拓扑绝缘体的普适电导涨落

李兆国; 张帅; 宋凤麒

doi:10.7498/aps.64.097202

摘要

拓扑绝缘体因其无能量耗散的拓扑表面输运而备受关注, 揭示拓扑表面态因其的贝利相位而产生的拓扑输运现象, 将有助于拓扑绝缘体相关器件的应用开发. 本文回顾了普适电导涨落(UCF) 揭示拓扑绝缘体奇异输运性质的研究进展. 通过调控温度、角度、门电压、垂直磁场和平行磁场等外部参量, 实现了对拓扑绝缘体的UCF 效应的系统研究, 证实了拓扑绝缘体中二维UCF 的输运现象, 并通过尺寸标度规律获得了UCF 的拓扑起源的实验证据, 讨论了拓扑表面态的UCF 的统计对称规律. 从而实现了对拓扑绝缘体UCF 效应的较为完整的理解.

关键词:

Abstract

As an exotic quantum condensed matter, the topological insulator (TI) is a bulk-insulating material with a Diractype conducting surface state. Such a dissipationless transport of topological surface state (TSS) is protected by the timereversal symmetry, which leads to the potential applications in spintronics and quantum computations. Understanding the topological symplectic transport of the Dirac fermions is a key issue to the study and design of the TI-based devices. There are many transport properties about Dirac fermions. And universal conductance fluctuation (UCF) is one of the most important transport manifestations of mesoscopic electronic interference. So the UCF effect in TI is a very meaningful research field It can provide an intriguing and special perspective to reveal the quantum transport of TSSs In this review, we introduce the research progress on the UCF of TSSs in a pedagogical way We review the achievements and the existing problems in order to inspire future research work.#br#We start this review with the basic UCF theory and the experimental observation. The UCF has been observed in TI earlier, but weather it originates from TSS has not been further studied. Then a series of work is carried out to prove the topological nature of UCF in TI Firstly, the UCF phenomenon in TIs is demonstrated to be from two-dimensional (2D) interference by magnetoconductance measurements. But the residual bulk state and the 2D electron gas (2DEG) on the surface can also bring about the 2D UCF The field-tilting regulation helps us exclude the distribution from the bulk And the classic self-averaging of UCF is investigated then to obtain the intrinsic UCF amplitude. By comparing with the theoretical prediction, the possibility has been ruled out that the 2D UCF may originate from the 2DEG So its topological nature is demonstrated. Secondly, we discuss the UCF effect in TI by a macroscopic perspective, i.e. the statistical symmetry of UCF, which should be more concise and reflect its universality. For a single TSS, the applied magnetic field will drive the system from a Gaussian symplectic ensemble into a Gaussian unitary ensemble. It results in a √2 fold increase of the UCF amplitude. However, the experiment reveals that the UCF amplitude is reduced by 1/√2. This is contradictory to the theoretical prediction. Actually, there are two TSSs and they are coherently coupled to each other in TIs since the sample’s thickness is smaller than its bulk dephasing length. This leads to a Gaussian orthogonal ensemble of the intersurface coupling system without an external field. In such a case, the UCF amplitude will be reduced by 1/√2 with field increasing. It is consistent with the experimental result. Finally, the other progress on UCFs is discussed, and the general outlook is also mentioned briefly.

Keywords:

作者及机构信息

1.
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

基金项目: 国家重点基础研究发展计划(批准号: 2013CB922103, 2011CB922103, 2014CB921103)、国家自然科学基金(批准号: 91421109, 11023002, 11134005, 61176088) 和江苏省自然科学基金(批准号: BK20130054) 资助的课题.

Authors and contacts

1.
National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, and Department of Physics, Nanjing University, Nanjing 210093, China

Funds: Project supported by the State Key Development Program for Basic Research of China (Grant Nos. 2013CB922103, 2011CB922103, 2014CB921103), the National Natural Science Foundation of China (Grant Nos. 91421109, 11023002, 11134005, 61176088), and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130054).

参考文献

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[22]	Yang P Y, Wang L Y, Hsu Y W, Lin J J 2012 Phys. Rev. B 85 085423
[23]	Beenakker C W J, Houten H V 1988 Phys. Rev. B 37 6544
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[37]	Xiong J, Khoo Y, Jia S, Cava R J, Ong N P 2013 Phys. Rev. B 88 035128
[38]	Baxter D V, Richter R, Trudeau M L, Cochrane R W, Strom-Olsen J O 1989 J. Phys. France 50 1673
[39]	Li Z G, Meng Y Z, Pan J, Chen T S, Hong X C, Li S Y, Wang X F, Song F Q, Wang B G 2014 Appl. Phys. Express 7 065202
[40]	Bianchi M, Guan D, Bao S, Mi J, Iversen B B, King P D C, Hofmann P 2010 Nat. Commun. 1 128
[41]	Bahramy M S, King P D C, de la Torre A, Chang J, Shi M, Patthey L, Balakrishnan G, Hofmann P, Arita R, Nagaosa N, Baumberger F 2012 Nat. Commun. 3 1159
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[43]	Benia H M, Lin C, Kern K, Ast C R 2011 Phys. Rev. Lett. 107 177602
[44]	Tian M, Ning W, Qu Z, Du H, Wang J, Zhang Y 2013 Sci. Rep. 3 1212
[45]	Cao H, Liu C, Tian J, Xu Y, Miotkowski I, Hasan M Z, Chen Y P 2014 arXiv 1409 3217
[46]	Adroguer P, Carpentier D, Cayssol J, Orignac E 2012 New J. Phys. 14 103027
[47]	Zhang L, Zhuang J, Xing Y, Li J, Wang J, Guo H 2014 Phys. Rev. B 89 245107
[48]	Pal A N, Kochat V, Ghosh A 2012 Phys. Rev. Lett. 109 196601
[49]	Rossi E, Bardarson J H, Fuhrer M S, Sarma S D 2012 Phys. Rev. Lett. 109 096801
[50]	Imry Y 1986 Europhys. Lett. 1 249
[51]	Buttiker M, Imry Y, Landauer R, Pinhas S 1985 Phys. Rev. B 31 6207
[52]	Muttalib K A, Pichard J L, Stone A D 1987 Phys. Rev. Lett. 59 2475
[53]	Mello P A, Akkermans E, Shapiro B 1988 Phys. Rev. Lett. 61 459
[54]	Zanon N, Pichard J L 1988 J. Phys. France 49 907
[55]	Stone A D 1989 Phys. Rev. B 39 10736
[56]	Mello P A 1988 Phys. Rev. Lett. 60 1089
[57]	Meir Y, Entin-Wohlman O 1993 Phys. Rev. Lett. 70 1988
[58]	Beenakker C W J 1993 Phys. Rev. Lett. 70 1155
[59]	Lyanda-Geller Y B, Mirlin A D 1994 Phys. Rev. Lett. 72 1894
[60]	Dyson F J 1962 J. Math. Phys. 3 140
[61]	Debray P, Pichard J L, Vicente J, Tung P N 1989 Phys. Rev. Lett. 63 2264
[62]	Mailly D, Sanquer M, Pichard J L, Pari P 1989 Europhys. Lett. 8 471
[63]	Moon J S, Birge N O, Golding B 1996 Phys. Rev. B 53 R4193
[64]	Moon J S, Birge N O, Golding B 1997 Phys. Rev. B 56 15124
[65]	Hoadley D, McConville P, Birge N O 1999 Phys. Rev. B 60 5617
[66]	Millo O, Klepper S J, Keller M W, Prober D E, Xiong S, Stone A D, Sacks R N 1990 Phys. Rev. Lett. 65 1494
[67]	Koga T, Nitta J, Akazaki T, Takayanagi H 2002 Phys. Rev. Lett. 89 046801
[68]	Bohra G, Somphonsane R, Aoki N, Ochiai Y, Akis R, Ferry D K, Bird J P 2012 Phys. Rev. B 86 161405
[69]	Rahman A, Guikema J W, Markovic N 2014 Phys. Rev. B 89 235407
[70]	Garate I, Glazman L 2012 Phys. Rev. B 86 035422
[71]	Fatemi V, Hunt B, Steinberg H, Eltinge S L, Mahmood F, Butch N P, Watanabe K, Taniguchi T, Gedik N, Ashoori R C, Jarillo-Herrero P 2014 Phys. Rev. Lett. 113 206801
[72]	Takagaki Y 2012 Phys. Rev. B 85 155308
[73]	Cheianov V, Glazman L I 2013 Phys. Rev. Lett. 110 206803
[74]	Xia B, Ren P, Sulaev A, Liu P, Shen S Q, Wang L 2013 Phys. Rev. B 87 085442
[75]	Alegria L D, Schroer M D, Chatterjee A, Poirier G R, Pretko M, Patel S K, Petta J R 2012 Nano Lett. 12 4711
[76]	Checkelsky J G, Hor Y S, Cava R J, Ong N P 2011 Phys. Rev. Lett. 106 196801
[77]	Matsuo S, Chida K, Chiba D, Ono T, Slevin K, Kobayashi K, Ohtsuki T, Chang C Z, He K, Ma X C, Xue Q K 2013 Phys. Rev. B 88 155438

施引文献

[1]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
[2]	Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
[3]	Ando Y 2013 J. Phys. Soc. Jpn. 82 102001
[4]	Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438
[5]	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, Shen Z X 2009 Science 325 178
[6]	Ren Z, Taskin A A, Sasaki S, Segawa K, Ando Y 2010 Phys. Rev. B 82 241306
[7]	Ren Z, Taskin A A, Sasaki S, Segawa K, Ando Y 2011 Phys. Rev. B 84 165311
[8]	Bardarson J H, Moore J E 2013 Rep. Prog. Phys. 76 056501
[9]	Qu D X, Hor Y S, Xiong J, Cava R J, Ong N P 2010 Science 329 821
[10]	Chen T, Chen Q, Schouteden K, Huang W, Wang X, Li Z, Miao F, Wang X, Li Z, Zhao B, Li S, Song F, Wang J, Wang B, Haesendonck C V, Wang G 2014 Nat. Commun. 5 5022
[11]	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
[12]	Peng H, Lai K, Kong D, Meister S, Chen Y, Qi X L, Zhang S C, Shen Z X, Cui Y 2010 Nat. Mater. 9 225
[13]	Li Z G, Qin Y Y, Song F Q, Wang Q H, Wang X F, Wang B G, Ding H F, Haesondonck C V, Wan J G, Zhang Y H, Wang G H 2012 Appl. Phys. Lett. 100 083107
[14]	Chen J, Qin H J, Yang F, Liu J, Guan T, Qu F M, Zhang G H, Shi J R, Xie X C, Yang C L, Wu K H, Li Y Q, Lu L 2010 Phys. Rev. Lett. 105 176602
[15]	Li Z G, Garate I, Pan J, Wan X G, Chen T S, Ning W, Zhang X O, Song F Q, Meng Y Z, Hong X C, Wang X F, Pi L, Wang X R, Wang B G, Li S Y, Reed M A, Glazman L, Wang G H 2015 Phys. Rev. B 91 041401
[16]	Akkermans E, Montambaux G 2007 Mesoscopic Physics of Electrons and Photons (New York: Cambridge University Press)
[17]	Li Z G 2014 Ph. D. Dissertation (Nanjing: Nanjing University) (in Chinese) [李兆国2014 博士论文(南京: 南京大学)]
[18]	Umbach C P, Washburn S, Laibowitz R B, Webb R A 1984 Phys. Rev. B 30 4048
[19]	Lee P A, Stone A D 1985 Phys. Rev. Lett. 55 1622
[20]	Webb R A, Washburn S, Umbach C P, Laibowitz R B 1985 Phys. Rev. Lett. 54 2696
[21]	Lee P A, Stone A D, Fukuyama H 1987 Phys. Rev. B 35 1039
[22]	Yang P Y, Wang L Y, Hsu Y W, Lin J J 2012 Phys. Rev. B 85 085423
[23]	Beenakker C W J, Houten H V 1988 Phys. Rev. B 37 6544
[24]	Licini J C, Bishop D J, Kastner M A, Melngailis J 1985 Phys. Rev. Lett. 55 2987
[25]	Webb R A, Washburn S, Umbach C P 1988 Phys. Rev. B 37 8455
[26]	Lien A S, Wang L Y, Chu C S, Lin J J 2011 Phys. Rev. B 84 155432
[27]	Altshuler B L 1985 JETP Lett. 41 648
[28]	Altshuler B L, Shklovskii B I 1986 Sov. Phys. JETP 64 127
[29]	Checkelsky J G, Hor Y S, Liu M H, Qu D X, Cava R J, Ong N P 2009 Phys. Rev. Lett. 103 246601
[30]	Matsuo S, Koyama T, Shimamura K, Arakawa T, Nishihara Y, Chiba D, Kobayashi K, Ono T, Chang C Z, He K, Ma X C, Xue Q K 2012 Phys. Rev. B 85 075440
[31]	Li Z G, Qin Y Y, Y. Mu W, Chen T S, Xu C H, He L B, Wan J G, Song F Q, Zhou J F, Han M, Wang G H 2011 J. Nanosci. Nanotechnol. 11 7042
[32]	Li Z G, Chen T S, Pan H Y, Song F Q, Wang B G, Han J H, Qin Y Y, Wang X F, Zhang R, Wan J G, Xing D Y, Wang G H 2012 Sci. Rep. 2 595
[33]	Kandala A, Richardella A, Zhang D, Flanagan T C, Samarth N 2013 Nano Lett. 13 2471
[34]	Lee J, Park J, Lee J H, Kim J S, Lee H J 2012 Phys. Rev. B 86 245321
[35]	Gehring P, Benia H M, Weng Y, Dinnebier R, Ast C R, Burghard M, Kern K 2013 Nano Lett. 13 1179
[36]	Tang C S, Xia B, Zou X, Chen S, Ou H W, Wang L, Rusydi A, Zhu J X, Chia E E M 2013 Sci. Rep. 3 3513
[37]	Xiong J, Khoo Y, Jia S, Cava R J, Ong N P 2013 Phys. Rev. B 88 035128
[38]	Baxter D V, Richter R, Trudeau M L, Cochrane R W, Strom-Olsen J O 1989 J. Phys. France 50 1673
[39]	Li Z G, Meng Y Z, Pan J, Chen T S, Hong X C, Li S Y, Wang X F, Song F Q, Wang B G 2014 Appl. Phys. Express 7 065202
[40]	Bianchi M, Guan D, Bao S, Mi J, Iversen B B, King P D C, Hofmann P 2010 Nat. Commun. 1 128
[41]	Bahramy M S, King P D C, de la Torre A, Chang J, Shi M, Patthey L, Balakrishnan G, Hofmann P, Arita R, Nagaosa N, Baumberger F 2012 Nat. Commun. 3 1159
[42]	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 E 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
[43]	Benia H M, Lin C, Kern K, Ast C R 2011 Phys. Rev. Lett. 107 177602
[44]	Tian M, Ning W, Qu Z, Du H, Wang J, Zhang Y 2013 Sci. Rep. 3 1212
[45]	Cao H, Liu C, Tian J, Xu Y, Miotkowski I, Hasan M Z, Chen Y P 2014 arXiv 1409 3217
[46]	Adroguer P, Carpentier D, Cayssol J, Orignac E 2012 New J. Phys. 14 103027
[47]	Zhang L, Zhuang J, Xing Y, Li J, Wang J, Guo H 2014 Phys. Rev. B 89 245107
[48]	Pal A N, Kochat V, Ghosh A 2012 Phys. Rev. Lett. 109 196601
[49]	Rossi E, Bardarson J H, Fuhrer M S, Sarma S D 2012 Phys. Rev. Lett. 109 096801
[50]	Imry Y 1986 Europhys. Lett. 1 249
[51]	Buttiker M, Imry Y, Landauer R, Pinhas S 1985 Phys. Rev. B 31 6207
[52]	Muttalib K A, Pichard J L, Stone A D 1987 Phys. Rev. Lett. 59 2475
[53]	Mello P A, Akkermans E, Shapiro B 1988 Phys. Rev. Lett. 61 459
[54]	Zanon N, Pichard J L 1988 J. Phys. France 49 907
[55]	Stone A D 1989 Phys. Rev. B 39 10736
[56]	Mello P A 1988 Phys. Rev. Lett. 60 1089
[57]	Meir Y, Entin-Wohlman O 1993 Phys. Rev. Lett. 70 1988
[58]	Beenakker C W J 1993 Phys. Rev. Lett. 70 1155
[59]	Lyanda-Geller Y B, Mirlin A D 1994 Phys. Rev. Lett. 72 1894
[60]	Dyson F J 1962 J. Math. Phys. 3 140
[61]	Debray P, Pichard J L, Vicente J, Tung P N 1989 Phys. Rev. Lett. 63 2264
[62]	Mailly D, Sanquer M, Pichard J L, Pari P 1989 Europhys. Lett. 8 471
[63]	Moon J S, Birge N O, Golding B 1996 Phys. Rev. B 53 R4193
[64]	Moon J S, Birge N O, Golding B 1997 Phys. Rev. B 56 15124
[65]	Hoadley D, McConville P, Birge N O 1999 Phys. Rev. B 60 5617
[66]	Millo O, Klepper S J, Keller M W, Prober D E, Xiong S, Stone A D, Sacks R N 1990 Phys. Rev. Lett. 65 1494
[67]	Koga T, Nitta J, Akazaki T, Takayanagi H 2002 Phys. Rev. Lett. 89 046801
[68]	Bohra G, Somphonsane R, Aoki N, Ochiai Y, Akis R, Ferry D K, Bird J P 2012 Phys. Rev. B 86 161405
[69]	Rahman A, Guikema J W, Markovic N 2014 Phys. Rev. B 89 235407
[70]	Garate I, Glazman L 2012 Phys. Rev. B 86 035422
[71]	Fatemi V, Hunt B, Steinberg H, Eltinge S L, Mahmood F, Butch N P, Watanabe K, Taniguchi T, Gedik N, Ashoori R C, Jarillo-Herrero P 2014 Phys. Rev. Lett. 113 206801
[72]	Takagaki Y 2012 Phys. Rev. B 85 155308
[73]	Cheianov V, Glazman L I 2013 Phys. Rev. Lett. 110 206803
[74]	Xia B, Ren P, Sulaev A, Liu P, Shen S Q, Wang L 2013 Phys. Rev. B 87 085442
[75]	Alegria L D, Schroer M D, Chatterjee A, Poirier G R, Pretko M, Patel S K, Petta J R 2012 Nano Lett. 12 4711
[76]	Checkelsky J G, Hor Y S, Cava R J, Ong N P 2011 Phys. Rev. Lett. 106 196801
[77]	Matsuo S, Chida K, Chiba D, Ono T, Slevin K, Kobayashi K, Ohtsuki T, Chang C Z, He K, Ma X C, Xue Q K 2013 Phys. Rev. B 88 155438

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