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For an ultra-thin Bi2Se3 film sandwiched between two ferromagnetic insulators (FIs), we investigate how its topological properties change with the angle between the magnetizations of the two FIs. The Chern numbers are calculated from the low-energy effective Hamiltonian for electrons in the surface states, and the bulk energy band and the edge states are simulated from the tight-binding model of a long ribbon with armchair edges on a two-dimensional honeycomb lattice, from which the topological phase of the system can be determined. It is found that with the magnetizations of the FIs varying from parallel to antiparallel, there appears a topological phase transition from the anomalous quantum Hall phase to the trivial insulating one at a critical angle.
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Keywords:
- topological insulator /
- exchange field /
- anomalous quantum Hall effect /
- edge state
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[2] Xia Y, Qian D, Hsieh D, Wray L, Pal A, Lin H, Bansil A, Grauer D, Hor Y S, Cava R J, Hasan M Z 2009 Nature Phys. 5 398
[3] Dai X, Hughes T L, Qi X L, Fang Z, Zhang S C 2008 Phys. Rev. B 77 125319
[4] Fu L, Kane C K, Mele E J 2007 Phys. Rev. Lett. 98 106803
[5] Zhang T, Cheng P, Chen X, Jia J F, Ma X C, He K, Wang L L, Zhang H J, Dai X, Fang Z, Xie X C, Xue Q K 2009 Phys. Rev. Lett. 103 266803
[6] Cheng P, Song C, Zhang T, Zhang Y Y, Wang Y L, Jia J F, Wang J, Wang Y Y, Zhu B F, Chen X, Ma X C, He K, Wang L L, Dai X, Fang Z, Xie X C, Qi X L, Liu C X, Zhang S C, Xue Q K 2010 Phys. Rev. Lett. 105 076801
[7] Hong S S, Kundhikanjana W, Cha J J, Lai K J, Kong D S, Stefan M, Kelly M A, Shen Z X, Cui Y 2010 Nano Lett. 10 3118
[8] Zhang Y, He K, Ma X C, Xue Q K 2011 Physics 40 07 (in Chinese) [张翼, 何珂, 马旭村, 薛其坤 2011 物理 40 07]
[9] Lu H Z, Shan W Y, Yao W, Niu Q, Shen S Q 2010 Phys. Rev. B 81 115407
[10] Li H C, Sheng L, Sheng D N, Xing D Y 2010 Phys. Rev. B 82 165104
[11] Li H C, Sheng L, Xing D Y 2011 Phys. Rev. B 83 195413
[12] Yu R, Zhang W, Weng H M, Dai X, Fang Z 2010 Physics 39 09 (in Chinese) [余睿, 张薇, 翁红明, 戴希, 方忠 2010 物理 39 09]
[13] Yang Y Y, Xu Z, Sheng L, Sheng R, Xing D Y 2011 Appl. Phys. Lett. 99 182101
[14] Thouless D J, Kohmoto M, Nightingale M P, Nijs M D 1982 Phys. Rev. Lett. 49 405
[15] Niu Q, Thouless D J, Wu Y S 1985 Phys. Rev. B 31 3372
[16] Xu Z, Yang Y Y, Sheng L, Xing D Y 2012 J. Phys. Condens Matter 18 185504
[17] Datta S 1995 Electronic Transport in Mesoscopic Systems (1st Edn.) (New York: Cambridge University Press) pp319-322
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[1] Zhang H J, Liu C X, Qi X L, Dai X, Zhong F, Zhang S C 2009 Nature Phys. 5 438
[2] Xia Y, Qian D, Hsieh D, Wray L, Pal A, Lin H, Bansil A, Grauer D, Hor Y S, Cava R J, Hasan M Z 2009 Nature Phys. 5 398
[3] Dai X, Hughes T L, Qi X L, Fang Z, Zhang S C 2008 Phys. Rev. B 77 125319
[4] Fu L, Kane C K, Mele E J 2007 Phys. Rev. Lett. 98 106803
[5] Zhang T, Cheng P, Chen X, Jia J F, Ma X C, He K, Wang L L, Zhang H J, Dai X, Fang Z, Xie X C, Xue Q K 2009 Phys. Rev. Lett. 103 266803
[6] Cheng P, Song C, Zhang T, Zhang Y Y, Wang Y L, Jia J F, Wang J, Wang Y Y, Zhu B F, Chen X, Ma X C, He K, Wang L L, Dai X, Fang Z, Xie X C, Qi X L, Liu C X, Zhang S C, Xue Q K 2010 Phys. Rev. Lett. 105 076801
[7] Hong S S, Kundhikanjana W, Cha J J, Lai K J, Kong D S, Stefan M, Kelly M A, Shen Z X, Cui Y 2010 Nano Lett. 10 3118
[8] Zhang Y, He K, Ma X C, Xue Q K 2011 Physics 40 07 (in Chinese) [张翼, 何珂, 马旭村, 薛其坤 2011 物理 40 07]
[9] Lu H Z, Shan W Y, Yao W, Niu Q, Shen S Q 2010 Phys. Rev. B 81 115407
[10] Li H C, Sheng L, Sheng D N, Xing D Y 2010 Phys. Rev. B 82 165104
[11] Li H C, Sheng L, Xing D Y 2011 Phys. Rev. B 83 195413
[12] Yu R, Zhang W, Weng H M, Dai X, Fang Z 2010 Physics 39 09 (in Chinese) [余睿, 张薇, 翁红明, 戴希, 方忠 2010 物理 39 09]
[13] Yang Y Y, Xu Z, Sheng L, Sheng R, Xing D Y 2011 Appl. Phys. Lett. 99 182101
[14] Thouless D J, Kohmoto M, Nightingale M P, Nijs M D 1982 Phys. Rev. Lett. 49 405
[15] Niu Q, Thouless D J, Wu Y S 1985 Phys. Rev. B 31 3372
[16] Xu Z, Yang Y Y, Sheng L, Xing D Y 2012 J. Phys. Condens Matter 18 185504
[17] Datta S 1995 Electronic Transport in Mesoscopic Systems (1st Edn.) (New York: Cambridge University Press) pp319-322
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