438
Z. Li et al.
Acknowledgements This work was supported by the National Natural Science Foundation of
China (NSFC) (Grants No. 12074057, 11604041 and 11704060), the National Key Research Development Program under Contract No. 2016YFA0300801, and the National Thousand-Young-Talent
Program of China. Z.-X. L. acknowledges the financial support of NSFC under Grant No. 11904048
and the China Postdoctoral Science Foundation under Grant No. 2019M663461. We acknowledged
Z.Y.W, C.W. and X.S.W. for helpful discussions.
References
1. M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)
2. X.-L. Qi, S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)
3. J.E. Moore, Nature 464, 194–198 (2010)
4. C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005)
5. C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 146802 (2005)
6. L. Lu, J.D. Joannopoulos, M. Soljacic, Nat. Photon. 8, 821–829 (2014)
7. A.B. Khanikaev, G. Shvets, Nat. Photon. 11, 763–773 (2017)
8. G. Harari, M. A. Bandres, Y. Lumer et al., Science 359, eaar4003 (2018)
9. M. A. Bandres, S. Wittek, G. Harari et al., Science 359, eaar4005 (2018)
10. T. Ozawa, H.M. Price, A. Amo et al., Rev. Mod. Phys. 91, 015006 (2019)
11. J. Paulose, B.G.G. Chen, V. Vitelli, Nat. Phys. 11, 153–156 (2015)
12. L.M. Nash, D. Kleckner, A. Read et al., PNAS 112, 14495 (2015)
13. S.D. Huber, Nat. Phys. 12, 621–623 (2016)
14. N.P. Mitchell, L.M. Nash, D. Hexner et al., Nat. Phys. 14, 380–385 (2018)
15. Z. Yang, F. Gao, X. Shi et al., Phys. Rev. Lett. 114, 114301 (2015)
16. C. He, X. Ni, H. Ge et al., Nat. Phys. 12, 1124–1129 (2016)
17. R. Fleury, A.B. Khanikaev, A. Alù, Nat. Commun. 7, 11744 (2016)
18. X. Zhang, M. Xiao, Y. Cheng et al., Commun. Phys. 1, 97 (2018)
19. L. Zhang, J. Ren, J.-S. Wang et al., Phys. Rev. B 87, 144101 (2013)
20. A. Mook, J. Henk, I. Mertig, Phys. Rev. B 90, 024412 (2014)
21. R. Chisnell, J.S. Helton, D.E. Freedman et al., Phys. Rev. Lett. 115, 147201 (2015)
22. A. Ruckriegel, A. Brataas, R.A. Duine, Phys. Rev. B 97, 081106(R) (2018)
23. W.A. Benalcazar, B.A. Bernevig, T.L. Hughes, Science 357, 61–66 (2017)
24. W.A. Benalcazar, B.A. Bernevig, T.L. Hughes, Phys. Rev. B 96, 245115 (2017)
25. M. Ezawa, Phys. Rev. Lett. 120, 026801 (2018)
26. Z. Song, Z. Fang, C. Fang, Phys. Rev. Lett. 119, 246402 (2017)
27. J. Langbehn, Y. Peng, L. Trifunovic et al., Phys. Rev. Lett. 119, 246401 (2017)
28. F. Schindler, A.M. Cook, M.G. Vergniory et al., Sci. Adv. 4, eaat0346 (2018)
29. R. Queiro, A. Stern, Phys. Rev. Lett. 123, 036802 (2019)
30. B.-Y. Xie, H.-F. Wang, H.-X. Wang et al., Phys. Rev. B 98, 205147 (2018)
31. J. Noh, W.A. Benalcazar, S. Huang et al., Nat. Photon. 12, 408–415 (2018)
32. A.E. Hassan, F.K. Kunst, A. Moritz et al., Nat. Photon. 13, 697–700 (2019)
33. S. Mittal, V.V. Orre, G. Zhu et al., Nat. Photon. 13, 692–696 (2019)
34. X.-D. Chen, W.-M. Deng, F.-L. Shi et al., Phys. Rev. Lett. 122, 233902 (2019)
35. B.-Y, Xie, G.-X. Su, H.-F. Wang et al., Phys. Rev. Lett. 122, 233903 (2019)
36. H. Xue, Y. Yang, F. Gao et al., Nat. Mater. 18, 108–112 (2019)
37. X. Ni, M. Weiner, A. Alu et al., Nat. Mater. 18, 113–120 (2019)
38. H. Xue, Y. Yang, G. Liu et al., Phys. Rev. Lett. 122, 244301 (2019)
39. C. He, S.-Y. Yu, H. Wang et al., Phys. Rev. Lett. 123, 195503 (2019)
40. X. Zhang, H.-X. Wang, Z.-K. Lin et al., Nat. Phys. 15, 582–588 (2019)
41. S. Imhof, C. Berger, F. Bayer et al., Nat. Phys. 14, 925–929 (2018)
42. M. Ezawa, Phys. Rev. B 98, 201402(R) (2018)
Z. Li et al.
Acknowledgements This work was supported by the National Natural Science Foundation of
China (NSFC) (Grants No. 12074057, 11604041 and 11704060), the National Key Research Development Program under Contract No. 2016YFA0300801, and the National Thousand-Young-Talent
Program of China. Z.-X. L. acknowledges the financial support of NSFC under Grant No. 11904048
and the China Postdoctoral Science Foundation under Grant No. 2019M663461. We acknowledged
Z.Y.W, C.W. and X.S.W. for helpful discussions.
References
1. M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)
2. X.-L. Qi, S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)
3. J.E. Moore, Nature 464, 194–198 (2010)
4. C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005)
5. C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 146802 (2005)
6. L. Lu, J.D. Joannopoulos, M. Soljacic, Nat. Photon. 8, 821–829 (2014)
7. A.B. Khanikaev, G. Shvets, Nat. Photon. 11, 763–773 (2017)
8. G. Harari, M. A. Bandres, Y. Lumer et al., Science 359, eaar4003 (2018)
9. M. A. Bandres, S. Wittek, G. Harari et al., Science 359, eaar4005 (2018)
10. T. Ozawa, H.M. Price, A. Amo et al., Rev. Mod. Phys. 91, 015006 (2019)
11. J. Paulose, B.G.G. Chen, V. Vitelli, Nat. Phys. 11, 153–156 (2015)
12. L.M. Nash, D. Kleckner, A. Read et al., PNAS 112, 14495 (2015)
13. S.D. Huber, Nat. Phys. 12, 621–623 (2016)
14. N.P. Mitchell, L.M. Nash, D. Hexner et al., Nat. Phys. 14, 380–385 (2018)
15. Z. Yang, F. Gao, X. Shi et al., Phys. Rev. Lett. 114, 114301 (2015)
16. C. He, X. Ni, H. Ge et al., Nat. Phys. 12, 1124–1129 (2016)
17. R. Fleury, A.B. Khanikaev, A. Alù, Nat. Commun. 7, 11744 (2016)
18. X. Zhang, M. Xiao, Y. Cheng et al., Commun. Phys. 1, 97 (2018)
19. L. Zhang, J. Ren, J.-S. Wang et al., Phys. Rev. B 87, 144101 (2013)
20. A. Mook, J. Henk, I. Mertig, Phys. Rev. B 90, 024412 (2014)
21. R. Chisnell, J.S. Helton, D.E. Freedman et al., Phys. Rev. Lett. 115, 147201 (2015)
22. A. Ruckriegel, A. Brataas, R.A. Duine, Phys. Rev. B 97, 081106(R) (2018)
23. W.A. Benalcazar, B.A. Bernevig, T.L. Hughes, Science 357, 61–66 (2017)
24. W.A. Benalcazar, B.A. Bernevig, T.L. Hughes, Phys. Rev. B 96, 245115 (2017)
25. M. Ezawa, Phys. Rev. Lett. 120, 026801 (2018)
26. Z. Song, Z. Fang, C. Fang, Phys. Rev. Lett. 119, 246402 (2017)
27. J. Langbehn, Y. Peng, L. Trifunovic et al., Phys. Rev. Lett. 119, 246401 (2017)
28. F. Schindler, A.M. Cook, M.G. Vergniory et al., Sci. Adv. 4, eaat0346 (2018)
29. R. Queiro, A. Stern, Phys. Rev. Lett. 123, 036802 (2019)
30. B.-Y. Xie, H.-F. Wang, H.-X. Wang et al., Phys. Rev. B 98, 205147 (2018)
31. J. Noh, W.A. Benalcazar, S. Huang et al., Nat. Photon. 12, 408–415 (2018)
32. A.E. Hassan, F.K. Kunst, A. Moritz et al., Nat. Photon. 13, 697–700 (2019)
33. S. Mittal, V.V. Orre, G. Zhu et al., Nat. Photon. 13, 692–696 (2019)
34. X.-D. Chen, W.-M. Deng, F.-L. Shi et al., Phys. Rev. Lett. 122, 233902 (2019)
35. B.-Y, Xie, G.-X. Su, H.-F. Wang et al., Phys. Rev. Lett. 122, 233903 (2019)
36. H. Xue, Y. Yang, F. Gao et al., Nat. Mater. 18, 108–112 (2019)
37. X. Ni, M. Weiner, A. Alu et al., Nat. Mater. 18, 113–120 (2019)
38. H. Xue, Y. Yang, G. Liu et al., Phys. Rev. Lett. 122, 244301 (2019)
39. C. He, S.-Y. Yu, H. Wang et al., Phys. Rev. Lett. 123, 195503 (2019)
40. X. Zhang, H.-X. Wang, Z.-K. Lin et al., Nat. Phys. 15, 582–588 (2019)
41. S. Imhof, C. Berger, F. Bayer et al., Nat. Phys. 14, 925–929 (2018)
42. M. Ezawa, Phys. Rev. B 98, 201402(R) (2018)