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晶体铋沿(111)面方向的双原子层及薄膜具有新奇的拓扑性质. 在实验生长或者实际应用中, 其必然与衬底接触. 本文采用紧束缚近似方法与第一性原理计算研究了Bi双原子层及其与Bi2Te3和Al2O3衬底形成的异质结的电子结构. 计算结果表明, Bi双层是具有0.2 eV的半导体. 当其与具有拓扑表面态的Bi2Te3形成异质结时, 两者电子态之间有很强的杂化,不利于Bi(111)双层拓扑电子态的观测. 将其放在绝缘体Al2O3(0001)时, 导带与价带与衬底电子态杂化较小, 并且展现出巨大的Rashba自旋劈裂. 这是由于衬底诱导Bi(111)双原子层中心反演对称性破缺和自旋-轨道耦合共同作用的结果. 进一步采用紧束缚近似计算得到的结果发现, 衬底Al2O3(0001)对Bi(111)双层的作用等效于一个约为0.5—0.6 V/Å(1 Å = 0.1 nm)的外电场. 此外, Bi(111)双原子层与衬底Bi2Te3电子态之间的强杂化会导致其发生拓扑相变, 即由二维拓扑绝缘体转变为平庸的绝缘体. 本文为人们在Bi(111)双层的生长和将其进行实际应用时如何选择合适的衬底并进行电子性质的调控提供了指导作用.
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关键词:
- Bi(111)双原子层 /
- Rashba效应 /
- 拓扑性质 /
- 自旋-轨道耦合
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.-
Keywords:
- Bi(111) bilayer /
- Rashba effect /
- topological properties /
- spin-orbit coupling
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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
Fig. 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.
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
Fig. 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.
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
Fig. 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.
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
Fig. 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.
图 5 Bi/1QL-Bi2Te3(111)旺尼尔电荷中心的演化
Fig. 5. Evolution of the Wannier charge center for Bi/1QL-Bi2Te3(111).
表 1 1BL-Bi的紧束缚近似参数. εα代表α轨道的在位能 (on-site energy); Vαβσ和Vαβπ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. εα denotes the on-site energies of orbital α. Vαβσ and (Vαβπ) denotes the hopping parameter for σ(π) bond between orbitals α and β.
On-site/eV εs εpx εpy εpz –9.477 –1.383 0.624 –0.154 Hopping/eV Vssσ Vspσ Vppσ Vppπ 1st NN –0.455 1.439 1.718 –0.646 2nd NN 0.001 0.315 0.168 –0.013 3rd NN 0.019 0.278 0.162 –0.123 4th NN –0.112 –0.096 0.162 –0.067 5th 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 物理学报 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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