Effects of Bi2Te3(111) and Al2O3(0001) substrates on electronic and topological properties of Bi(111) bilayer

Sun Hai-Ming

doi:10.7498/aps.71.20220060

Abstract

The bilayer and thin films of Bi(111) have demonstrated novel topological properties. Here, we investigate the electronic structures of Bi/Bi₂Te₃(111) and Bi/Al₂O₃(0001) by combining first-principles and tight-binding approximation calculations. Our results show that the Bi(111) bilayer is a semiconductor with a gap of about 0.2 eV. Its electronic states are strongly disturbed by the interaction with Bi₂Te₃(111) thin films, no matter whether the substrate has a band gap or Dirac surface state. Moreover, it is hard to see Rashba-type band splittings in such systems. In contrast, it demonstrates clean and giant Rashba-type splittings as strongly hybridized with insulating Al₂O₃(0001), which is due to the broken inversion symmetry induced by interfacing and the strong atomic spin-orbit coupling in Bi. Our tight-binding approximation analyses further reveal that the effect of substrate Al₂O₃(0001) on the band structure of the Bi(111) bilayer is equivalent to the action of external electric field in a range between 0.5 and 0.6 V/Å. Moreover, we find that the strong hybridization between Bi(111) bilayer and the electronic state of the substrate Bi₂Te₃(111) can lead to a topological phase transition, i.e. the change from a two-dimensional topological insulator into a mediocre insulator. Our study thus provides an insight into the interface-engineering of electronic states of Bi(111) bilayer.

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Authors and contacts

Sun Hai-Ming

School of Physics and Electronics, Hunan Normal University, Changsha 410081, China

Corresponding author: Sun Hai-Ming, 201930132023@hunnu.edu.cn

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References

[1]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802 Google Scholar
[2]	Fu L, Kane C L, Mele E J 2007 Phys. Rev. Lett. 98 106803 Google Scholar
[3]	Moore J E 2010 Nature 464 194 Google Scholar
[4]	Hasan M Z, Kane C L, 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[5]	Qi X L, Zhang S C, 2011 Rev. Mod. Phys. 83 1057 Google Scholar
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[9]	Liu Z, Liu C X, Wu Y S, Duan W H, Liu Feng, Wu J 2011 Phys. Rev. Lett. 107 136805 Google Scholar
[10]	Hirahara T, Bihlmayer G, Sakamoto Y, Yamada M, Miyazaki H, Kimura S, Blügel S, Hasegawa S 2011 Phys. Rev. Lett. 107 166801 Google Scholar
[11]	Yang F, Miao L, Wang Z F, Yao M Y, Zhu F F, Song Y R, Wang M X, Xu J P, Fedorov A V, Sun Z, Zhang G B, Liu C H, Liu F, Qian D, Gao C L, Jia J F 2012 Phys. Rev. Lett. 109 016801 Google Scholar
[12]	Chen M, Peng J P, Zhang H M, Wang L L, He K, Ma X C, Xue Q K 2012 Appl. Phys. Lett. 101 081603 Google Scholar
[13]	Chang C Z, Tang P, Feng X, Li K, Ma X C, Duan W, He K, Xue Q K 2015 Phys. Rev. Lett. 115 136801 Google Scholar
[14]	Shokri R, Meyerheim H L, Roy S, Mohseni K, Ernst A, Otrokov M M, Chulkov E V, Kirschner J 2015 Phys. Rev. B 91 205430 Google Scholar
[15]	Yao M Y, Zhu F F, Han C Q, Guan D D, Liu C H, Qian D, Jia J F 2016 Sci. Rep. 6 21326 Google Scholar
[16]	Schouteden K, Govaerts K, Debehets J, Thupakula U, Chen T, Li Z, Netsou A, Song F Q, Lamoen D, Haesendonck C V, Partoens B, Park K 2016 ACS Nano 10 8778 Google Scholar
[17]	Su S H, Chuang P Y, Chen S W, Chen H Y, Tung Y, Chen W C, Wang C H, Yang Y W, Huang J C A, Chang T R, Lin H, Jeng H T, Cheng C M, Tsuei K D, Su H L, Wu Y C 2017 Chem. Mater. 29 8992 Google Scholar
[18]	Zhu H S, Zhou W M, Yarmoff J A 2018 Thin Solid Films 660 343 Google Scholar
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[20]	胡金平, 何丙辰, 王红兵, 张欢, 黄朝钦, 谢磊, 郭晓, 陈石, 黄寒, 宋飞 2022 72 026101 Google Scholar Hu J P, He B C, Wang H B, Zhang H, Huang C Q, Xie L, Guo X, Chen S, Huang H, Song F 2022 Acta Phys. Sin. 72 026101 Google Scholar
[21]	Chen M, Liu F 2021 Natl. Sci. Rev. 8 nwaa241 Google Scholar
[22]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[23]	Blochl P E 1994 Phys. Rev. B 50 17953 31
[24]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[25]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[26]	Grimme S, Antony J, Ehrlich S, Krieg S 2010 J. Chem. Phys. 132 154104 Google Scholar
[27]	Slater J C, Koster G F 1954 Phys. Rev. 94 1498 Google Scholar
[28]	Maassena J, Lundstrom M 2013 Appl. Phys. Lett. 102 093103 Google Scholar
[29]	Acosta C M, Lima M P, Silva A J R D, Fazzio A, Lewenkopf C H 2018 Phys. Rev. B 98 035106 Google Scholar
[30]	Hirahara T, Nagao T, Matsuda I, Bihlmayer G, Chulkov E V, Koroteev Y M, Echenique P M, Saito M, Hasegawa S 2006 Phys. Rev. Lett. 97 146803 Google Scholar
[31]	Hirahara T, Nagao T, Matsuda I, Bihlmayer G, Chulkov E V, Koroteev Y M, Hasegawa S 2007 Phys. Rev. B 75 035422 Google Scholar
[32]	Yu R, Qi X L, Bernevig A, Fang Z, Dai X 2011 Phys. Rev. B 84 075119 Google Scholar

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图 1 1BL-Bi的几何结构和能带 (a) (b)结构的俯视图和侧视图; (c)平衡体积时的能带; (d) (e)减小和增大晶格常数时的能带结构, 其数值对应Bi₂Te₃(111)和Al₂O₃(0001)的晶格常数. (a) 图中的菱形代表原胞, (c)—(e) 图中的虚线代表费米能级

Figure 1. Geometric and band structures of 1BL-Bi: (a) (b) Top and side views of the structure; (c) band structure for the equilibrium lattice constant; (d) (e) band structures for a decreased and enlarged lattice constant, respectively. The black box in (a) represents the primitive cell. The dashed lines in (c)–(e) denote the Fermi level.

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图 2 Bi/Bi₂Te₃异质结界面的结构和能带左侧给出Bi/1QL-Bi₂Te₃四种构型(用C1, C2, C3和C4表示)的俯视图和侧视图. Bi/3QL-Bi₂Te₃与其类似, 差别在于衬底有3个QL. (a) 1QL-Bi₂Te₃的能带结构; (b) Bi/1QL-Bi₂Te₃的能带结构; (c) 和 (d) 分别代表将能带投影到1BL-Bi和衬底1QL-Bi₂Te₃; (e) 1QL-Bi₂Te₃的能带结构; (f) Bi/3QL-Bi₂Te₃的能带结构; (g) 和 (h) 分别代表将能带投影到1BL-Bi和衬底3QL-Bi₂Te₃. 图(c), (d), (g)和(h)给出的是1BL-Bi或者Bi₂Te₃在异质结能带中所占的权重

Figure 2. Geometric and band structures of Bi/Bi₂Te₃ heterostructures: Left panel shows the geometric structures of four configurations for Bi/1QL-Bi₂Te₃, which are denoted as C1, C2, C3, and C4, respectively. The geometric structure for Bi/3QL-Bi₂Te₃ are similar to those for Bi/1QL-Bi₂Te₃. (a) For the free-standing 1QL-Bi₂Te₃ and (b) for Bi/1QL-Bi₂Te₃; (c) and (d) show the layer-projections of the band structure onto 1BL-Bi and 1QL-Bi₂Te₃, respectively; (e)–(h) corresponding plots for Bi/3QL-Bi₂Te₃.

DownLoad: Full-Size Img PowerPoint

图 3 绝缘体Al₂O₃对1BL-Bi电子结构的影响　(a) Bi/Al₂O₃(0001)异质结界面的能带; (b) 异质结能带在1BL-Bi上的投影

Figure 3. Effects of insulating Al₂O₃ on the band structure of 1L-Bi: (a) The band structure of Bi/Al₂O₃(0001); (b) layer-projection of the band structure onto 1L-Bi.

DownLoad: Full-Size Img PowerPoint

图 4 电场对1BL-Bi能带结构的影响　(a) 能带结构的紧束缚近似拟合; (b)—(d)不同电场作用下紧束缚近似计算得到的能带结构

Figure 4. Effects of electric field on the band structure of 1L-Bi: (a) Tight-binding fitting of the band structure of 1L-Bi; (b)–(d) band structures of 1L-Bi under different electric fields derived from the tight-binding method.

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图 5 Bi/1QL-Bi₂Te₃(111)旺尼尔电荷中心的演化

Figure 5. Evolution of the Wannier charge center for Bi/1QL-Bi₂Te₃(111).

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表 1 1BL-Bi的紧束缚近似参数. ε_α代表α轨道的在位能 (on-site energy); V_αβσ和V_αβπ分别代表α 和β轨道形成σ键和π键的跃迁参数. SOC强度λ为1.23 eV

Table 1. Tight-binding parameters for 1BL-Bi. ε_α denotes the on-site energies of orbital α. V_αβσ and (V_αβπ) denotes the hopping parameter for σ(π) bond between orbitals α and β.

On-site/eV
ε_s		ε_px		ε_py		ε_pz
–9.477		–1.383		0.624		–0.154
Hopping/eV
	V_ssσ		V_spσ		V_ppσ		V_ppπ
1^st NN	–0.455		1.439		1.718		–0.646
2^nd NN	0.001		0.315		0.168		–0.013
3^rd NN	0.019		0.278		0.162		–0.123
4^th NN	–0.112		–0.096		0.162		–0.067
5^th NN	–0.046		0.037		0.000		0.028

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[1]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802 Google Scholar
[2]	Fu L, Kane C L, Mele E J 2007 Phys. Rev. Lett. 98 106803 Google Scholar
[3]	Moore J E 2010 Nature 464 194 Google Scholar
[4]	Hasan M Z, Kane C L, 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[5]	Qi X L, Zhang S C, 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[6]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757 Google Scholar
[7]	König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766
[8]	Murakami S 2006 Phys. Rev. Lett. 97 236805 Google Scholar
[9]	Liu Z, Liu C X, Wu Y S, Duan W H, Liu Feng, Wu J 2011 Phys. Rev. Lett. 107 136805 Google Scholar
[10]	Hirahara T, Bihlmayer G, Sakamoto Y, Yamada M, Miyazaki H, Kimura S, Blügel S, Hasegawa S 2011 Phys. Rev. Lett. 107 166801 Google Scholar
[11]	Yang F, Miao L, Wang Z F, Yao M Y, Zhu F F, Song Y R, Wang M X, Xu J P, Fedorov A V, Sun Z, Zhang G B, Liu C H, Liu F, Qian D, Gao C L, Jia J F 2012 Phys. Rev. Lett. 109 016801 Google Scholar
[12]	Chen M, Peng J P, Zhang H M, Wang L L, He K, Ma X C, Xue Q K 2012 Appl. Phys. Lett. 101 081603 Google Scholar
[13]	Chang C Z, Tang P, Feng X, Li K, Ma X C, Duan W, He K, Xue Q K 2015 Phys. Rev. Lett. 115 136801 Google Scholar
[14]	Shokri R, Meyerheim H L, Roy S, Mohseni K, Ernst A, Otrokov M M, Chulkov E V, Kirschner J 2015 Phys. Rev. B 91 205430 Google Scholar
[15]	Yao M Y, Zhu F F, Han C Q, Guan D D, Liu C H, Qian D, Jia J F 2016 Sci. Rep. 6 21326 Google Scholar
[16]	Schouteden K, Govaerts K, Debehets J, Thupakula U, Chen T, Li Z, Netsou A, Song F Q, Lamoen D, Haesendonck C V, Partoens B, Park K 2016 ACS Nano 10 8778 Google Scholar
[17]	Su S H, Chuang P Y, Chen S W, Chen H Y, Tung Y, Chen W C, Wang C H, Yang Y W, Huang J C A, Chang T R, Lin H, Jeng H T, Cheng C M, Tsuei K D, Su H L, Wu Y C 2017 Chem. Mater. 29 8992 Google Scholar
[18]	Zhu H S, Zhou W M, Yarmoff J A 2018 Thin Solid Films 660 343 Google Scholar
[19]	Zhu H S, Zhou W M, Yarmoff J A 2018 J. Phys. Chem. C 122 16122 Google Scholar
[20]	胡金平, 何丙辰, 王红兵, 张欢, 黄朝钦, 谢磊, 郭晓, 陈石, 黄寒, 宋飞 2022 72 026101 Google Scholar Hu J P, He B C, Wang H B, Zhang H, Huang C Q, Xie L, Guo X, Chen S, Huang H, Song F 2022 Acta Phys. Sin. 72 026101 Google Scholar
[21]	Chen M, Liu F 2021 Natl. Sci. Rev. 8 nwaa241 Google Scholar
[22]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[23]	Blochl P E 1994 Phys. Rev. B 50 17953 31
[24]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[25]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[26]	Grimme S, Antony J, Ehrlich S, Krieg S 2010 J. Chem. Phys. 132 154104 Google Scholar
[27]	Slater J C, Koster G F 1954 Phys. Rev. 94 1498 Google Scholar
[28]	Maassena J, Lundstrom M 2013 Appl. Phys. Lett. 102 093103 Google Scholar
[29]	Acosta C M, Lima M P, Silva A J R D, Fazzio A, Lewenkopf C H 2018 Phys. Rev. B 98 035106 Google Scholar
[30]	Hirahara T, Nagao T, Matsuda I, Bihlmayer G, Chulkov E V, Koroteev Y M, Echenique P M, Saito M, Hasegawa S 2006 Phys. Rev. Lett. 97 146803 Google Scholar
[31]	Hirahara T, Nagao T, Matsuda I, Bihlmayer G, Chulkov E V, Koroteev Y M, Hasegawa S 2007 Phys. Rev. B 75 035422 Google Scholar
[32]	Yu R, Qi X L, Bernevig A, Fang Z, Dai X 2011 Phys. Rev. B 84 075119 Google Scholar

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Effects of Bi₂Te₃(111) and Al₂O₃(0001) substrates on electronic and topological properties of Bi(111) bilayer

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Corresponding author: Sun Hai-Ming, 201930132023@hunnu.edu.cn

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