臺灣博碩士論文加值系統

使用第一原理計算方法，本研究廣泛探討了已知的二維拓撲絕緣體錫和鉍雙分子層成長於三維拓撲絕緣體三碲化二鉍時的電子結構與拓撲性質。在錫成長於三碲化二鉍基板時，三碲化二鉍的拓撲表面態能帶下降，這是由於錫雙分子層電子轉移而導致的n 型參雜。此外，由錫雙分子層貢獻在K 點的能隙受基板影響而增大。為了明白錫雙分子層與三碲化二鉍基板間交互作用而進一步調整它們的間距。此外，也探討了由錫和鉍雙分子層組成的二層雙分子層在有無三碲化二鉍基板下的結構穩定性。當錫和鉍雙分子放上三碲化二鉍基板時呈現拓撲半金屬態。最後，我們呈現了錫和鉍雙分子層在三維拓撲絕緣體三碲化二鉍上的能帶結構。

Using first-principles calculations, the electronic structures and topological
properties of stanene (Sn) and bismuthene (Bi) bilayers grown Bi2Te3,
which are known two-dimensional (2D) and three-dimensional (3D) topological
insulators (TIs), were extensive explored in this report. In the case of Sn
on Bi2Te3 substrate, the topological surface state of Bi2Te3 is shifted down
which results from the n-type doping due to the charge transformation of Sn bilayer. In addition, the gap contributed from Sn bilayer became larger at the K point due to the substrate effect. We further adjusted the distance between Sn bilayer and Bi2Te3 substrate in order to realize the interaction between them. Furthermore, the structural stability of two-bilayer system composed of Sn and Bi bilayers with and without Bi2Te3 substrate was also investigated. A topological semi-metal phase is exhibited when the Sn and Bi bilayer system is placed on the Bi2Te3 substrate. Finally, we presented band structure of Sn and Bi bilayer on the Bi2Te3 as 3D TIs.

論文審定書i
誌謝ii
中文摘要iii
英文摘要iv
1 緒論1
2 理論及計算方法3
2.1 計算軟體設定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Z2 拓撲不變量. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 錫雙分子層成長於三碲化二鉍基板5
3.1 三碲化二鉍基板結構計算. . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 錫雙分子層結構成長於三碲化二鉍基板之結構預測. . . . . . . . . . 8
3.3 錫雙分子層結構成長於三碲化二鉍基板之能帶結構. . . . . . . . . . 10
3.4 錫雙分子層結構與三碲化二鉍在不同間距下的能帶結構. . . . . . . 12
4 錫和鉍之二層薄膜14
4.1 錫和鉍之二層薄膜的原子結構預測. . . . . . . . . . . . . . . . . . . 14
4.2 錫和鉍之二層薄膜的應變效應及拓撲相變. . . . . . . . . . . . . . . 16
5 錫和鉍二層薄膜成長於三碲化二鉍基板21
5.1 錫和鉍二層薄膜成長於三碲化二鉍基板之結構預測. . . . . . . . . . 21
5.2 錫和鉍二層薄膜成長於三碲化二鉍基板之能帶結構. . . . . . . . . . 23
6 結論26
參考文獻27

[1] C. L. Kane and E. J. Mele, Science 314, 1692 (2006).
[2] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
[3] B. I. Halperin, Phys. Rev. B 25, 2185 (1982).
[4] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
[5] B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Science 314, 1757 (2006).
[6] M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X. L. Qi, and S. C. Zhang, Science 318, 766 (2007).
[7] C. Liu, T. L. Hughes, X. L. Qi, K. Wang, and S. C. Zhang, Phys. Rev. Lett. 100, 236601 (2008).
[8] I. Knez, R. R. Du, and G. Sullivan, Phys. Rev. Lett. 107, 136603 (2011).
[9] Y. Xu, B. Yan, H. J. Zhang, J. Wang, G. Xu, P. Tang, W. Duan, and S. C. Zhang, Phys. Rev. Lett. 111, 136804 (2013).
[10] B. H. Chou, Z. Q. Huang, C.H. Hsu, F. C. Chuang, Y. T. Liu, H. Lin, and A. Bansil, New J. Phys. 16, 115008 (2014).
[11] Y. Ma, X. Li, L. Kou, B. Yan, C. Niu, Y. Dai, and T. Heine, Phys. Rev. B 91, 235306 (2015).
[12] C. P. Crisostomo, L. Z. Yao, Z. Q. Huang, C. H. Hsu, F. C. Chuang, H. Lin, M. A. Albao, and A. Bansil, Nano Lett. 15, 6568 (2015).
[13] L. Li, X. Zhang, X. Chen, and M. Zhao, Nano Lett. 15, 1296 (2015).
[14] M. Zhao, X. Chen, L. Li, and X. Zhang, Sci. Rep. 5, 8441 (2015).
[15] Z. Q. Huang, C. H. Hsu, F. C. Chuang, Y. T. Liu, H. Lin, W. S. Su, V. Ozolins, and A. Bansil, New J. Phys. 16, 105018 (2014).
[16] S. Murakami, Phys. Rev. Lett. 97, 236805 (2006).
[17] M. Wada, S. Murakami, F. Freimuth, and G. Bihlmayer, Phys. Rev. Lett. 83, 121310(R) (2011).
[18] Y. Xu, Z. Gan, and S. C. Zhang, Phys. Rev. Lett. 112, 226801 (2014).
[19] J. Wang, Y. Xu, and S. C. Zhang, Phys. Rev. B 90, 054503 (2014).
[20] S. C. Wu, G. Shan, and B. Yan, Phys. Rev. Lett. 113, 256401 (2014).
[21] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature 452, 06843 (2008).
[22] Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature Physics 5, 398 (2009).
[23] 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).
[24] K. F. Zhang, Fang Yang, Y. R. Song, C. Liu, D. Qian, C. L. Gao, and J. F. Jia, Appl. Phys. Lett. 107, 121601 (2015).
[25] M. Chen, J. P. Peng, H. M. Zhang, L. L. Wang, K. He, X. C. Ma, and Q. K. Xue, Appl. Phys. Lett. 101, 081603 (2012).
[26] F. F. Zhu, W. J. Chen, Y. Xu, C. L. Gao, D.D. Guan, C. H. Liu, D. Qian, S. C. Zhang, and J. F. Jia, Nature Materials 14, 1020 (2015).
[27] G. Kresse, and J. Hafner, Phys. Rev. B 47, 558 (1993).
[28] G. Kresse, and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
[29] G. Kresse, and D. Joubert, Phys. Rev. B 59, 1758 (1999).
[30] J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
[31] H.J. Monkhorst, and J.D. Pack, Phys. Rev. B 13, 5188 (1976).
[32] C.L. Kane, and E.J. Mele, Phys. Rev. Lett. 95, 146802 (2005).
[33] L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98, 106803 (2007).
[34] T. Fukui and Y. Hatsugai, J. Phys. Soc. Jpn. 76, 053702 (2007).
[35] H. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang and S. C. Zhang, Nature Physics 5, 438 (2009).