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运用第一性原理方法,研究了拓扑绝缘体Bi2Se3块体和薄膜中的层堆垛对其结构、电子态、拓扑态和自旋劈裂的影响. 发现不同的堆垛会引起Bi2Se3层间的相互作用,改变系统的中心对称性. 块体的ABC和AAA堆垛都具有中心对称性和相似的能带结构. ABA堆垛破坏了体系的中心对称性,能带发生很大改变,并且产生了很大的能带自旋劈裂. 用能带反转的方法判定体系的拓扑相,在不同堆垛的Bi2Se3块体中,考虑自旋轨道耦合时都发生了能带反转,因而具有不同堆垛的Bi2Se3 仍是拓扑绝缘体. 进一步研究了Bi2Se3薄膜中的堆垛效应,发现非中心对称的ABA堆垛在Bi2Se3薄膜中引起明显的自旋劈裂,并且提出和验证了用应变调控自旋劈裂的方法.By using first-principles method, we study the stacking effects on the electronic structure, topological phase and spin splitting in the bulk and film of topological insulator Bi2Se3. It is found that the different stackings can lead to different interlayer interactions and change the centrosymmetry of Bi2Se3. The centrosymmetric ABC and AAA stackings in bulk Bi2Se3 have similar band structures. ABA stacking breaks the centrosymmetry, giving rise to considerable changes of the band structure and large spin splitting. We further study the stacking effects in the film of Bi2Se3 and find that the non-centrosymmetric ABA stacking can induce large spin splitting in Bi2Se3 film. It is proposed and illustrated that the strain can tune the spin splitting effectively.
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Keywords:
- topological insulator /
- topological phase /
- spin-orbit coupling /
- spin splitting
[1] Kane C, Mele E 2005 Phys. Rev. Lett. 95 146802
[2] Bernevig B, Hughes T, Zhang S C 2006 Science 314 1757
[3] Fu L, Kane C, Mele E 2007 Phys. Rev. Lett. 98 106803
[4] Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
[5] Hasan M, Kane C 2010 Rev. Mod. Phys. 82 3045
[6] Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438
[7] 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 Nat. Phys. 5 398
[8] Yu R, Zhang W, Weng H M, Dai X, Fang Z 2010 Physics 39 618(in Chinese)[余睿, 张薇, 翁红明, 戴希, 方忠 2010 物理 39 618]
[9] Ding Y, Shen J, Pang Y, Liu G T, Fan J, Ji Z Q, Yang C L, L L 2013 Acta Phys. Sin. 62 167401(in Chinese)[丁玥, 沈洁, 庞远, 刘广同, 樊洁, 姬忠庆, 杨昌黎, 吕力 2013 物理学报 62 167401]
[10] Wang X T, Dai X F, Jia H Y, Wang L Y, Liu R, Li Y, Liu X C, Zhang X M, Wang W H, Wu G H, Liu G D 2014 Acta Phys. Sin. 63 023101(in Chinese)[王啸天, 代学芳, 贾红英, 王立英, 刘然, 李勇, 刘笑闯, 张小明, 王文洪, 吴光恒, 刘国栋 2014 物理学报 63 023101]
[11] Zhang Y, He K, Chang C, Song C, Wang L, Chen X, Jia J, Fang Z, Dai X, Shan W, Shen S, Niu Q, Qi X, Zhang S, Ma X, Xue Q K 2010 Nat. Phys. 6 584
[12] Liu Y M, Shao H H, Zhou X Y, Zhou G H 2013 Chin. Phys. B 22 077310
[13] Jia Y F, Guo H M, Qin J H, Chen Z Y, Feng S P 2013 Chin. Phys. B 22 090308
[14] Li X G, Zhang G F, Wu G F, Chen H, Culcer D, Zhang Z Y 2013 Chin. Phys. B 22 097306
[15] He K, Ma X C, Chen X, Lu L, Wang Y Y, Xue Q K 2013 Chin. Phys. B 22 067305
[16] Bao W, Jing L, Velasco J, Lee Y, Liu G, Tran D, Standley B, Aykol M, Cronin S, Smirnov D, Koshino M, McCann E, Bockrath M, Lau C 2011 Nat. Phys. 7 948
[17] Ishizaka K, Bahramy M, Murakawa H, Sakano M, Shimojima T, Sonobe T, Koizumi K, Shin S, Miyahara H, Kimura A, Miyamoto K, Okuda T, Namatame H, Taniguchi M, Arita R, NagaosaKaneko Y, Onose Y, Tokura Y 2011 Nat.Mater. 10 521
[18] Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
[19] Kresse G, Furthmller J 1996 Comput. Mater. Sci. 6 15
[20] Perdew J, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[21] Blöchl P 1994 Phys. Rev. B 50 17953
[22] Liu W L, Peng X Y, Wei X L, Yang H, Stocks G M, Zhong J X 2013 Phys. Rev. B 87 205315
[23] Bianchi M, Hatch R C, Mi J, Iversen B B, Hofmann P 2011 Phys. Rev. Lett. 107 086802
[24] King P D C, Hatch R C, Bianchi M, Ovsyannikov R, Lupulescu C, Landolt G, Slomski B, Dil J H, Guan D, Mi J L, Rienks D L, Fink J, Lindblad A, Svensson S, Bao S, Balakrishnan G, Iversen B B, Osterwalder J, Eberhardt W, Baumberger F, Hofmann P 2011 Phys. Rev. Lett. 107 096802
[25] Yang H, Peng X Y, Wei X L, Liu W L, Zhu W G, Xiao D, Stocks G M, Zhong J X 2012 Phys. Rev. B 86 155317
[26] Sakamoto K, Kakuta H, Sugawara K, Miyamoto K, Kimura A, Kuzumaki T, Ueno N, Annese E, Fujii J, Kodama A, Shishidou T, Namatame H, Taniguchi M, Sato T, Takahashi T, Oguchi T 2009 Phys. Rev. Lett. 103 56801
[27] Liu W L, Peng X Y, Tang C, Sun L Z, Zhang K W, Stocks G M, Zhong J X 2011 Phys. Rev. B 84 245105
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[1] Kane C, Mele E 2005 Phys. Rev. Lett. 95 146802
[2] Bernevig B, Hughes T, Zhang S C 2006 Science 314 1757
[3] Fu L, Kane C, Mele E 2007 Phys. Rev. Lett. 98 106803
[4] Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
[5] Hasan M, Kane C 2010 Rev. Mod. Phys. 82 3045
[6] Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438
[7] 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 Nat. Phys. 5 398
[8] Yu R, Zhang W, Weng H M, Dai X, Fang Z 2010 Physics 39 618(in Chinese)[余睿, 张薇, 翁红明, 戴希, 方忠 2010 物理 39 618]
[9] Ding Y, Shen J, Pang Y, Liu G T, Fan J, Ji Z Q, Yang C L, L L 2013 Acta Phys. Sin. 62 167401(in Chinese)[丁玥, 沈洁, 庞远, 刘广同, 樊洁, 姬忠庆, 杨昌黎, 吕力 2013 物理学报 62 167401]
[10] Wang X T, Dai X F, Jia H Y, Wang L Y, Liu R, Li Y, Liu X C, Zhang X M, Wang W H, Wu G H, Liu G D 2014 Acta Phys. Sin. 63 023101(in Chinese)[王啸天, 代学芳, 贾红英, 王立英, 刘然, 李勇, 刘笑闯, 张小明, 王文洪, 吴光恒, 刘国栋 2014 物理学报 63 023101]
[11] Zhang Y, He K, Chang C, Song C, Wang L, Chen X, Jia J, Fang Z, Dai X, Shan W, Shen S, Niu Q, Qi X, Zhang S, Ma X, Xue Q K 2010 Nat. Phys. 6 584
[12] Liu Y M, Shao H H, Zhou X Y, Zhou G H 2013 Chin. Phys. B 22 077310
[13] Jia Y F, Guo H M, Qin J H, Chen Z Y, Feng S P 2013 Chin. Phys. B 22 090308
[14] Li X G, Zhang G F, Wu G F, Chen H, Culcer D, Zhang Z Y 2013 Chin. Phys. B 22 097306
[15] He K, Ma X C, Chen X, Lu L, Wang Y Y, Xue Q K 2013 Chin. Phys. B 22 067305
[16] Bao W, Jing L, Velasco J, Lee Y, Liu G, Tran D, Standley B, Aykol M, Cronin S, Smirnov D, Koshino M, McCann E, Bockrath M, Lau C 2011 Nat. Phys. 7 948
[17] Ishizaka K, Bahramy M, Murakawa H, Sakano M, Shimojima T, Sonobe T, Koizumi K, Shin S, Miyahara H, Kimura A, Miyamoto K, Okuda T, Namatame H, Taniguchi M, Arita R, NagaosaKaneko Y, Onose Y, Tokura Y 2011 Nat.Mater. 10 521
[18] Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
[19] Kresse G, Furthmller J 1996 Comput. Mater. Sci. 6 15
[20] Perdew J, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[21] Blöchl P 1994 Phys. Rev. B 50 17953
[22] Liu W L, Peng X Y, Wei X L, Yang H, Stocks G M, Zhong J X 2013 Phys. Rev. B 87 205315
[23] Bianchi M, Hatch R C, Mi J, Iversen B B, Hofmann P 2011 Phys. Rev. Lett. 107 086802
[24] King P D C, Hatch R C, Bianchi M, Ovsyannikov R, Lupulescu C, Landolt G, Slomski B, Dil J H, Guan D, Mi J L, Rienks D L, Fink J, Lindblad A, Svensson S, Bao S, Balakrishnan G, Iversen B B, Osterwalder J, Eberhardt W, Baumberger F, Hofmann P 2011 Phys. Rev. Lett. 107 096802
[25] Yang H, Peng X Y, Wei X L, Liu W L, Zhu W G, Xiao D, Stocks G M, Zhong J X 2012 Phys. Rev. B 86 155317
[26] Sakamoto K, Kakuta H, Sugawara K, Miyamoto K, Kimura A, Kuzumaki T, Ueno N, Annese E, Fujii J, Kodama A, Shishidou T, Namatame H, Taniguchi M, Sato T, Takahashi T, Oguchi T 2009 Phys. Rev. Lett. 103 56801
[27] Liu W L, Peng X Y, Tang C, Sun L Z, Zhang K W, Stocks G M, Zhong J X 2011 Phys. Rev. B 84 245105
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