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Multiple Dirac points including potential spin-orbit Dirac points in nonsymmorphic HfGe0.92Te

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Abstract

The search for new materials with Dirac points has been a fascinating subject of condensed matter physics. Here we first report the growth and band structure of HfGe0.92Te single crystals featuring three different types of Dirac points. HfGe0.92Te crystallizes in a nonsymmorphic tetragonal space group P4/nmm (No. 129), having a square Ge-atom plane with vacancies of about 8%. Using angle-resolved photoemission spectroscopy (ARPES), the Dirac nodal line composed of conventional Dirac points vulnerable to spin-orbit coupling (SOC) is observed, accompanied by robust Dirac points protected by the nonsymmorphic symmetry against SOC and vacancies. In particular, spin-orbit Dirac points (SDPs) originating from the surface formed under significant SOC could exist based on ARPES and calculations. Quasi-two-dimensional (quasi-2D) characteristics are confirmed by angular-resolved magnetoresistance. HfGe0.92Te bulk crystals can be easily exfoliated to flakes with a thickness of approximately 5 nm for the quasi-2D nature. Thus, HfGe0.92Te provides a good platform to explore exotic topological phases or topological properties with three different types of Dirac points, which is a potential candidate to achieve novel 2D SDPs.

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References

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

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

    Article  ADS  Google Scholar 

  4. 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.

    Article  ADS  Google Scholar 

  5. Y. L. Chen, J. G. Analytis, J. H. Chu, Z. K. Liu, S. K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z. X. Shen, Science 325, 178 (2009).

    Article  ADS  Google Scholar 

  6. R. Yu, W. Zhang, H. J. Zhang, S. C. Zhang, X. Dai, and Z. Fang, Science 329, 61 (2010), arXiv: 1002.0946.

    Article  ADS  Google Scholar 

  7. C. Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, M. Guo, K. Li, Y. Ou, P. Wei, L. L. Wang, Z. Q. Ji, Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S. C. Zhang, K. He, Y. Wang, L. Lu, X. C. Ma, and Q. K. Xue, Science 340, 167 (2013), arXiv: 1605.08829.

    Article  ADS  Google Scholar 

  8. H. M. Weng, R. Yu, X. Hu, X. Dai, and Z. Fang, Adv. Phys. 64, 227 (2015), arXiv: 1508.02967.

    Article  ADS  Google Scholar 

  9. L. Fu, Phys. Rev. Lett. 106, 106802 (2011), arXiv: 1010.1802.

    Article  ADS  Google Scholar 

  10. H. Chen, J. Gao, L. Chen, G. Wang, H. Li, Y. Wang, J. Liu, J. Wang, D. Geng, Q. Zhang, J. Sheng, F. Ye, T. Qian, L. Chen, H. Weng, J. Ma, and X. Chen, Adv. Mater. 34, 2110664 (2022).

    Article  Google Scholar 

  11. Z. Wang, Y. Sun, X. Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, and Z. Fang, Phys. Rev. B 85, 195320 (2012).

    Article  ADS  Google Scholar 

  12. Z. Wang, H. Weng, Q. Wu, X. Dai, and Z. Fang, Phys. Rev. B 88, 125427 (2013), arXiv: 1305.6780.

    Article  ADS  Google Scholar 

  13. Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S. K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, Science 343, 864 (2014), arXiv: 1310.0391.

    Article  ADS  Google Scholar 

  14. Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S. K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, Nat. Mater. 13, 677 (2014).

    Article  ADS  Google Scholar 

  15. H. M. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai, Phys. Rev. X 5, 011029 (2015), arXiv: 1501.00060.

    Google Scholar 

  16. B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, Phys. Rev. X 5, 031013 (2015), arXiv: 1502.04684.

    Google Scholar 

  17. S. M. Huang, S. Y. Xu, I. Belopolski, C. C. Lee, G. Chang, B. K. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, and M. Z. Hasan, Nat. Commun. 6, 7373 (2015).

    Article  ADS  Google Scholar 

  18. S. Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C. C. Lee, S. M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. K. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, Science 349, 613 (2015), arXiv: 1502.03807.

    Article  ADS  Google Scholar 

  19. B. Q. Lv, N. Xu, H. M. Weng, J. Z. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, C. E. Matt, F. Bisti, V. N. Strocov, J. Mesot, Z. Fang, X. Dai, T. Qian, M. Shi, and H. Ding, Nat. Phys. 11, 724 (2015), arXiv: 1503.09188.

    Article  Google Scholar 

  20. S. Y. Xu, N. Alidoust, I. Belopolski, Z. Yuan, G. Bian, T. R. Chang, H. Zheng, V. N. Strocov, D. S. Sanchez, G. Chang, C. Zhang, D. Mou, Y. Wu, L. Huang, C. C. Lee, S. M. Huang, B. K. Wang, A. Bansil, H. T. Jeng, T. Neupert, A. Kaminski, H. Lin, S. Jia, and M. Z. Hasan, Nat. Phys. 11, 748 (2015).

    Article  Google Scholar 

  21. C. Liu, J. L. Shen, J. C. Gao, C. J. Yi, D. Liu, T. Xie, L. Yang, S. Danilkin, G. C. Deng, W. H. Wang, S. L. Li, Y. G. Shi, H. M. Weng, E. K. Liu, and H. Q. Luo, Sci. China-Phys. Mech. Astron. 64, 217062 (2021), arXiv: 2006.07339.

    Article  ADS  Google Scholar 

  22. E. V. Gorbar, V. A. Miransky, and I. A. Shovkovy, Phys. Rev. B 88, 165105 (2013), arXiv: 1307.6230.

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  24. H. Q. Huang, Y. Xu, J. F. Wang, and W. H. Duan, WIREs Comput. Mol. Sci. 7, e1296 (2017).

    Article  Google Scholar 

  25. Y. F. Ren, Z. H. Qiao, and Q. Niu, Rep. Prog. Phys. 79, 066501 (2016), arXiv: 1509.09016.

    Article  ADS  Google Scholar 

  26. Z. F. Wang, Z. Liu, and F. Liu, Phys. Rev. Lett. 110, 196801 (2013), arXiv: 1302.1088.

    Article  ADS  Google Scholar 

  27. S. M. Young, and C. L. Kane, Phys. Rev. Lett. 115, 126803 (2015), arXiv: 1504.07977.

    Article  ADS  Google Scholar 

  28. Y. H. Lu, D. Zhou, G. Q. Chang, S. Guan, W. G. Chen, Y. Z. Jiang, J. Z. Jiang, X. S. Wang, S. A. Yang, Y. P. Feng, Y. Kawazoe, and H. Lin, npj Comput. Mater. 2, 16011 (2016), arXiv: 1509.05629.

    Article  ADS  Google Scholar 

  29. A. K. Singh, and R. G. Hennig, Appl. Phys. Lett. 105, 042103 (2014).

    Article  ADS  Google Scholar 

  30. P. J. Kowalczyk, S. A. Brown, T. Maerkl, Q. Lu, C. K. Chiu, Y. Liu, S. A. Yang, X. Wang, I. Zasada, F. Genuzio, T. O. Menteş, A. Locatelli, T. C. Chiang, and G. Bian, ACS Nano 14, 1888 (2020).

    Article  Google Scholar 

  31. Q. N. Xu, Z. D. Song, S. M. Nie, H. Weng, Z. Fang, and X. Dai, Phys. Rev. B 92, 205310 (2015), arXiv: 1509.01686.

    Article  ADS  Google Scholar 

  32. I. Lee, S. I. Hyun, and J. H. Shim, Phys. Rev. B 103, 165106 (2021).

    Article  ADS  Google Scholar 

  33. W. Tremel, and R. Hoffmann, J. Am. Chem. Soc. 109, 124 (1987).

    Article  Google Scholar 

  34. L. M. Schoop, M. N. Ali, C. Straßer, A. Topp, A. Varykhalov, D. Marchenko, V. Duppel, S. S. P. Parkin, B. V. Lotsch, and C. R. Ast, Nat. Commun. 7, 11696 (2016), arXiv: 1509.00861.

    Article  ADS  Google Scholar 

  35. M. Neupane, I. Belopolski, M. M. Hosen, D. S. Sanchez, R. Sankar, M. Szlawska, S. Y. Xu, K. Dimitri, N. Dhakal, P. Maldonado, P. M. Oppeneer, D. Kaczorowski, F. Chou, M. Z. Hasan, and T. Durakiewicz, Phys. Rev. B 93, 201104 (2016), arXiv: 1604.00720.

    Article  ADS  Google Scholar 

  36. J. Hu, Z. J. Tang, J. Y. Liu, X. Liu, Y. L. Zhu, D. Graf, K. Myhro, S. Tran, C. N. Lau, J. Wei, and Z. Q. Mao, Phys. Rev. Lett. 117, 016602 (2016), arXiv: 1604.06860.

    Article  ADS  Google Scholar 

  37. T. T. Zhang, Y. Jiang, Z. D. Song, H. Huang, Y. Q. He, Z. Fang, H. M. Weng, and C. Fang, Nature 566, 475 (2019), arXiv: 1807.08756.

    Article  ADS  Google Scholar 

  38. Y. Y. Lv, B. B. Zhang, X. Li, S. H. Yao, Y. B. Chen, J. Zhou, S. T. Zhang, M. H. Lu, and Y. F. Chen, Appl. Phys. Lett. 108, 244101 (2016), arXiv: 1604.01864.

    Article  ADS  Google Scholar 

  39. M. R. van Delft, S. Pezzini, T. Khouri, C. S. A. Müller, M. Breitkreiz, L. M. Schoop, A. Carrington, N. E. Hussey, and S. Wiedmann, Phys. Rev. Lett. 121, 256602 (2018), arXiv: 1806.10592.

    Article  ADS  Google Scholar 

  40. S. M. Chi, F. Liang, H. X. Chen, W. D. Tian, H. Zhang, H. H. Yu, G. Wang, Z. S. Lin, J. P. Hu, and H. J. Zhang, Adv. Mater. 32, 1904498 (2020).

    Article  Google Scholar 

  41. P. Li, B. J. Lv, Y. Fang, W. Guo, Z. Z. Wu, Y. Wu, D. W. Shen, Y. F. Nie, L. Petaccia, C. Cao, Z. A. Xu, and Y. Liu, Sci. China-Phys. Mech. Astron. 64, 237412 (2021), arXiv: 2011.11267.

    Article  ADS  Google Scholar 

  42. S. Guan, Y. Liu, Z. M. Yu, S. S. Wang, Y. G. Yao, and S. A. Yang, Phys. Rev. Mater. 1, 054003 (2017), arXiv: 1706.08692.

    Article  Google Scholar 

  43. X. F. Wang, X. C. Pan, M. Gao, J. H. Yu, J. Jiang, J. R. Zhang, H. K. Zuo, M. H. Zhang, Z. X. Wei, W. Niu, Z. C. Xia, X. Wan, Y. L. Chen, F. Q. Song, Y. B. Xu, B. G. Wang, G. H. Wang, and R. Zhang, Adv. Electron. Mater. 2, 1600228 (2016).

    Article  Google Scholar 

  44. Y. Yao, F. Ye, X. L. Qi, S. C. Zhang, and Z. Fang, Phys. Rev. B 75, 041401 (2007), arXiv: cond-mat/0606350.

    Article  ADS  Google Scholar 

  45. Y. J. Jin, B. B. Zheng, X. L. Xiao, Z. J. Chen, Y. Xu, and H. Xu, Phys. Rev. Lett. 125, 116402 (2020), arXiv: 2008.10175.

    Article  ADS  Google Scholar 

  46. H. Onken, K. Vierheilig, and H. Hahn, Z. Anorg. Allg. Chem. 333, 267 (1964).

    Article  Google Scholar 

  47. P. C. Canfield, T. Kong, U. S. Kaluarachchi, and N. H. Jo, Philos. Mag. 96, 84 (2016), arXiv: 1509.08131.

    Article  ADS  Google Scholar 

  48. J. Rodríguez-Carvajal, Phys. B-Condens. Matter 192, 55 (1993).

    Article  ADS  Google Scholar 

  49. G. Kresse, and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).

    Article  ADS  Google Scholar 

  50. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 78, 1396 (1997).

    Article  ADS  Google Scholar 

  51. F. Tran, and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009).

    Article  ADS  Google Scholar 

  52. A. D. Becke, and E. R. Johnson, J. Chem. Phys. 124, 221101 (2006).

    Article  ADS  Google Scholar 

  53. A. A. Mostofi, J. R. Yates, G. Pizzi, Y. S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, Comput. Phys. Commun. 185, 2309 (2014).

    Article  ADS  Google Scholar 

  54. Q. S. Wu, S. N. Zhang, H. F. Song, M. Troyer, and A. A. Soluyanov, Comput. Phys. Commun. 224, 405 (2018), arXiv: 1703.07789.

    Article  ADS  Google Scholar 

  55. R. van Noorden, Nature 483, S32 (2012).

    Article  ADS  Google Scholar 

  56. X. C. Wang, Q. Q. Liu, Y. X. Lv, W. B. Gao, L. X. Yang, R. C. Yu, F. Y. Li, and C. Q. Jin, Solid State Commun. 148, 538 (2008), arXiv: 0806.4688.

    Article  ADS  Google Scholar 

  57. D. Takane, Z. Wang, S. Souma, K. Nakayama, C. X. Trang, T. Sato, T. Takahashi, and Y. Ando, Phys. Rev. B 94, 121108 (2016), arXiv: 1606.07957.

    Article  ADS  Google Scholar 

  58. R. Lou, J. Z. Ma, Q. N. Xu, B. B. Fu, L. Y. Kong, Y. G. Shi, P. Richard, H. M. Weng, Z. Fang, S. S. Sun, Q. Wang, H. C. Lei, T. Qian, H. Ding, and S. C. Wang, Phys. Rev. B 93, 241104 (2016), arXiv: 1601.07294.

    Article  ADS  Google Scholar 

  59. C. C. Liu, W. Feng, and Y. Yao, Phys. Rev. Lett. 107, 076802 (2011), arXiv: 1104.1290.

    Article  ADS  Google Scholar 

  60. C. C. Wang, and T. Hughbanks, Inorg. Chem. 34, 5524 (1995).

    Article  Google Scholar 

  61. M. N. Ali, L. M. Schoop, C. Garg, J. M. Lippmann, E. Lara, B. Lotsch, and S. S. P. Parkin, Sci. Adv. 2, e1601742 (2016), arXiv: 1603.09318.

    Article  ADS  Google Scholar 

  62. W. Wang, S. Y. Dai, X. D. Li, J. R. Yang, D. J. Srolovitz, and Q. S. Zheng, Nat. Commun. 6, 7853 (2015), arXiv: 1506.00536.

    Article  ADS  Google Scholar 

  63. J. W. Liu, H. Wang, C. Fang, L. Fu, and X. F. Qian, Nano Lett. 17, 467 (2017), arXiv: 1605.03903.

    Article  ADS  Google Scholar 

  64. S. Zhao, Z. Li, and J. Yang, J. Am. Chem. Soc. 136, 13313 (2014).

    Article  Google Scholar 

  65. R. Zacharia, H. Ulbricht, and T. Hertel, Phys. Rev. B 69, 155406 (2004), arXiv: cond-mat/0308451.

    Article  ADS  Google Scholar 

  66. M. Yi, and Z. Shen, J. Mater. Chem. A 3, 11700 (2015).

    Article  Google Scholar 

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Correspondence to Chen Liu, Jia’ou Wang, Hongming Weng or Gang Wang.

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This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 51832010, 51902055, 11925408, 12005251, and 11921004), and National Key Research and Development Program of China (Grant Nos. 2018YFE0202602, 2018YFA0305700, and 2017YFA0302902). L. Chen and G. Wang would like to thank professor X. L. Chen from the Institute of Physics, Chinese Academy of Sciences, for useful discussions.

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Chen, L., Zhou, L., Zhou, Y. et al. Multiple Dirac points including potential spin-orbit Dirac points in nonsymmorphic HfGe0.92Te. Sci. China Phys. Mech. Astron. 66, 217011 (2023). https://doi.org/10.1007/s11433-022-1992-x

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