The robustness of quantum spin Hall effect to the thickness fluctuation in HgTe quantum wells

doi:10.1088/1674-1056/21/11/117301

中国物理B ›› 2012, Vol. 21 ›› Issue (11): 117301-117301.doi: 10.1088/1674-1056/21/11/117301

• RAPID COMMUNICATION • 上一篇下一篇

The robustness of quantum spin Hall effect to the thickness fluctuation in HgTe quantum wells

郭怀明^a, 张相林^b, 冯世平^b

a Department of Physics, Beihang University, Beijing 100191, China;
b Department of Physics, Beijing Normal University, Beijing 100875, China

收稿日期:2012-06-01 修回日期:2012-07-26 出版日期:2012-10-01 发布日期:2012-10-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11104189 and 11074023) and the National Basic Research Program of China (Grant Nos. 2011CBA00102, 2011CB921700, and 2012CB821403).

The robustness of quantum spin Hall effect to the thickness fluctuation in HgTe quantum wells

Guo Huai-Ming (郭怀明)^a, Zhang Xiang-Lin (张相林)^b, Feng Shi-Ping (冯世平 )^b

a Department of Physics, Beihang University, Beijing 100191, China;
b Department of Physics, Beijing Normal University, Beijing 100875, China

Received:2012-06-01 Revised:2012-07-26 Online:2012-10-01 Published:2012-10-01
Contact: Guo Huai-Ming E-mail:hmguo@buaa.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11104189 and 11074023) and the National Basic Research Program of China (Grant Nos. 2011CBA00102, 2011CB921700, and 2012CB821403).

摘要/Abstract

摘要： The quantum spin Hall effect (QSHE) was first realized in HgTe quantum wells (QWs), which remain the only known two-dimensional topological insulator so far. In this paper, we have systematically studied the effect of the thickness fluctuation of HgTe QWs on the QSHE. We start with the case of constant mass with random distributions, and reveal that the disordered system can be well described by a virtual uniform QW with an effective mass when the number of components is small. When the number is infinite and corresponds to the real fluctuation, we find that the QSHE is not only robust, but also can be generated by relatively strong fluctuation. Our results imply that the thickness fluctuation does not cause backscattering, and the QSHE is robust to it.

关键词: quantum spin Hall effect, HgTe quantum wells, disorder effect

Abstract: The quantum spin Hall effect (QSHE) was first realized in HgTe quantum wells (QWs), which remain the only known two-dimensional topological insulator so far. In this paper, we have systematically studied the effect of the thickness fluctuation of HgTe QWs on the QSHE. We start with the case of constant mass with random distributions, and reveal that the disordered system can be well described by a virtual uniform QW with an effective mass when the number of components is small. When the number is infinite and corresponds to the real fluctuation, we find that the QSHE is not only robust, but also can be generated by relatively strong fluctuation. Our results imply that the thickness fluctuation does not cause backscattering, and the QSHE is robust to it.

Key words: quantum spin Hall effect, HgTe quantum wells, disorder effect

中图分类号: (Weak or Anderson localization)

73.20.Fz

72.80.Sk (Insulators) 72.15.Rn (Localization effects (Anderson or weak localization))

郭怀明, 张相林, 冯世平 . The robustness of quantum spin Hall effect to the thickness fluctuation in HgTe quantum wells[J]. 中国物理B, 2012, 21(11): 117301-117301.

Guo Huai-Ming (郭怀明), Zhang Xiang-Lin (张相林), Feng Shi-Ping (冯世平 ). The robustness of quantum spin Hall effect to the thickness fluctuation in HgTe quantum wells[J]. Chin. Phys. B, 2012, 21(11): 117301-117301.

参考文献 32

[1]	Moore J E 2010 Nature 464 194
[2]	Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
[3]	Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
[4]	Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 226801
[5]	Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 146802
[6]	Fu L and Kane C L 2007 Phys. Rev. B 76 045302
[7]	Bernevig B A, Hughes T L and Zhang S C 2006 Science 314 1757
[8]	König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp L W, Qi X L and Zhang S C 2007 Science 318 766
[9]	Hsieh D, Qian D, Wray L, Xia Y, Hor Y S, Cava R J and Hasan M Z 2008 Nature 452 970
[10]	Hsieh D, Xia Y, Wray L, Qian D, Pal A, Dil J H, Osterwalder J, Meier F, Bihlmayer G, Kane C L, Hor Y S, Cava R J and Hasan M Z 2009 Science 323 919
[11]	Zhang H, Liu C X, Qi X L, Dai X, Fang Z and Zhang S C 2009 Nature Phys. 5 438
[12]	Xia Y, Qian D, Hsieh D, Wray L, Pal A, Lin H, Bansil A, Grauer D, Hor Y S, Cava R J and Hasan M Z 2009 Nature Phys. 5 398
[13]	Chen Y L, Analytis J G, Chu J H, Liu Z K, Mo S K, Qi X L, Zhang H J, Lu D H, Dai X, Fang Z, Zhang S C, Fisher I R, Hussain Z and Shen Z X 2009 Science 325 178
[14]	Guo H M and Feng S P 2012 Chin. Phys. B 21 077303
[15]	Yuan J H, Cheng Z, Zhang J J, Zeng Q J and Zhang J P 2012 Chin. Phys. B 21 047203
[16]	Roushan P, Jungpil S, Parker C V, Hor Y S, Hsieh D, Qian D, Richardella A, Hasan M Z, Cava R J and Yazdani A 2009 Nature 460 1106
[17]	Li J, Chu R L, Jain J K and Shen S Q 2009 Phys. Rev. Lett. 102 136806
[18]	Jiang H, Wang L, Sun Q F and Xie X C 2009 Phys. Rev. B 80 165316
[19]	Groth C W, Wimmer M, Akhmerov A R, Tworzydlo J and Beenakker C W J 2009 Phys. Rev. Lett. 103 196805
[20]	Guo H M, Rosenberg G, Refael G and Franz M 2010 Phys. Rev. Lett. 105 216601
[21]	Tkachov G, Thienel C, Pinneker V, Buttner B, Brune C, Buhmann H, Molenkamp L W and Hankiewicz E M 2011 Phys. Rev. Lett. 106 076802
[22]	Büttner B, Liu C X, Tkachov G, Novik E G, Brüne C, Buhmann H, Hankiewicz E M, Recher P, Trauzettel B, Zhang S C and Molenkamp L W 2011 Nature Phys. 7 418
[23]	Guo H M, Feng S P and Shen S Q 2011 Phys. Rev. B 83 045114
[24]	Metalidis G and Bruno P 2005 Phys. Rev. B 72 235304
[25]	Landauer R 1970 Philos. Mag. 21 863
[26]	Büttiker M 1988 Phys. Rev. B 38 9375
[27]	Niu Q, Thouless D J and Wu Y S 1985 Phys. Rev. B 31 3372
[28]	Essin A M and Moore J E 2007 Phys. Rev. B 76 165307
[29]	Guo H M 2010 Phys. Rev. B 82 115122
[30]	Weeks C, Hu J, Alicea J, Franz M and Wu R Q 2011 Phys. Rev. X 1 021001
[31]	Bardarson J H, Medvedyeva M V, Tworzydlo J, Akhmerov A R and Beenakker C W J 2010 Phys. Rev. B 81 121414(R)
[32]	Shen S Q, Shan W Y and Lu H Z 2011 Spin 1 33

The robustness of quantum spin Hall effect to the thickness fluctuation in HgTe quantum wells

The robustness of quantum spin Hall effect to the thickness fluctuation in HgTe quantum wells

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 32

相关文章 11

Metrics

本文评价

推荐阅读 0

[1]	Wenming Xue(薛文明), Jin Li(李金), Chaoyu He(何朝宇), Tao Ouyang(欧阳滔), Xiongying Dai(戴雄英), and Jianxin Zhong(钟建新). Coexistence of giant Rashba spin splitting and quantum spin Hall effect in H-Pb-F[J]. 中国物理B, 2023, 32(3): 37101-037101.
[2]	Zhengyang Wan(万正阳), Hao Huan(郇昊), Hairui Bao(鲍海瑞), Xiaojuan Liu(刘晓娟), and Zhongqin Yang(杨中芹). Electronic structures and topological properties of TeSe₂ monolayers[J]. 中国物理B, 2021, 30(11): 117304-117304.
[3]	侯延辉, 张腾, 孙家涛, 刘立巍, 姚裕贵, 王业亮. Progress on 2D topological insulators and potential applications in electronic devices[J]. 中国物理B, 2020, 29(9): 97304-097304.
[4]	刘宏芳, 苏子贤, 张智强, 江华. Topological Anderson insulator in two-dimensional non-Hermitian systems[J]. 中国物理B, 2020, 29(5): 50502-050502.
[5]	苏子贤, 康艳卓, 张博峰, 张智强, 江华. Disorder induced phase transition in magnetic higher-order topological insulator: A machine learning study[J]. 中国物理B, 2019, 28(11): 117301-117301.
[6]	周雪, 姜泽禹, 张柯楠, 姚维, 颜明哲, 张红云, 段文晖, 周树云. Electronic structure of molecular beam epitaxy grown 1T'-MoTe₂ film and strain effect[J]. 中国物理B, 2019, 28(10): 107307-107307.
[7]	Majeed Ur Rehman,A A Abid. Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures[J]. 中国物理B, 2017, 26(12): 127304-127304.
[8]	吴冰兰, 宋俊涛, 周娇娇, 江华. Disorder effects in topological states: Brief review of the recent developments[J]. 中国物理B, 2016, 25(11): 117311-117311.
[9]	修发贤, 赵彤彤. Topological insulator nanostructures and devices[J]. 中国物理B, 2013, 22(9): 96104-096104.
[10]	盛利, 李会超, 杨运友, 盛冬宁, 邢定钰. Spin Chern numbers and time-reversal-symmetry-broken quantum spin Hall effect[J]. 中国物理B, 2013, 22(6): 67201-067201.
[11]	郭怀明, 冯世平. Quantum spin Hall effect in a square-lattice model under a uniform magnetic field[J]. 中国物理B, 2012, 21(7): 77303-077303.