleytronics in metagate-tuned graphene. Phys. Rev. Lett. 121(8), 086807 (2018)

    ADS  Google Scholar 

  10. 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(17), 174202 (2020)

    Google Scholar 

  11. S.H. Mousavi, A.B. Khanikaev, Z. Wang, Topologically protected elastic waves in phononic metamaterials. Nat. Commun. 6(1), 8682 (2015)

    ADS  Google Scholar 

  12. P. Wang, L. Lu, K. Bertoldi, Topological phononic crystals with one-way elastic edge waves. Phys. Rev. Lett. 115(10), 104302 (2015)

    ADS  Google Scholar 

  13. 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(12), 1124–1129 (2016)

    Google Scholar 

  14. A.B. Khanikaev, R. Fleury, S.H. Mousavi, A. Alu, Topologically robust sound propagation in an angular-momentum-biased graphene-like resonator lattice. Nat. Commun. 6(1), 8260 (2015)

    ADS  Google Scholar 

  15. Z.J. Yang, F. Gao, X.H. Shi, X. Lin, Z. Gao, Y.D. Chong, B.L. Zhang, Topological acoustics. Phys. Rev. Lett. 114(11), 114301 (2015)

    ADS  Google Scholar 

  16. H. Mao, F. Chen, K. Guo, Z. Guo, Broadband topological valley-projected edge-states transport in composite structure phononic crystal. Chinese Phys B. 30(8), 084302 (2021)

    ADS  Google Scholar 

  17. Z.W. Zhang, Q. Wei, Y. Cheng, T. Zhang, D.J. Wu, X.J. Liu, Topological creation of acoustic pseudospin multipoles in a flow-free symmetry-broken metamaterial lattice. Phys. Rev. Lett. 118(8), 084303 (2017)

    ADS  Google Scholar 

  18. Y.G. Peng, Y.X. Shen, D.G. Zhao, X.F. Zhu, Low-loss and broadband anomalous Floquet topological insulator for airborne sound. Appl. Phys. Lett. 110(17), 173505 (2017)

    ADS  Google Scholar 

  19. Q. Wei, Y. Tian, S.Y. Zuo, Y. Cheng, X.J. Liu, Experimental demonstration of topologically protected efficient sound propagation in an acoustic waveguide network. Phys. Rev. B 95(9), 094305 (2017)

    ADS  Google Scholar 

  20. J.Y. Lu, C.Y. Qiu, L.P. Ye, X.Y. Fan, M.Z. Ke, F. Zhang, Z.Y. Liu, Observation of topological valley transport of sound in sonic crystals. Nat. Phys. 13(4), 369–374 (2017)

    Google Scholar 

  21. J.Y. Lu, C.Y. Qiu, M.Z. Ke, Z.Y. Liu, Valley vortex states in sonic crystals. Phys. Rev. Lett. 116(9), 093901 (2016)

    ADS  Google Scholar 

  22. Y.C. Deng, M.H. Lu, Y. Jing, A comparison study between acoustic topological states based on valley Hall and quantum spin Hall effects. J. Acoust. Soc. Am. 146(1), 721–728 (2019)

    ADS  Google Scholar 

  23. W. Wang, B. Bonello, B.D. Rouhani, Y. Pennec, Topological valley, pseudospin, and pseudospin-valley protected edge states in symmetric pillared phononic crystals. Phys. Rev. B 100(14), 140101 (2019)

    ADS  Google Scholar 

  24. W. Wang, B. Bonello, B.D. Rouhani, Y. Pennec, Polarization-dependent and valley-protected Lamb waves in asymmetric pillared phononic crystals. J. Phys. D: Appl. Phys. 52(50), 505302 (2019)

    Google Scholar 

  25. H. Dai, T. Chen, J. Jiao, B. Xia, D. Yu, Topological valley vortex manipulation of microparticles in phononic crystals. J. Appl. Phys. 126(14), 145101 (2019)

    ADS  Google Scholar 

  26. L.Y. Yang, K.P. Yu, B. Bonello, B.D. Rouhani, W. Wang, Y. Wu, Abnormal topological refraction into free medium at subwavelength scale in valley phononic crystal plates. Phys. Rev. B 103(18), 184303 (2021)

    ADS  Google Scholar 

  27. W.T. Yuan, J.F. Zhao, Y. Long, J. Ren, Z. Zhong, Multi-branch valley-chiral edge states of antisymmetric plate wave in phononic crystal plates with double-sided symmetric pillars. Int. J. Mech. Sci. 197, 106347 (2021)

    Google Scholar 

  28. Z.W. Zhang, Y. Tian, Y. Cheng, Q. Wei, X.J. Liu, J. Christensen, Topological Acoustic Delay Line. Phys. Rev. Applied 9(3), 034032 (2018)

    ADS  Google Scholar 

  29. Z.X. Zhu, X.Q. Huang, J.Y. Lu, M. Yan, F. Li, W.Y. Deng, Z.Y. Liu, Negative refraction and partition in acoustic valley materials of a square lattice. Phys. Rev. Applied 12(2), 024007 (2019)

    ADS  Google Scholar 

  30. Z.Y. Wang, Y.Z. Yang, H.Y. Li, H. Jia, J.L. Luo, J. Huang, Z.N. Wang, B. Jiang, N.J. Yang, G.J. Jin, H. Yang, Multichannel topological transport in an acoustic valley Hall insulator. Phys. Rev. Applied 15(2), 024019 (2021)

    ADS  Google Scholar 

  31. Z.H. Tian, C. Shen, J.F. Li, E. Reit, H. Bachman, J.E.S. Socolar, S.A. Cummer, T.J. Huang, Dispersion tuning and route reconfiguration of acoustic waves in valley topological phononic crystals. Nat. Commun. 11(1), 762 (2020)

    ADS  Google Scholar 

  32. D. Jia, Y. Ge, H.R. Xue, S.Q. Yuan, H.X. Sun, Y.H. Yang, X.J. Liu, B.L. Zhang, Topological refraction in dual-band valley sonic crystals. Phys. Rev. B 103(14), 144309 (2021)

    ADS  Google Scholar 

  33. S.Y. Huo, J.J. Chen, H.B. Huang, G.L. Huang, Simultaneous multi-band valley protected topological edge states of shear vertical wave in twodimensional phononic crystals with veins. Sci. Rep. 7(1), 10335 (2017)

    ADS  Google Scholar 

  34. J.W. Ma, X. Xi, X.K. Sun, Experimental demonstration of dual-band nano-electromechanical valley-hall topological metamaterials. Adv. Mater. 33(10), 2006521 (2021)

    Google Scholar 

  35. Q.L. Chen, L. Zhang, M.J. He, Z.J. Wang, X. Lin, F. Gao, Y.H. Yang, B.L. Zhang, H.S. Chen, Valley-Hall photonic topological insulators with dual-band kink states. Adv. Opt. Mater. 7(15), 1900036 (2019)

    Google Scholar 

  36. 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(1), 872 (2019)

    ADS  Google Scholar 

  37. 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(1), 31–34 (2019)

    ADS  Google Scholar 

  38. I. Martin, Y.M. Blanter, A.F. Morpurgo, Topological confinement in bilayer graphene. Phys. Rev. Lett. 100(3), 036804 (2008)

    ADS  Google Scholar 

  39. G.W. Semenoff, V. Semenoff, F. Zhou, Domain walls in gapped graphene. Phys. Rev. Lett. 101(8), 087204 (2008)

    ADS  Google Scholar 

  40. F. Gao, H.R. Xue, Z.J. Yang, K.F. Lai, Y. Yu, X. Lin, Y.D. Chong, G. Shvets, B.L. Zhang, Topologically-protected refraction of robust kink states in valley photonic crystals. Nat. Phys. 14(2), 140–144 (2018)

    Google Scholar 

  41. M. Yan, J. Lu, F. Li, W. Deng, X. Huang, J. Ma, Z. Liu, On-chip valley topological materials for elastic wave manipulation. Nature Mater. 17(11), 993–998 (2018)

    ADS  Google Scholar 

  42. 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(36), 1803229 (2018)

    Google Scholar 

  43. L. Zhang, Y. Yang, M. He, H. X. Wang, Z. Yang, E. Li, F. Gao, B. Zhang, R. Singh, J. H. Jiang, and H. Chen, Manipulation of topological valley kink states in an ultrathin substrate-integrated photonic circuitry. Preprint at arXiv:1805.03954 (2018).

  44. J. Mei, Z.G. Chen, Y. Wu, Pseudo-time-reversal symmetry and topological edge states in two dimensional acoustic crystals. Sci. Rep. 6(1), 32752 (2016)

    ADS  Google Scholar 

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Funding

National Natural Science Foundation of China (61775050, 11804073).

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Conceptualization: Qianlong kang, Hongyong mao; Methodology: Qianlong kang, Fujia Chen, Hongyong mao; Formal analysis and investigation: Keya Zhou, Kai Guo, Shutian Liu, Zhongyi Guo; Writing—original draft preparation: Qianlong kang; Writing—review and editing: Keya Zhou, Kai Guo, Shutian Liu, Zhongyi Guo; Funding acquisition: Zhongyi Guo; Supervision: Zhongyi Guo.

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Correspondence to Zhongyi Guo.

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Kang, Q., Chen, F., Mao, H. et al. Dual-band valley-protected topological edge states in graphene-like phononic crystals with waveguide. Eur. Phys. J. B 96, 40 (2023). https://doi.org/10.1140/epjb/s10051-023-00503-4

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