Research progress of quantum Hall effect in topological insulator

Zhang Shuai; Song Feng-Qi

doi:10.7498/aps.72.20230698

Abstract

Three-dimensional topological insulators (TIs) with gapless topological surface states (TSSs) have attracted considerable attention because of their unique properties. The transport of TSS is an essential means to explore the novel properties. The quantum Hall effect (QHE) of TSS is an important content in the study of topological insulator, for it is an important characteristic of the pure TSS transport. This paper briefly reviews the recent research progress of QHE in TIs. Firstly, we introduce the fundamental concepts of the QHE in TIs. In a three-dimensional TI, each TSS contributes to a half-integer QHE. An integer QHE should be observed due to the existence of top and bottom surface in TI. Then, we review the realization and development of QHE. With the optimization of TI materials, the QHE of TSS is observed in bulk-insulating TIs. Next, the phase transition and scaling law behavior of QHE in TIs are discussed. The dominance of electron-electron interaction of the TSS is revealed by the anomalous critical exponent. Also, the experimental studies of the magnetic proximity and gate voltage modulation of the QHE are reviewed in detail. Finally, the perspectives of QHE in TIs are discussed.

Keywords:

Authors and contacts

Collaborative Innovation Center of Advanced Microstructures, National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China

Corresponding author: Song Feng-Qi, songfengqi@nju.edu.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2022YFA1402404) and the National Natural Science Foundation of China (Grant Nos. 92161201, T2221003, 12025404, 11904166).

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References

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[43]	Salehi M, Shapourian H, Rosen I T, Han M G, Moon J, Shibayev P, Jain D, Goldhaber-Gordon D, Oh S 2019 Adv. Mater. 31 1901091 Google Scholar
[44]	Tang C, Chang C Z, Zhao G, Liu Y, Jiang Z, Liu C X, McCartney M R, Smith D J, Chen T, Moodera J S, Shi J 2017 Sci. Adv. 3 e1700307 Google Scholar
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[46]	Yoshimi R, Yasuda K, Tsukazaki A, Takahashi K S, Nagaosa N, Kawasaki M, Tokura Y 2015 Nat. Commun. 6 8530 Google Scholar
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[50]	Li C, de Ronde B, Nikitin A, Huang Y, Golden M S, de Visser A, Brinkman A 2017 Phys. Rev. B 96 195427 Google Scholar
[51]	Chong S K, Han K B, Sparks T D, Deshpande V V 2019 Phys. Rev. Lett. 123 036804 Google Scholar
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[56]	Novoselov K S, Jiang Z, Zhang Y, Morozov S V, Stormer H L, Zeitler U, Maan J C, Boebinger G S, Kim P, Geim A K 2007 Science 315 1379 Google Scholar
[57]	Morimoto T, Furusaki A, Nagaosa N 2015 Phys. Rev. Lett. 114 146803 Google Scholar
[58]	Morimoto T, Furusaki A, Nagaosa N 2015 Phys. Rev. B 92 085113 Google Scholar
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Cited By

图 1 量子霍尔效应与朗道能级　(a) 量子霍尔效应的典型输运特征; (b) 传统二维电子气在磁场下的朗道能级示意图; (c) 二维狄拉克费米子体系在磁场下的朗道能级示意图; (d) 传统二维电子气量子霍尔手性边缘态示意图; (e) 拓扑绝缘体上下表面量子霍尔手性边缘态示意图.

Figure 1. Quantum Hall effect and Landau levels: (a) Transport characteristics of quantum Hall effect; (b) Landau level diagram of conventional two-dimensional electron gas in magnetic field; (c) Landau level diagram of two-dimensional Dirac fermion system in magnetic field; (d) diagram of quantum Hall chiral edge states in conventional two-dimensional electron gas; (e) diagram of quantum Hall chiral edge states of top and bottom surface states in topological insulator.

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图 2 拓扑绝缘体中的量子霍尔态　(a) Sn-Bi_1.1Sb_0.9Te₂S器件中高质量的量子霍尔态^[35]; (b)三维拓扑绝缘体中量子霍尔态的观测温度、厚度及体能隙间的关系^[36]

Figure 2. Quantum Hall states in topological insulators: (a) High-quality Quantum Hall states in Sn-Bi_1.1Sb_0.9Te₂S device^[35]; (b) relationship among temperature, thickness and energy gap of quantum Hall states in topological insulators^[36].

DownLoad: Full-Size Img PowerPoint

图 3 量子霍尔态的重整化群流　(a)半圆形标度的重整化群流; (b)拓扑绝缘体中栅压驱动的重整化群流^[40]

Figure 3. Renormalization group flow of quantum Hall states: (a) Semi-circle renormalization group flow; (b) gate-driven renormalization group flow in a topological insulator^[40].

DownLoad: Full-Size Img PowerPoint

图 4 拓扑绝缘体量子霍尔态的标度律行为^[35]　(a)量子霍尔平台在不同温度下的转变, 上图为霍尔电阻的转变, 下图为纵向电阻的转变; (b)量子霍尔平台转变中的标度律, 上图为dR_xy/dB随温度的关系, 下图为ΔB随温度的关系

Figure 4. Scaling law of quantum Hall states in topological insulators^[35]: (a) Quantum Hall plateaus transition, Hall resistance (upper) and longitudinal resistance (lower); (b) scaling law in plateau transition region, relationship between dR_xy/dB and temperature (upper) and relationship between ΔB and temperature (lower).

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图 5 磁性修饰与近邻下的量子霍尔态. 磁性团簇修饰前(a)和磁性团簇修饰后(b)的量子霍尔态的重整化群流^[47]; h-BN作为介电层(c)和Cr₂Ge₂Te₆作为介电层(d)的量子霍尔态^[48]

Figure 5. Quantum Hall states tuned by magnetic modification and proximity. Renormalization group flow of quantum Hall States before (a) and after (b) magnetic cluster modification^[47]; quantum Hall states with h-BN as the dielectric layer (c) and Cr₂Ge₂Te₆ as the dielectric layer (d)^[48].

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图 6 拓扑表面态量子霍尔效应的双栅调控　(a)—(c)随厚度减小, 量子霍尔态在双栅调控下的不同行为^[40,50,51]

Figure 6. Dual-gate-tuned quantum Hall states of topological surface states: (a)–(c) different behavior of quantum Hall states with decreasing thickness^[40,50,51].

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表 1 不同拓扑绝缘体中量子霍尔态的特征

Table 1. Properties of quantum Hall state in topological insulators.

Method	Material		*T@B@v = 1	Thickness/nm	Reference
Exfoliated	五元Sn-(Bi, Sb)₂(Te, S)₃		2 K@ 8 T	3×10³	Ichimura等^[36]
	五元Sn-(Bi, Sb)₂(Te, S)₃		20 K@ 12 T	82	Xie等^[35]
	四元 (Bi, Sb)₂(Te, Se)₃		10 K@ 31 T	80	Xu等^[28]
MBE	三元	(Bi, Sb)₂Te₃	0.04 K@ 14 T	8	Yoshimi等^[29]
		Ca-Bi₂Se₃	0.3 K@ 25 T	8	Moon等^[32]
		Ti-Sb₂Te₃	0.35 K@30 T	10	Salehi等^[43]
	二元 Bi₂Se₃		20 K@35 T	8	Koirala等^[33]
注: “*”表示报道的观测到ν = 1量子霍尔平台(且要求此时R_xx < 0.04 h/e²)对应的最高温度和对应该温度的最低磁场大小.

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[1]	Klitzing K, Dorda G, Pepper M 1980 Phys. Rev. Lett. 45 494 Google Scholar
[2]	Thouless D J, Kohmoto K, Nightingale M P, den Nijs M 1982 Phys. Rev. Lett. 49 405 Google Scholar
[3]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801 Google Scholar
[4]	Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802 Google Scholar
[5]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757 Google Scholar
[6]	König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766 Google Scholar
[7]	Moore J E, Balents L 2007 Phys. Rev. B 75 121306 Google Scholar
[8]	Fu L, Kane C L 2007 Phys. Rev. B 76 045302.Google Scholar
[9]	Hsieh D, Qian D, Wray L, Xia Y Q, Hor Y S, Cava R J, Hasan M Z 2008 Nature 452 970 Google Scholar
[10]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[11]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057 Google Scholar
[12]	Ando Y 2013 J. Phys. Soc. Jpn. 82 102001 Google Scholar
[13]	Moore J E 2010 Nature 464 194 Google Scholar
[14]	Lu H Z, Shen S Q 2014 Proc. SPIE 9167 Spintronics VII 91672E
[15]	Bardarson J H, Moore J E 2013 Rep. Prog. Phys. 76 056501 Google Scholar
[16]	Qu D X, Hor Y S, Xiong J, Cava R J, Ong N P 2010 Science 329 821 Google Scholar
[17]	Li Z, Zhang S, Song F 2015 Acta Phys. Sin. 64 097202 Google Scholar
[18]	Goerbig M O 2009 arXiv: 0909.1998
[19]	Tong D 2016 arXiv: 1606.06687
[20]	Nielsen H B, Ninomiya M 1981 Phys. Lett. B 105 219 Google Scholar
[21]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197 Google Scholar
[22]	Zhang Y, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201 Google Scholar
[23]	Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438 Google Scholar
[24]	Heremans J P, Cava R J, Samarth N 2017 Nat. Rev. Mater. 2 17049 Google Scholar
[25]	Ren Z, Taskin A A, Sasaki S, Segawa K, Ando Y 2011 Phys. Rev. B 84 165311 Google Scholar
[26]	Arakane T, Sato T, Souma S, Kosaka K, Nakayama K, Komatsu M, Takahashi M, Ren Z, Segawa K, Ando Y 2012 Nat. Commun. 3 636 Google Scholar
[27]	Brüne C, Liu C X, Novik E G, Hankiewicz E M, Buhmann H, Chen Y L, Qi X L, Shen Z X, Zhang S C, Molenkamp L W 2011 Phys. Rev. Lett. 106 126803 Google Scholar
[28]	Xu Y, Miotkowski I, Liu C, Tian J, Nam H, Alidoust N, Hu J, Shih C K, Hasan M Z, Chen Y P 2014 Nat. Phys. 10 956 Google Scholar
[29]	Yoshimi R, Tsukazaki A, Kozuka Y, Falson J, Takahashi K S, Checkelsky J G, Nagaosa N, Kawasaki M, Tokura Y 2015 Nat. Commun. 6 6627 Google Scholar
[30]	Zou W, Wang W, Kou X, Lang M, Fan Y, Choi E S, Fedorov A V, Wang K, He L, Xu Y, Wang K L 2017 Appl. Phys. Lett. 110 212401 Google Scholar
[31]	Koirala N, Brahlek M, Salehi M, Wu L, Dai J, Waugh J, Nummy T, Han M G, Moon J, Zhu Y, Dessau D, Wu W, Armitage N P, Oh S 2015 Nano Lett. 15 8245 Google Scholar
[32]	Moon J, Koirala N, Salehi M, Zhang W, Wu W, Oh S, 2018 Nano Lett. 18 820 Google Scholar
[33]	Koirala N, Salehi M, Moon J, Oh S 2019 Phys. Rev. B 100 085404 Google Scholar
[34]	Kushwaha S K, Pletikosic´ I, Liang T, Gyenis A, Lapidus S H, Tian Y, Zhao H, Burch K S, Lin J, Wang W, Ji H, Fedorov A V, Yazdani A, Ong N P, Valla T, Cava R J 2016 Nat. Commun. 7 11456 Google Scholar
[35]	Xie F, Zhang S, Liu Q, Xi C, Kang T T, Wang R, Wei B, Pan X C, Zhang M, Fei F, Wang X, Pi L, Yu G L, Wang B, Song F 2019 Phys. Rev. B 99 081113(R Google Scholar
[36]	Ichimura K, Matsushita S Y, Huynh K K, Tanigaki K 2019 Appl. Phys. Lett. 115 052104 Google Scholar
[37]	Khmelnitskii D 1983 JETP Lett. 38 454
[38]	Murzin S S, Dorozhkin S I, Maude D K, Jansen A G M 2005 Phys. Rev. B 72 195317 Google Scholar
[39]	Checkelsky J G, Yoshimi R, Tsukazaki A, Takahashi K S, Kozuka Y, Falson J, Kawasaki M, Tokura Y 2014 Nat. Phys. 10 731 Google Scholar
[40]	Xu Y, Miotkowski I, Chen Y P 2016 Nat. Commun. 7 11434 Google Scholar
[41]	Huckestein B 1995 Rev. Mod. Phys. 67 357 Google Scholar
[42]	Sondhi S L, Girvin S M, Carini J P, Shahar D 1997 Rev. Mod. Phys. 69 315 Google Scholar
[43]	Salehi M, Shapourian H, Rosen I T, Han M G, Moon J, Shibayev P, Jain D, Goldhaber-Gordon D, Oh S 2019 Adv. Mater. 31 1901091 Google Scholar
[44]	Tang C, Chang C Z, Zhao G, Liu Y, Jiang Z, Liu C X, McCartney M R, Smith D J, Chen T, Moodera J S, Shi J 2017 Sci. Adv. 3 e1700307 Google Scholar
[45]	Watanabe R, Yoshimi R, Kawamura M, Mogi M, Tsukazaki A, Yu X Z, Nakajima K, Takahashi K S, Kawasaki M, Tokura Y 2019 Appl. Phys. Lett. 115 102403 Google Scholar
[46]	Yoshimi R, Yasuda K, Tsukazaki A, Takahashi K S, Nagaosa N, Kawasaki M, Tokura Y 2015 Nat. Commun. 6 8530 Google Scholar
[47]	Zhang S, Pi L, Wang R, Yu G, Pan X C, Wei Z, Zhang J, Xi C, Bai Z, Fei F, Wang M, Liao J, Li Y, Wang X, Song F, Zhang Y, Wang B, Xing D, G. Wang G 2017 Nat. Commun. 8 977 Google Scholar
[48]	Chong S K, Han K B, Nagaoka A, Tsuchikawa R, Liu R, Liu H, Vardeny Z V, Pesin D C, Lee C, Sparks T D, Deshpande V V 2018 Nano Lett. 18 8047 Google Scholar
[49]	Mogi M, Okamura Y, Kawamura M, Yoshimi R, Yasuda K, Tsukazaki A, Takahashi K S, Morimoto T, Nagaosa N, Kawasaki M, Takahashi Y, Tokura Y 2022 Nat. Phys. 18 390 Google Scholar
[50]	Li C, de Ronde B, Nikitin A, Huang Y, Golden M S, de Visser A, Brinkman A 2017 Phys. Rev. B 96 195427 Google Scholar
[51]	Chong S K, Han K B, Sparks T D, Deshpande V V 2019 Phys. Rev. Lett. 123 036804 Google Scholar
[52]	Banerjee A, Sundaresh A, Biswas S, Ganesan R, Sen D, Anil Kumar P S 2019 Nanoscale 11 5317 Google Scholar
[53]	Xie F, Lian Z, Zhang S, Wang T, Miao S, Song Z, Ying Z, Pan X C, Long M, Zhang M, Fei F, Hu W, Yu G, Song F, Kang T T, Shi S F 2021 Nanotechnology 32 17LT01 Google Scholar
[54]	Chong S K, Tsuchikawa R, Harmer J, Sparks T D, Deshpande V V 2020 ACS Nano 14 1158 Google Scholar
[55]	Wang J, Gorini C, Richter K, Wang Z, Ando Y, Weiss D 2020 Nano Lett. 20 8493 Google Scholar
[56]	Novoselov K S, Jiang Z, Zhang Y, Morozov S V, Stormer H L, Zeitler U, Maan J C, Boebinger G S, Kim P, Geim A K 2007 Science 315 1379 Google Scholar
[57]	Morimoto T, Furusaki A, Nagaosa N 2015 Phys. Rev. Lett. 114 146803 Google Scholar
[58]	Morimoto T, Furusaki A, Nagaosa N 2015 Phys. Rev. B 92 085113 Google Scholar
[59]	Seradjeh B, Moore J E, Franz M 2009 Rev. Lett. 103 066402 Google Scholar
[60]	Ilan R, de Juan F, Moore J E 2015 Phys. Rev. Lett. 115 096802 Google Scholar
[61]	Seredinski A, Draelos A W, Arnault E G, Wei M T, Li H, Fleming T, Watanabe K, Taniguchi T, Amet F, Finkelstein G 2019 Sci. Adv. 5 eaaw8693 Google Scholar
[62]	Qi X L, Hughes T L, Zhang S C 2011 Phys. Rev. B 83 1057 Google Scholar
[63]	Liu J, Hsieh T H, Wei P, Duan W, Moodera J, Fu L 2014 Nat. Mater. 13 178 Google Scholar

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Vol. 72, Issue 17 - 2023-09-05

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