volume | PIER Journals

Abstract

Topological refractions created by valley sonic crystals (VSCs) have attracted great attentions in the communities of physics and engineering owing to the advantage of zero reflection of sound and the potential for designing advanced acoustic devices. In previous works, topological refractions of valley edge states are demonstrated to be determined by the projections of the valleys K and K′, and two types of topological refractions generally exist at opposite terminals or different frequency bands. However, the realization of tunable topological refractions at the fixed frequency band and terminal still poses great challenge. To overcome this, we report the realization of tunable topological refractions by VSCs with triple valley Hall phase transitions. By simply rotating rods, we realize 3 types of topological waveguides (T1, T2 and T3) composed of two VSCs, in which the projections of the observed valley edge states can be modulated between K and K′. Additionally, based on the measured transmittance spectra, we experimentally demonstrate that these valleyedge states are almost immune to backscattering against sharp bends. More importantly, we realize tunable topological refractions at the fixed frequency band and terminal, and experimentally observe the coexistence of positive and negative refractions for T1 and T3, and negative refractions for T2. The proposed tunable topological refractions have potential applications in designing multi-functional sound antennas and advanced communication devices.

1. Xiao, D., W. Yao, and Q. Niu, "Valley-contrasting physics in graphene: Magnetic moment and topological transport," Phys. Rev. Lett., Vol. 99, No. 23, 236809, 2007, doi: 10.1103/PhysRevLett.99.236809.
doi:10.1103/PhysRevLett.99.236809

2. Zeng, H., J. Dai, W. Yao, D. Xiao, and X. Cui, "Valley polarization in Mos2 monolayers by optical pumping," Nat. Nanotechnol., Vol. 7, No. 8, 490-493, 2012, doi: 10.1038/nnano.2012.95.
doi:10.1038/nnano.2012.95

3. Zhang, F., A. H. MacDonald, and E. J. Mele, "Valley chern numbers and boundary modes in gapped bilayer graphene," Proc. Natl. Acad. Sci., Vol. 110, No. 26, 10546-10551, USA, 2013, doi: 10.1073/pnas.1308853110.
doi:10.1073/pnas.1308853110

4. Ju, L., Z. Shi, N. Nair, Y. Lv, C. Jin, J. Velasco, Jr., C. Ojeda-Aristizabal, H. A. Bechtel, M. C. Martin, A. Zettl, J. Analytis, and F. Wang, "Topological valley transport at bilayer graphene domain walls," Nature, Vol. 520, No. 7549, 650-655, 2015, doi: 10.1038/nature14364.
doi:10.1038/nature14364

5. Schaibley, J. R., H. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W. Yao, and X. Xu, "Valleytronics in 2D materials," Nat. Rev. Maters, Vol. 1, No. 11, 16055, 2016, doi: 10.1038/natrevmats.2016.55.
doi:10.1038/natrevmats.2016.55

6. Li, J., R. X. Zhang, Z. Yin, J. Zhang, K. Watanabe, T. Taniguchi, C. Liu, and J. Zhu, "A valley valve and electron beam splitter," Science, Vol. 362, No. 6419, 1149-1152, 2018, doi: 10.1126/science.aao5989.
doi:10.1126/science.aao5989

7. Ma, T. and G. Shvets, "All-Si valley-Hall photonic topological insulator," New J. Phys., Vol. 18, No. 2, 025012, 2016, doi: 10.1088/1367-2630/18/2/025012.
doi:10.1088/1367-2630/18/2/025012

8. Wu, X., Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, "Direct observation of valley-polarized topological edge states in designer surface plasmon crystals," Nat. Commun., Vol. 8, No. 1, 1304, 2017, doi: 10.1038/s41467-017-01515-2.
doi:10.1038/s41467-017-01515-2

9. Dong, J. W., X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, "Valley photonic crystals for control of spin and topology," Nat. Mater., Vol. 16, No. 3, 298-302, 2017, doi: 10.1038/nmat4807.
doi:10.1038/nmat4807

10. Chen, X. D., F. L. Zhao, M. Chen, and J. W. Dong, "Valley-contrasting physics in all-dielectric photonic crystals: Orbital angular momentum and topological propagation," Phys. Rev. B, Vol. 96, No. 2, 020202, 2017, doi: 10.1103/PhysRevB.96.020202.
doi:10.1103/PhysRevB.96.020202

11. Gao, F., H. R. Xue, Z. J. Yang, K. F. Lai, Y. Yu, X. Lin, Y. D. Chong, G. Shvets, and B. L. Zhang, "Topologically protected refraction of robust kink states in Valley photonic crystals," Nat. Phys., Vol. 14, No. 2, 140-144, 2017, doi: 10.1038/nphys4304.
doi:10.1038/nphys4304

12. Gao, Z., Z. J. Yang, F. Gao, H. R. Xue, Y. H. Yang, J. W. Dong, and B. L. Zhang, "Valley surface-wave photonic crystal and its bulk edge transport," Phys. Rev. B, Vol. 96, No. 20, 201402, 2017, doi: 10.1103/PhysRevB.96.201402.
doi:10.1103/PhysRevB.96.201402

13. Chen, Q. L., L. Zhang, M. J. He, Z. J. Wang, X. Lin, F. Gao, Y. H. Yang, B. L. Zhang, and H. S. Chen, "Valley-Hall photonic topological insulators with dual-band kink states," Adv. Opt. Mate., Vol. 7, No. 15, 1900036, 2019, doi: 10.1002/adom.201900036.
doi:10.1002/adom.201900036

14. Kang, Y. H., X. Ni, X. J. Cheng, A. B. Khanikaev, and A. Z. Genack, "Pseudo-spin-valley coupled edge states in a photonic topological insulator," Nat. Commun., Vol. 9, No. 1, 1-7, 2018, doi: 10.1038/s41467-018-05408-w.
doi:10.1038/s41467-017-02088-w

15. Shalaev, M. I., W. Walasik, A. Tsukernik, Y. Xu, and N. M. Litchinitser, "Robust topologically protected transport in photonic crystals at telecommunication wavelengths," Nat. Nanotech., Vol. 14, No. 1, 31, 2018, doi: 10.1038/s41565-018-0297-6.
doi:10.1038/s41565-018-0297-6

16. Noh, J., S. Huang, K. P. Chen, and M. C. Rechtsman, "Observation of photonic topological valley Hall edge states," Phys. Rev. Lett., Vol. 120, No. 6, 063902, 2018, doi: 10.1103/PhysRevLett.120.063902.
doi:10.1103/PhysRevLett.120.063902

17. Yang, Y., H. Jiang, and Z. H. Hang, "Topological valley transport in two-dimensional honeycomb photonic crystals," Sci. Rep., Vol. 8, No. 1, 1588, 2018, doi: 10.1038/s41598-018-20001-3.
doi:10.1038/s41598-018-20001-3

18. Yang, Y. H., Z. Gao, H. R. Xue, L. Zhang, M. J. He, Z. J. Yang, R. Singh, Y. D. Chong, B. L. Zhang, and H. S. Chen, "Realization of a three-dimensional photonic topological insulator," Nature, Vol. 565, No. 7741, 622-626, 2019, doi: 10.1038/s41586-018-0829-0.
doi:10.1038/s41586-018-0829-0

19. Zeng, Y., U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y. Chong, and Q. J. Wang, "Electrically pumped topological laser with valley edge modes," Nature, Vol. 578, No. 7794, 246-250, 2020, doi: 10.1038/s41586-020-1981-x.
doi:10.1038/s41586-020-1981-x

20. Pal, R. K. and M. Ruzzene, "Edge waves in plates with resonators: An elastic analogue of the quantum valley Hall effect," New J. Phys., Vol. 19, No. 2, 025001, 2017, doi: 10.1088/1367-2630/aa56a2.
doi:10.1088/1367-2630/aa56a2

21. Huo, S. Y., J. J. Chen, H. B. Huang, and G. L. Huang, "Simultaneous multi-band valley-protected topological edge states of shear vertical wave in two-dimensional phononic crystals with veins," Sci. Rep., Vol. 7, No. 1, 10335, 2017, doi: 10.1038/s41598-017-10857-2.
doi:10.1038/s41598-017-10857-2

22. Yan, M., J. Y. Lu, F. Li, W. Y. Deng, X. Q. Huang, J. H. Ma, and Z. Y. Liu, "On-chip valley topological materials for elastic wave manipulation," Nat. Mater., Vol. 17, No. 11, 993-998, 2018, doi: 10.1038/s41563-018-0191-5.
doi:10.1038/s41563-018-0191-5

23. Wang, J. and J. Mei, "Topological valley-chiral edge states of lamb waves in elastic thin plates," Appl. Phys. Express, Vol. 11, No. 5, 057302, 2018, doi: 10.7567/apex.11.057302.
doi:10.7567/APEX.11.057302

24. Fan, H., B. Xia, L. Tong, S. Zheng, and D. Yu, "Elastic higher-order topological insulator with topologically protected corner states," Phys. Rev. Lett., Vol. 122, No. 20, 204301, 2019, doi: 10.1103/PhysRevLett.122.204301.
doi:10.1103/PhysRevLett.122.204301

25. Yang, L. Y., K. P. Yu, B. Bonello, B. Djafari-Rouhani, W. Wang, and Y. Wu, "Abnormal topological refraction into free medium at subwavelength scale in valley phononic crystal plates," Phys. Rev. B, Vol. 103, No. 18, 184303, 2021, doi: 10.1103/PhysRevB.103.184303.
doi:10.1103/PhysRevB.103.184303

26. Huang, H. B., J. J. Chen, and S. Y. Hou, "Recent advances in topologic alelastic metamaterials," J. Phys. Condens. Mat., Vol. 33, No. 50, 503002, 2021, doi: 10.1088/1361-648X/ac27d8.
doi:10.1088/1361-648X/ac27d8

27. Ye, L. P., C. Y. Qiu, J. Y. Lu, X. H. Wen, Y. Y. Shen, M. Z. Ke, F. Zhang, and Z. Y. Liu, "Observation of acoustic valley vortex states and valley-chirality locked beam splitting," Phys. Rev. B, Vol. 95, No. 17, 174106, 2017, doi: 10.1103/PhysRevB.95.174106.
doi:10.1103/PhysRevB.95.174106

28. Lu, J. Y., C. Y. Qiu, L. P. Ye, X. Y. Fan, M. Z. Ke, F. Zhang, and Z. Y. Liu, "Observation of topological valley transport of sound in sonic crystals," Nat. Phys., Vol. 13, No. 4, 369-374, 2016, doi: 10.1038/nphys3999.
doi:10.1038/nphys3999

29. Lu, J. Y., C. Y. Qiu, W. Y. Deng, X. Q. Huang, F. Li, F. Zhang, S. Q. Chen, and Z. Y. Liu, "Valley topological phases in bilayer sonic crystals," Phys. Rev. Lett., Vol. 120, No. 11, 116802, 2018, doi: 10.1103/PhysRevLett.120.116802.
doi:10.1103/PhysRevLett.120.116802

30. Zhang, Z., Y. Tian, Y. H. Wang, S. X. Gao, Y. Cheng, X. J. Liu, and J. Christensen, "Directional acoustic antennas based on valley-Hall topological insulators," Adv. Mater, Vol. 30, 1803229, 2018, doi: 10.1002/adma.201803229.
doi:10.1002/adma.201803229

31. Zhang, Z. W., Y. Tian, Y. Cheng, Q. Wei, X. J. Liu, and J. Christensen, "Topological acoustic delay line," Phys. Rev. Appl., Vol. 9, No. 3, 034032, 2018, doi: 10.1103/PhysRevApplied.9.034032.
doi:10.1103/PhysRevApplied.9.034032

32. He, C., S. Y. Yu, H. Ge, H. Wang, Y. Tian, H. Zhang, X. C. Sun, Y. B. Chen, J. Zhou, M. H. Lu, and Y. F. Chen, "Three-dimensional topological acoustic crystals with pseudospin-valley coupled saddle surface states," Nat. Commun., Vol. 9, No. 1, 4555, 2018, doi: 10.1038/s41467-018-07030-2.
doi:10.1038/s41467-018-07030-2

33. Yang, Y. H., Z. J. Yang, and B. L. Zhang, "Acoustic valley edge states in a graphene-like resonator system," J. Appl. Phys., Vol. 123, No. 9, 091713, 2018, doi: 10.1063/1.5009626.
doi:10.1063/1.5009626

34. Zhu, Z. X., X. Q. Huang, J. Y. Lu, M. Yan, F. Li, W. Y. Deng, and Z. Y. Liu, "Negative refraction and partition in acoustic valley materials of a square lattice," Phys. Rev. Appl., Vol. 12, No. 2, 024007, 2019, doi: 10.1103/PhysRevApplied.12.024007.
doi:10.1103/PhysRevApplied.12.024007

35. Shen, Y. Y., C. Y. Qiu, X. X. Cai, L. P. Ye, J. Y. Lu, M. Z. Ke, and Z. Y. Liu, "Valley-projected edge modes observed in underwater sonic crystals," Appl. Phys. Lett., Vol. 114, No. 2, 023501, 2019, doi: 10.1063/1.5049856.
doi:10.1063/1.5049856

36. Xie, B. Y., H. Liu, H. Cheng, Z. Y. Liu, S. Q. Chen, and J. G. Tian, "Acoustic topological transport and refraction in a Kekulé lattice," Phys. Rev. Appl., Vol. 11, No. 4, 044086, 2019, doi: 10.1103/physrevapplied.11.044086.
doi:10.1103/PhysRevApplied.11.044086

37. Tian, Z., C. Shen, J. Li, E. Reit, H. Bachman, J. E. S. Socolar, S. A. Cummer, and T. J. Huang, "Dispersion tuning and route reconfiguration of acoustic waves in valley topological phononic crystals," Nat. Commun., Vol. 11, No. 1, 762, 2020, doi: 10.1038/s41467-020-14553-0.
doi:10.1038/s41467-020-14553-0

38. Wang, M. D., W. Y. Zhou, L. Y. Bi, C. Y. Qiu, M. Z. Ke, and Z. Y. Liu, "Valley-locked waveguide transport in acoustic heterostructures," Nat. Commun., Vol. 11, No. 1, 3000, 2020, doi: 10.1038/s41467-020-16843-z.
doi:10.1038/s41467-020-16843-z

39. Jia, D., Y. Ge, H. R. Xue, S. Q. Yuan, H. X. Sun, Y. H. Yang, X. J. Liu, and B. L. Zhang, "Topological refraction in dual-band valley sonic crystals," Phys. Rev. B, Vol. 103, No. 14, 144309, 2021, doi: 10.1103/PhysRevB.103.144309.
doi:10.1103/PhysRevB.103.144309

40. Huang, Z., J. H. Wu, C. Wang, S. K. Yang, and F. Y. Ma, "Resonant-scattering hybrid device for multiband acoustic topology valley transmission," Phys. Rev. B, Vol. 104, No. 9, 094110, 2021, doi: 10.1103/PhysRevB.104.094110.
doi:10.1103/PhysRevB.104.094110

41. Qu, H. F., X. N. Liu, and G. K. Hu, "Topological valley states in sonic crystals with Willis coupling," Appl. Phys. Lett., Vol. 119, No. 5, 051903, 2021, doi: 10.1063/5.0055789.
doi:10.1063/5.0055789

42. He, H. L., C. Y. Qiu, L. P. Ye, X. X. Cai, X. Y. Fan, M. Z. Ke, F. Zhang, and Z. Y. Liu, "Topological negative refraction of surface acoustic waves in a Weyl phononic crystal," Nature, Vol. 560, No. 7716, 61-64, 2018, doi: 10.1038/s41586-018-0367-9.
doi:10.1038/s41586-018-0367-9

43. Yang, Y. H., H. X. Sun, J. P. Xia, H. R. Xue, Z. Gao, Y. Ge, D. Jia, Y. D. Chong, and B. L. Zhang, "Topological triply degenerate point with double Fermi arcs," Nat. Phys., Vol. 15, No. 7, 645-649, 2019, doi: 10.1038/s41567-019-0502-z.
doi:10.1038/s41567-019-0502-z

Dr. Ding Jia

Dr. Yin Wang

Dr. Yong Ge

Dr. Shou-Qi Yuan

Prof. Hong-Xiang Sun