Skip to main content
Log in

Emergent Z2 topological invariant and robust helical edge states in two-dimensional topological metals

  • Article
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

In this work, we study the effects of disorder on topological metals that support a pair of helical edge modes deeply embedded inside the gapless bulk states. Strikingly, we predict that a quantum spin Hall (QSH) phase can be obtained from such topological metals without opening a global band gap. To be specific, disorder can lead to a pair of robust helical edge states which is protected by an emergent Z2 topological invariant, giving rise to a quantized conductance plateau in transport measurements. These results are instructive for solving puzzles in various transport experiments on QSH materials that are intrinsically metallic. This work also will inspire experimental realization of the QSH effect in disordered topological metals.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. Z. Hasan, and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010), arXiv: 1002.3895.

    ADS  Google Scholar 

  2. X. L. Qi, and S. C. Zhang, Rev. Mod. Phys. 83, 1057 (2011), arXiv: 1008.2026.

    Article  ADS  Google Scholar 

  3. C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005), arXiv: cond-mat/0411737.

    ADS  Google Scholar 

  4. C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005), arXiv: cond-mat/0506581.

    ADS  Google Scholar 

  5. B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Science 314, 1757 (2006), arXiv: cond-mat/0611399.

    ADS  Google Scholar 

  6. M. Konig, S. Wiedmann, C. Brune, A. Roth, H. Buhmann, L. W. Molenkamp, X. L. Qi, and S. C. Zhang, Science 318, 766 (2007), arXiv: 0710.0582.

    ADS  Google Scholar 

  7. A. Roth, C. Brune, H. Buhmann, L. W. Molenkamp, J. Maciejko, X. L. Qi, and S. C. Zhang, Science 325, 294 (2009), arXiv: 0905.0365.

    ADS  Google Scholar 

  8. I. Knez, R. R. Du, and G. Sullivan, Phys. Rev. Lett. 107, 136603 (2011), arXiv: 1105.0137.

    ADS  Google Scholar 

  9. X. Qian, J. Liu, L. Fu, and J. Li, Science 346, 1344 (2014).

    ADS  Google Scholar 

  10. Y. H. Song, Z. Y. Jia, D. Zhang, X. Y. Zhu, Z. Q. Shi, H. Wang, L. Zhu, Q. Q. Yuan, H. Zhang, D. Y. Xing, and S. C. Li, Nat. Commun. 9, 4071 (2018), arXiv: 1711.07286.

    ADS  Google Scholar 

  11. Z. F. Wang, H. Zhang, D. Liu, C. Liu, C. Tang, C. Song, Y. Zhong, J. Peng, F. Li, C. Nie, L. Wang, X. J. Zhou, X. Ma, Q. K. Xue, and F. Liu, Nat. Mater. 15, 968 (2016).

    ADS  Google Scholar 

  12. C. Liu, T. L. Hughes, X. L. Qi, K. Wang, and S. C. Zhang, Phys. Rev. Lett. 100, 236601 (2008), arXiv: 0801.2831.

    ADS  Google Scholar 

  13. I. Knez, C. T. Rettner, S. H. Yang, S. S. P. Parkin, L. Du, R. R. Du, and G. Sullivan, Phys. Rev. Lett. 112, 026602 (2014).

    ADS  Google Scholar 

  14. Z. Fei, T. Palomaki, S. Wu, W. Zhao, X. Cai, B. Sun, P. Nguyen, J. Finney, X. Xu, and D. H. Cobden, Nat. Phys. 13, 677 (2017), arXiv: 1610.07924.

    Google Scholar 

  15. S. Tang, C. Zhang, D. Wong, Z. Pedramrazi, H. Z. Tsai, C. Jia, B. Moritz, M. Claassen, H. Ryu, S. Kahn, J. Jiang, H. Yan, M. Hashimoto, D. Lu, R. G. Moore, C. C. Hwang, C. Hwang, Z. Hussain, Y. Chen, M. M. Ugeda, Z. Liu, X. Xie, T. P. Devereaux, M. F. Crommie, S. K. Mo, and Z. X. Shen, Nat. Phys. 13, 683 (2017).

    Google Scholar 

  16. S. Wu, V. Fatemi, Q. D. Gibson, K. Watanabe, T. Taniguchi, R. J. Cava, and P. Jarillo-Herrero, Science 359, 76 (2018), arXiv: 1711.03584.

    ADS  MathSciNet  Google Scholar 

  17. P. W. Anderson, Phys. Rev. 109, 1492 (1958).

    ADS  Google Scholar 

  18. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).

    ADS  Google Scholar 

  19. M. Onoda, Y. Avishai, and N. Nagaosa, Phys. Rev. Lett. 98, 076802 (2007), arXiv: cond-mat/0605510.

    ADS  Google Scholar 

  20. J. Li, R. L. Chu, J. K. Jain, and S. Q. Shen, Phys. Rev. Lett. 102, 136806 (2009), arXiv: 0811.3045.

    ADS  Google Scholar 

  21. H. Jiang, L. Wang, Q. Sun, and X. C. Xie, Phys. Rev. B 80, 165316 (2009), arXiv: 0905.4550.

    ADS  Google Scholar 

  22. C. W. Groth, M. Wimmer, A. R. Akhmerov, J. Tworzydlo, and C. W. J. Beenakker, Phys. Rev. Lett. 103, 196805 (2009), arXiv: 0908.0881.

    ADS  Google Scholar 

  23. J. Song, H. Liu, H. Jiang, Q. Sun, and X. C. Xie, Phys. Rev. B 85, 195125 (2012), arXiv: 1212.6538.

    ADS  Google Scholar 

  24. D. Xu, J. Qi, J. Liu, V. Sacksteder, X. C. Xie, and H. Jiang, Phys. Rev. B 85, 195140 (2012), arXiv: 1201.4224.

    ADS  Google Scholar 

  25. A. Girschik, F. Libisch, and S. Rotter, Phys. Rev. B 88, 014201 (2013), arXiv: 1212.0735.

    ADS  Google Scholar 

  26. A. Yamakage, K. Nomura, K. I. Imura, and Y. Kuramoto, Phys. Rev. B 87, 205141 (2013), arXiv: 1211.5026.

    ADS  Google Scholar 

  27. Y. Y. Zhang, M. Shen, X. T. An, Q. F. Sun, X. C. Xie, K. Chang, and S. S. Li, Phys. Rev. B 90, 054205 (2014), arXiv: 1403.4369.

    ADS  Google Scholar 

  28. Y. Y. Zhang, J. Hu, B. A. Bernevig, X. R. Wang, X. C. Xie, and W. M. Liu, Phys. Rev. Lett. 102, 106401 (2009), arXiv: 0810.1996.

    ADS  Google Scholar 

  29. C. Z. Chen, H. Liu, H. Jiang, Q. Sun, Z. Wang, and X. C. Xie, Phys. Rev. B 91, 214202 (2015), arXiv: 1504.04172.

    ADS  Google Scholar 

  30. X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Phys. Rev. B 83, 205101 (2011), arXiv: 1007.0016.

    ADS  Google Scholar 

  31. Y. Yang, Z. Xu, L. Sheng, B. Wang, D. Y. Xing, and D. N. Sheng, Phys. Rev. Lett. 107, 066602 (2011), arXiv: 1103.4473.

    ADS  Google Scholar 

  32. T. T. Heikkilä, and G. E. Volovik, Jetp Lett. 93, 59 (2011), arXiv: 1011.4185.

    ADS  Google Scholar 

  33. A. A. Burkov, M. D. Hook, and L. Balents, Phys. Rev. B 84, 235126 (2011), arXiv: 1110.1089.

    ADS  Google Scholar 

  34. S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge Studies in Semiconductor Physics and Microelectronic Engineering (Cambridge University Press, Cambridge, 1995).

    Google Scholar 

  35. D. N. Sheng, Z. Y. Weng, L. Sheng, and F. D. M. Haldane, Phys. Rev. Lett. 97, 036808 (2006), arXiv: cond-mat/0603054.

    ADS  Google Scholar 

  36. L. Sheng, D. N. Sheng, C. S. Ting, and F. D. M. Haldane, Phys. Rev. Lett. 95, 136602 (2005), arXiv: cond-mat/0506589.

    ADS  Google Scholar 

  37. E. Prodan, Phys. Rev. B 80, 125327 (2009), arXiv: 0904.1894.

    ADS  Google Scholar 

  38. E. Prodan, J. Phys. A: Mathemat. Theoret. 44, 113001 (2011).

    ADS  Google Scholar 

  39. A. MacKinnon, and B. Kramer, Phys. Rev. Lett. 47, 1546 (1981).

    ADS  Google Scholar 

  40. A. MacKinnon, and B. Kramer, Z. Phys. B-Condensed Matter 53, 1 (1983).

    ADS  Google Scholar 

  41. B. Kramer, and A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993).

    ADS  Google Scholar 

  42. A. Altland, and M. R. Zirnbauer, Phys. Rev. B 55, 1142 (1997), arXiv: cond-mat/9602137.

    ADS  Google Scholar 

  43. A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Phys. Rev. B 78, 195125 (2008), arXiv: 0803.2786.

    ADS  Google Scholar 

  44. L. Du, I. Knez, G. Sullivan, and R. R. Du, Phys. Rev. Lett. 114, 096802 (2015).

    ADS  Google Scholar 

  45. F. Zheng, C. Cai, S. Ge, X. Zhang, X. Liu, H. Lu, Y. Zhang, J. Qiu, T. Taniguchi, K. Watanabe, S. Jia, J. Qi, J. H. Chen, D. Sun, and J. Feng, Adv. Mater. 28, 4845 (2016).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to X. C. Xie.

Additional information

This work was supported by the National Basic Research Program of China (Grant No. 2015CB921102), the National Natural Science Foundation of China (Grant Nos. 11534001, 11822407, 11704106, and 11974256), and the Fundamental Research Funds for the Central Universities. Hua Jiang and Chui-Zhen Chen are also funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions and National Natural Science Foundation of China of Jiangsu province (Grant No. BK20190813). Dong-Hui Xu is also supported by the Chutian Scholars Program in Hubei Province. We thank HaiWen Liu and Rui-Rui Du for illuminating discussions.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, CZ., Jiang, H., Xu, DH. et al. Emergent Z2 topological invariant and robust helical edge states in two-dimensional topological metals. Sci. China Phys. Mech. Astron. 63, 107811 (2020). https://doi.org/10.1007/s11433-019-1523-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-019-1523-6

Keywords

Navigation