在本篇論文中，我們調查在圴向應變和基板效應下皺屈和平⾯蜂巢結構的拓撲相變。
⾸先，我們利⽤第⼀原理調查元素周期表中四族（碳, 矽, 鍺, 鍚和鉛）和五族 (砷, 銻和鉍) 懸空雙原⼦層的皺屈和平⾯結構在均向應⼒下的拓撲和電⼦性質。⽽相變也被發現。接著，為了實際應⽤，放置薄膜在基板上，所以蜂巢結構需要在基板上。因此，我們依序研究矽烯的 1 x1 相放在鉍/矽 (111)-√3x√3 基板和鉍/銻平⾯蜂巢結構放在碳化矽 (0001) 上。雖然矽烯在鉍/矽 (111) 是平凡相但是垂直表⾯的外加電場可以⽤來調節能隙並且回復為非平凡相。平⾯鉍/矽蜂巢在碳化矽 (0001) 被發現具有0.56 電⼦伏特的非平凡能隙並且存在狄拉克錐在能隙中。最後，藉由增加平⾯⽅向的應變, 皺屈鉍/銻變成平⾯結構。我們預測平⾯鉍/銻蜂巢擁有⼆維拓撲晶態絕緣體相。

In this dissertation, we investigated the topological phase transitions of materials in the buckled and planar honeycomb structures under isotropic strain and the eff ects of the substrates. First, we investigated the topological and electronic properties of freestanding bilayers of group IV (C, Si, Ge, Sn, and Pb) and V (As, Sb, and Bi) elements of the periodic table in buckled and planar honeycomb structures under isotropic strain using first-principles calculations. The phase transition were identifi ed. Next, for practical applications, thin films placed on substrate, the honeycomb would need to be on top of a substrate. Thus, we studied 1 1 phase of silicene on Bi/Si(111)-√3x√3 substrate and Bi/Sb planar honeycombs on SiC(0001), respectively. The silicene on Bi/Si(111) is found to be trivial, but an out-of-the-plane external electric field can be used to tune the band gap and restore the non-trivial topological phase. The Bi/Sb planar honeycombs on SiC(0001) are shown to support a nontrivial band gap as large as 0.56 eV, which harbors a Dirac cone lying within the band gap. Finally, with increasing in-plane strain, buckled Sb and Bi honeycombs become planar. We predicted planar Sb/Bi honeycomb to harbor a two-dimensional (2D) topological crystalline insulator (TCI) phase.

摘要 i
ABSTRACT ii
LIST OF FIGURES v
LIST OF TABLES vii
1 GENERAL INTRODUCTION 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Dissertation Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 STRAIN DRIVEN TOPOLOGICAL PHASE TRANSITIONS IN
ATOMICALLY THIN FILMS OF GROUP IV AND V ELEMENTS
IN THE HONEYCOMB STRUCTURES 4
2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Computational Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.6 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 TUNABLE TOPOLOGICAL ELECTRONIC STRUCTURE OF SILICENE ON SEMICONDUCTING Bi/Si(111)-√3x√3 SUBSTRATE:
A FIRST-PRINCIPLES STUDY 19
3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Computational Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.6 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4 THE NONTRIVIAL ELECTRONIC STRUCTURE OF Bi/Sb HONEYCOMBS ON SiC(0001) 31
4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.6 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5 TWO-DIMENSIONAL TOPOLOGICAL CRYSTALLINE INSULATOR PHASE IN Sb/Bi PLANAR HONEYCOMB WITH TUNABLE DIRAC GAP 44
5.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.5 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
REFERENCE 56

[1] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
[2] X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
[3] L. Fu and C. L. Kane, Phys. Rev. B 76, 045302 (2007).
[4] B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314, 1757 (2006).
[5] M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Science 318, 766 (2007).
[6] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).
[7] C.-C. Liu, W. Feng, and Y. Yao, Phys. Rev. Lett. 107, 076802 (2011).
[8] C.-C. Liu, H. Jiang, and Y. Yao, Phys. Rev. B 84, 195430 (2011).
[9] M. Wada, S. Murakami, F. Freimuth, and G. Bihlmayer, Phys. Rev. B 83, 121310
(2011).
[10] Z.-Q. Huang, F.-C. Chuang, C.-H. Hsu, Y.-T. Liu, H.-R. Chang, H. Lin, and
A. Bansil, Phys. Rev. B 88, 165301 (2013).
[11] A. Kara, H. Enriquez, A. P. Seitsonen, L. C. Lew Yan Voon, S. Vizzini, B. Aufray, and H. Oughaddou, Surf. Sci. Rep. 67, 1 (2012).
[12] B. Lalmi, H. Oughaddou, H. Enriquez, A. Kara, S. Vizzini, B. Ealet, and B. Aufray, Appl. Phys. Lett. 97, 223109 (2010).
[13] P. Vogt, P. De Padova, C. Quaresima, J. Avila, E. Frantzeskakis, M. C. Asensio, A. Resta, B. Ealet, and G. Le Lay, Phys. Rev. Lett. 108, 155501 (2012).
[14] B. Feng, Z. Ding, S. Meng, Y. Yao, X. He, P. Cheng, L. Chen, and K. Wu, Nano
Lett. 12, 3507 (2012).
[15] L. Chen, H. Li, B. Feng, Z. Ding, J. Qiu, P. Cheng, K. Wu, and S. Meng, Phys. Rev. Lett. 110, 085504 (2013).
[16] P. D. Padova, P. Vogt, A. Resta, J. Avila, I. Razado-Colambo, C. Quaresima,
C. Ottaviani, B. Olivieri, T. Bruhn, T. Hirahara, T. Shirai, S. Hasegawa, M. C. Asensio, and G. L. Lay, Appl. Phys. Lett. 102, 163106 (2013).
[17] L. Chen, B. Feng, and K. Wu, Appl. Phys. Lett. 102, 081602 (2013).
[18] L. Meng, Y. Wang, L. Zhang, S. Du, R. Wu, L. Li, Y. Zhang, G. Li, H. Zhou, W. A. Hofer, and H.-J. Gao, Nano Lett. 13, 685 (2013).
[19] M. R. Tchalala, H. Enriquez, A. J. Mayne, A. Kara, S. Roth, M. G. Silly, A. Bendounan, F. Sirotti, T. Greber, B. Aufray, G. Dujardin, M. A. Ali, and H. Oughaddou, Appl. Phys. Lett. 102, 083107 (2013).
[20] M. C. Cottin, C. A. Bobisch, J. Schaff ert, G. Jnawali, G. Bihlmayer, and R. Möller, Nano Lett. 13, 2717 (2013).
[21] C. Sabater, D. Gosálbez-Martínez, J. Fernández-Rossier, J. G. Rodrigo, C. Untiedt, and J. J. Palacios, Phys. Rev. Lett. 110, 176802 (2013).
[22] A. Takayama, T. Sato, S. Souma, T. Oguchi, and T. Takahashi, Nano Lett. 12,
1776 (2012).
[23] T. Hirahara, G. Bihlmayer, Y. Sakamoto, M. Yamada, H. Miyazaki, S.-i. Kimura,
S. Blügel, and S. Hasegawa, Phys. Rev. Lett. 107, 166801 (2011).
[24] F. Yang, L. Miao, Z. F. Wang, M.-Y. Yao, F. Zhu, Y. R. Song, M.-X. Wang, J.-P.
Xu, A. V. Fedorov, Z. Sun, G. B. Zhang, C. Liu, F. Liu, D. Qian, C. L. Gao, and
J.-F. Jia, Phys. Rev. Lett. 109, 016801 (2012).
[25] L. Miao, Z. F. Wang, W. Ming, M.-Y. Yao, M. Wang, F. Yang, Y. R. Song, F. Zhu, A. V. Fedorov, Z. Sun, C. L. Gao, C. Liu, Q.-K. Xue, C.-X. Liu, F. Liu, D. Qian, and J.-F. Jia, Proc. Natl. Acad. Sci. 110, 2758 (2013).
[26] Z. F. Wang, M.-Y. Yao, W. Ming, L. Miao, F. Zhu, C. Liu, C. L. Gao, D. Qian,J.-F. Jia, and F. Liu, Nat. Commun. 4, 1384 (2013).
[27] L. Fu, Phys. Rev. Lett. 106, 106802 (2011).
[28] T. H. Hsieh, H. Lin, J. Liu, W. Duan, A. Bansil, and L. Fu, Nat. Commun. 3, 982 (2012).
[29] E. O. Wrasse and T. M. Schmidt, Nano Lett. 14, 5717 (2014).
[30] S. Cahangirov, M. Topsakal, E. Aktürk, H. Şahin, and S. Ciraci, Phys. Rev. Lett. 102, 236804 (2009).
[31] Y. M. Koroteev, G. Bihlmayer, E. V. Chulkov, and S. Blügel, Phys. Rev. B 77, 045428 (2008).
[32] H. L. Zhuang, A. K. Singh, and R. G. Hennig, Phys. Rev. B 87, 165415 (2013).
[33] 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).
[34] F.-C. Chuang, L.-Z. Yao, Z.-Q. Huang, Y.-T. Liu, C.-H. Hsu, T. Das, H. Lin, and A. Bansil, Nano Lett. 14, 2505 (2014).
[35] F.-C. Chuang, C.-H. Hsu, C.-Y. Chen, Z.-Q. Huang, V. Ozolins, H. Lin, and A. Bansil, Appl. Phys. Lett. 102, 022424 (2013).
[36] L. Chen, Z. F. Wang, and F. Liu, Phys. Rev. B 87, 235420 (2013).
[37] G. G. Guzmán-Verri and L. C. Lew Yan Voon, Phys. Rev. B 76, 075131 (2007).
[38] G. Gupta, H. Lin, A. Bansil, M. B. A. Jalil, C.-Y. Huang, W.-F. Tsai, and G. Liang, Appl. Phys. Lett. 104, 032410 (2014).
[39] T. Saari, C.-Y. Huang, J. Nieminen, W.-F. Tsai, H. Lin, and A. Bansil, Appl. Phys. Lett. 104, 173104 (2014).
[40] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
[41] P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
[42] P. E. Blöchl, Phys. Rev. B 50, 17953 (1994); G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999).
[43] G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993); G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
[44] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[45] W.-F. Tsai, C.-Y. Huang, T.-R. Chang, H. Lin, H.-T. Jeng, and A. Bansil, Nat. Commun. 4, 1500 (2013).
[46] X.-L. Qi and S.-C. Zhang, Phys. Today 63, 33 (2010).
[47] J. M. Nicholls, B. Reihl, and J. E. Northrup, Phys. Rev. B 35, 4137 (1987).
[48] A. Kawazu and H. Sakama, Phys. Rev. B 37, 2704 (1988).
[49] H. B. Elswijk, D. Dijkkamp, and E. J. van Loenen, Phys. Rev. B 44, 3802 (1991).
[50] M. Göthelid, M. Björkqvist, T. M. Grehk, G. Le Lay, and U. O. Karlsson, Phys. Rev. B 52, R14352 (1995).
[51] V. Yeh, L. Berbil-Bautista, C. Z. Wang, K. M. Ho, and M. C. Tringides, Phys. Rev. Lett. 85, 5158 (2000).
[52] M. H. Upton, C. M. Wei, M. Y. Chou, T. Miller, and T.-C. Chiang, Phys. Rev. Lett. 93, 026802 (2004).
[53] R. Shioda, A. Kawazu, A. A. Baski, C. F. Quate, and J. Nogami, Phys. Rev. B 48, 4895 (1993).
[54] R. Z. Bakhtizin, C. Park, T. Hashizume, and T. Sakurai, J. Vac. Sci. Technol., B 12, 2052 (1994).
[55] T. M. Schmidt, R. H. Miwa, and G. P. Srivastava, Braz. J. Phys. 34, 629 (2004).
[56] C. Cheng and K. Kunc, Phys. Rev. B 56, 10283 (1997).
[57] I. Gierz, T. Suzuki, E. Frantzeskakis, S. Pons, S. Ostanin, A. Ernst, J. Henk, M. Grioni, K. Kern, and C. R. Ast, Phys. Rev. Lett. 103, 046803 (2009).
[58] E. Frantzeskakis, S. Pons, and M. Grioni, Phys. Rev. B 82, 085440 (2010).
[59] C.-H. Hsu, H.-R. Chang, F.-C. Chuang, Y.-T. Liu, Z.-Q. Huang, H. Lin, V. Ozolinš, and A. Bansil, Surf. Sci. 626, 68 (2014).
[60] C.-H. Hsu, V. Ozolins, and F.-C. Chuang, Surf. Sci. 616, 149 (2013).
[61] C.-H. Hsu, W.-H. Lin, V. Ozolins, and F.-C. Chuang, Appl. Phys. Lett. 100, 063115 (2012).
[62] K. He, T. Hirahara, T. Okuda, S. Hasegawa, A. Kakizaki, and I. Matsuda, Phys. Rev. Lett. 101, 107604 (2008).
[63] E. Frantzeskakis, S. Pons, H. Mirhosseini, J. Henk, C. R. Ast, and M. Grioni, Phys. Rev. Lett. 101, 196805 (2008).
[64] H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976).
[65] N. D. Drummond, V. Zólyomi, and V. I. Fal’ko, Phys. Rev. B 85, 075423 (2012).
[67] T. Fukui and Y. Hatsugai, J. Phys. Soc. Jpn. 76, 053702 (2007).
[68] A. Roth, C. Brüne, H. Buhmann, L. W. Molenkamp, J. Maciejko, X.-L. Qi, and S.-C. Zhang, Science 325, 294 (2009).
[69] C. Liu, T. L. Hughes, X.-L. Qi, K. Wang, and S.-C. Zhang, Phys. Rev. Lett. 100, 236601 (2008).
[70] I. Knez, R.-R. Du, and G. Sullivan, Phys. Rev. Lett. 107, 136603 (2011).
[71] Z. F. Wang, Z. Liu, and F. Liu, Nat. Commun. 4, 1471 (2013).
[72] Z. F. Wang, Z. Liu, and F. Liu, Phys. Rev. Lett. 110, 196801 (2013).
[73] Z. F. Wang, N. Su, and F. Liu, Nano Lett. 13, 2842 (2013).
[74] Z.-Q. Huang, C.-H. Hsu, F.-C. Chuang, Y.-T. Liu, H. Lin, W.-S. Su, V. Ozolins, and Arun Bansil, New J. Phys. 16, 105018 (2014).
[75] J. O. Sofo, A. S. Chaudhari, and G. D. Barber, Phys. Rev. B 75, 153401 (2007).
[76] Z. Song, C.-C. Liu, J. Yang, J. Han, M. Ye, B. Fu, Y. Yang, Q. Niu, J. Lu, and Y. Yao, arXiv (2014), 1402.2399 .
[78] M. Zhou, W. Ming, Z. Liu, Z. Wang, Y. Yao, and F. Liu, Sci. Rep. 4 (2014).
[79] M. Zhou, W. Ming, Z. Liu, Z. Wang, P. Li, and F. Liu, Proc. Natl. Acad. Sci. 111, 14378 (2014).
[80] C.-H. Hsu, W.-H. Lin, V. Ozolins, and F.-C. Chuang, Phys. Rev. B 85, 155401
(2012).
[81] F.-C. Chuang, Z.-Q. Huang, W.-H. Lin, M. A. Albao, and W.-S. Su, Nanotechnology 22, 135703 (2011).
[82] L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98, 106803 (2007).
[83] X.-L. Qi, T. L. Hughes, and S.-C. Zhang, Phys. Rev. B 78, 195424 (2008).
[84] L. Fu and C. L. Kane, Phys. Rev. Lett. 102, 216403 (2009).
[85] Y. Ando, J. Phys. Soc. Jpn. 82, 102001 (2013).
[86] Y. Tanaka, Z. Ren, T. Sato, K. Nakayama, S. Souma, T. Takahashi, K. Segawa, and Y. Ando, Nat. Phys. 8, 800 (2012).
[87] Y. J. Wang, W.-F. Tsai, H. Lin, S.-Y. Xu, M. Neupane, M. Z. Hasan, and A. Bansil, Phys. Rev. B 87, 235317 (2013).
[88] C.-H. Yan, H. Guo, J. Wen, Z.-D. Zhang, L.-L. Wang, K. He, X.-C. Ma, S.-H. Ji, X. Chen, and Q.-K. Xue, Surf. Sci. 621, 104 (2014).
[89] S.-Y. Xu, C. Liu, N. Alidoust, M. Neupane, D. Qian, I. Belopolski, J. D. Denlinger, Y. J. Wang, H. Lin, L. A. Wray, G. Landolt, B. Slomski, J. H. Dil, A. Marcinkova, E. Morosan, Q. Gibson, R. Sankar, F. C. Chou, R. J. Cava, A. Bansil, and M. Z. Hasan, Nat. Commun. 3, 1192 (2012).
[90] H. Guo, C.-H. Yan, J.-W. Liu, Z.-Y. Wang, R. Wu, Z.-D. Zhang, L.-L. Wang,
K. He, X.-C. Ma, S.-H. Ji, W.-H. Duan, X. Chen, and Q.-K. Xue, APL Mater. 2, 056106 (2014).
[91] P. Dziawa, B. J. Kowalski, K. Dybko, R. Buczko, A. Szczerbakow, M. Szot,
E. Łusakowska, T. Balasubramanian, B. M. Wojek, M. H. Berntsen, O. Tjernberg,
and T. Story, Nat. Mater. 11, 1023 (2012).
[92] B. M. Wojek, R. Buczko, S. Safaei, P. Dziawa, B. J. Kowalski, M. H. Berntsen,
T. Balasubramanian, M. Leandersson, A. Szczerbakow, P. Kacman, T. Story, and
O. Tjernberg, Phys. Rev. B 87, 115106 (2013).
[93] I. Zeljkovic, Y. Okada, C.-Y. Huang, R. Sankar, D. Walkup, W. Zhou, M. Serbyn, F. Chou, W.-F. Tsai, H. Lin, A. Bansil, L. Fu, M. Z. Hasan, and V. Madhavan, Nat. Phys. 10, 572 (2014).
[94] J. C. Garcia, D. B. de Lima, L. V. C. Assali, and J. F. Justo, J. Phys. Chem. C 115, 13242 (2011).
[95] C.-w. Zhang and S.-s. Yan, J. Phys. Chem. C 116, 4163 (2012).
[96] W. Rui, W. Shaofeng, and W. Xiaozhi, J. Appl. Phys. 116, 024303 (2014).
[97] 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).
[98] C.-H. Hsu, Z.-Q. Huang, F.-C. Chuang, C.-C. Kuo, Y.-T. Liu, H. Lin, and A. Bansil, New J. Phys. 17, 025005 (2015).
[99] C.-C. Liu, S. Guan, Z. Song, S. A. Yang, J. Yang, and Y. Yao, Phys. Rev. B 90,
085431 (2014).
[100] Z. Song, C.-C. Liu, J. Yang, J. Han, M. Ye, B. Fu, Y. Yang, Q. Niu, J. Lu, and Y. Yao, NPG Asia Mater. 6, e147 (2014).
[101] 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).
[102] L.-Z. Yao, C. P. Crisostomo, C.-C. Yeh, S.-M. Lai, Z.-Q. Huang, C.-H. Hsu, F.-C. Chuang, H. Lin, and A. Bansil, Sci. Rep. 5, 15463 (2015).
[103] H. Jiang, Z. Qiao, H. Liu, and Q. Niu, Phys. Rev. B 85, 045445 (2012).