拓扑绝缘体中量子霍尔效应的研究进展

张帅; 宋凤麒

doi:10.7498/aps.72.20230698

摘要

三维拓扑绝缘体因其独特的物性备受研究人员关注, 而拓扑表面态的输运是探索其新奇物性的重要手段. 其中, 拓扑表面态的量子霍尔效应则是拓扑绝缘体输运研究的一个重要内容. 本文简要回顾了拓扑绝缘体中量子霍尔效应的实现与发展. 比较了拓扑表面态量子霍尔效应与其他体系的差别, 讨论了其材料体系的发展, 并介绍了其中的标度律行为. 之后详细回顾了实验上对拓扑表面态量子霍尔效应磁性近邻与栅压调控等方面的研究. 最后, 展望了拓扑绝缘体中量子霍尔态的研究前景, 希望能促进拓扑绝缘体的应用.

关键词:

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:

作者及机构信息

张帅,
宋凤麒

南京大学物理学院, 固体微结构物理国家重点实验室, 人工微结构科学与技术协同创新中心, 南京　210093

通信作者: 宋凤麒, songfengqi@nju.edu.cn

基金项目: 国家重点基础研究发展计划(批准号: 2022YFA1402404)和国家自然科学基金(批准号: 92161201, T2221003, 12025404, 11904166)资助的课题.

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).

文章全文 : translate this paragraph

参考文献

[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

施引文献

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.

Fig. 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.

下载: 全尺寸图片幻灯片

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]

Fig. 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].

下载: 全尺寸图片幻灯片

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]

Fig. 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].

下载: 全尺寸图片幻灯片

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

Fig. 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).

下载: 全尺寸图片幻灯片

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]

Fig. 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].

下载: 全尺寸图片幻灯片

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]

Fig. 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].

下载: 全尺寸图片幻灯片

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.

下载: 导出CSV

[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

[1]	李锦芳, 何东山, 王一平. 一维耦合腔晶格中磁子-光子拓扑相变和拓扑量子态的调制. 物理学报, 2024, 73(4): 044203. doi: 10.7498/aps.73.20231519
[2]	郑智勇, 陈立杰, 向吕, 王鹤, 王一平. 一维超导微波腔晶格中反旋波效应对拓扑相变和拓扑量子态的调制. 物理学报, 2023, 72(24): 244204. doi: 10.7498/aps.72.20231321
[3]	刘畅, 王亚愚. 磁性拓扑绝缘体中的量子输运现象. 物理学报, 2023, 72(17): 177301. doi: 10.7498/aps.72.20230690
[4]	刘浪, 王一平. 基于可调频光力晶格中声子-光子拓扑性质的模拟和探测. 物理学报, 2022, 71(22): 224202. doi: 10.7498/aps.71.20221286
[5]	王伟, 王一平. 一维超导传输线腔晶格中的拓扑相变和拓扑量子态的调制. 物理学报, 2022, 71(19): 194203. doi: 10.7498/aps.71.20220675
[6]	贾亮广, 刘猛, 陈瑶瑶, 张钰, 王业亮. 单层二维量子自旋霍尔绝缘体1T'-WTe₂研究进展. 物理学报, 2022, 71(12): 127308. doi: 10.7498/aps.71.20220100
[7]	王航天, 赵海慧, 温良恭, 吴晓君, 聂天晓, 赵巍胜. 高性能太赫兹发射: 从拓扑绝缘体到拓扑自旋电子. 物理学报, 2020, 69(20): 200704. doi: 10.7498/aps.69.20200680
[8]	向天, 程亮, 齐静波. 拓扑绝缘体中的超快电荷自旋动力学. 物理学报, 2019, 68(22): 227202. doi: 10.7498/aps.68.20191433
[9]	刘畅, 刘祥瑞. 强三维拓扑绝缘体与磁性拓扑绝缘体的角分辨光电子能谱学研究进展. 物理学报, 2019, 68(22): 227901. doi: 10.7498/aps.68.20191450
[10]	许楠, 张岩. 三聚化非厄密晶格中具有趋肤效应的拓扑边缘态. 物理学报, 2019, 68(10): 104206. doi: 10.7498/aps.68.20190112
[11]	贾鼎, 葛勇, 袁寿其, 孙宏祥. 基于蜂窝晶格声子晶体的双频带声拓扑绝缘体. 物理学报, 2019, 68(22): 224301. doi: 10.7498/aps.68.20190951
[12]	高艺璇, 张礼智, 张余洋, 杜世萱. 二维有机拓扑绝缘体的研究进展. 物理学报, 2018, 67(23): 238101. doi: 10.7498/aps.67.20181711
[13]	钟青, 王雪深, 李劲劲, 鲁云峰, 李正坤, 王文新, 孙庆灵. 1 k量子霍尔阵列电阻标准器件研制. 物理学报, 2016, 65(22): 227301. doi: 10.7498/aps.65.227301
[14]	王青, 盛利. 磁场中的拓扑绝缘体边缘态性质. 物理学报, 2015, 64(9): 097302. doi: 10.7498/aps.64.097302
[15]	李兆国, 张帅, 宋凤麒. 拓扑绝缘体的普适电导涨落. 物理学报, 2015, 64(9): 097202. doi: 10.7498/aps.64.097202
[16]	李平原, 陈永亮, 周大进, 陈鹏, 张勇, 邓水全, 崔雅静, 赵勇. 拓扑绝缘体Bi2Te3的热膨胀系数研究. 物理学报, 2014, 63(11): 117301. doi: 10.7498/aps.63.117301
[17]	陈艳丽, 彭向阳, 杨红, 常胜利, 张凯旺, 钟建新. 拓扑绝缘体Bi2Se3中层堆垛效应的第一性原理研究. 物理学报, 2014, 63(18): 187303. doi: 10.7498/aps.63.187303
[18]	丁玥, 沈洁, 庞远, 刘广同, 樊洁, 姬忠庆, 杨昌黎, 吕力. Bi2Te3拓扑绝缘体表面颗粒化铅膜诱导的超导邻近效应. 物理学报, 2013, 62(16): 167401. doi: 10.7498/aps.62.167401
[19]	曾伦武, 张浩, 唐中良, 宋润霞. 拓扑绝缘体椭球粒子的电磁散射. 物理学报, 2012, 61(17): 177303. doi: 10.7498/aps.61.177303
[20]	舒强, 舒永春, 张冠杰, 刘如彬, 姚江宏, 皮彪, 邢晓东, 林耀望, 许京军, 王占国. 调制掺杂GaAs/AlGaAs 2DEG材料持久光电导及子带电子特性研究. 物理学报, 2006, 55(3): 1379-1383. doi: 10.7498/aps.55.1379

计量

文章访问数: 6121
PDF下载量: 418
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板