Electron transport properties of three-dimensional topological insulators
Yong-qing Li, Ke-hui Wu, Jun-ren Shi, Xin-cheng Xie
Electron transport properties of three-dimensional topological insulators
We review experimental advances in the study of the electron transport in three-dimensional topological insulators with emphasis on experiments that attempted to identify the surface transport. Recent results on transport properties of topological insulator thin films will be discussed in the context of weak antilocalization and electron–electron interactions. Current status of gate-voltage control of the chemical potential in topological insulators will also be described.
topological insulator / electron transport / localization / electron–electron interaction / spin–orbit coupling
[1] |
K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett., 1980, 45(6): 494
CrossRef
ADS
Google scholar
|
[2] |
M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X. L. Qi, and S.-C. Zhang, Science, 2007, 318(5851): 766
CrossRef
ADS
Google scholar
|
[3] |
B. A. Bernevig, T. A. Hughes, and S.-C. Zhang, Science, 2006, 314(5806): 1757
CrossRef
ADS
Google scholar
|
[4] |
C. L. Kane and E. J. Mele, Phys. Rev. Lett., 2005, 95(22): 226801
CrossRef
ADS
Google scholar
|
[5] |
C. L. Kane and E. J. Mele, Phys. Rev. Lett., 2005, 95(14): 146802
CrossRef
ADS
Google scholar
|
[6] |
L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett., 2007, 98(10): 106803
CrossRef
ADS
Google scholar
|
[7] |
J. E. Moore and L. Balents, Phys. Rev. B, 2007, 75(12): 121306(R)
CrossRef
ADS
Google scholar
|
[8] |
R. Roy, . Phys Rev. B, 2009, 79(19): 195322
CrossRef
ADS
Google scholar
|
[9] |
L. Fu and C. L. Kane, Phys. Rev. B, 2007, 76(4): 045302
CrossRef
ADS
Google scholar
|
[10] |
D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature (London), 2008, 452(7190): 970
CrossRef
ADS
Google scholar
|
[11] |
Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nat. Phys., 2009, 5(6): 398
CrossRef
ADS
Google scholar
|
[12] |
Y. L. Chen, J. G. Analytis, J. H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S.-C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, Science, 2009, 325(5937): 178
CrossRef
ADS
Google scholar
|
[13] |
P. Roushan, J. Seo, C. V. Parker, Y. S. Hor, D. Hsieh, D. Qian, A. Richardella, M. Z. Hasan, R. J. Cava, and A. Yazdani, Nature (London), 2009, 460(7259): 1106
CrossRef
ADS
Google scholar
|
[14] |
T. Zhang, P. Cheng, X. Chen, J. F. Jia, X. C. Ma, K. He, L. L. Wang, H. J. Zhang, X. Dai, Z. Fang, X. C. Xie, and Q. K. Xue, Phys. Rev. Lett., 2009, 103(26): 266803
CrossRef
ADS
Google scholar
|
[15] |
M. Z. Hasan and C. L. Kane, Rev. Mod. Phys., 2010, 82(4): 3045
CrossRef
ADS
Google scholar
|
[16] |
X. L. Qi and S.-C. Zhang, arXiv:1008.2026, 2010
|
[17] |
M. Z. Hasan and J. E. Moore, arXiv:1011.5462, 2010
|
[18] |
A. V. Geim and K. S. Novoselov, Nat. Mater., 2007, 6(3): 183
CrossRef
ADS
Google scholar
|
[19] |
D. Schoenberg, Magnetic Oscillations in Metals, Cambridge: Cambridge University Press, 1984
CrossRef
ADS
Google scholar
|
[20] |
H. Köhler, Phys. Stat. Sol. B, 1973, 58(1): 91
CrossRef
ADS
Google scholar
|
[21] |
H. Köhler, Solid State Commun., 1973, 13(10): 1585
CrossRef
ADS
Google scholar
|
[22] |
H. Köhler and E. Wuechner, Phys. Stat. Sol. B, 1975, 67(2): 665
CrossRef
ADS
Google scholar
|
[23] |
H. Köhler, Phys. Stat. Sol. B, 1976, 73(1): 95
CrossRef
ADS
Google scholar
|
[24] |
H. Köhler, Phys. Stat. Sol. B, 1976, 75(1): 127
CrossRef
ADS
Google scholar
|
[25] |
A. A. Taskin and Y. Ando, Phys. Rev. B, 2009, 80(8): 085303
CrossRef
ADS
Google scholar
|
[26] |
H. J. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, Nat. Phys., 2009, 5(6): 438
CrossRef
ADS
Google scholar
|
[27] |
L. Fu and C. L. Kane, Phys. Rev. Lett., 2008, 100(9): 096407
CrossRef
ADS
Google scholar
|
[28] |
L. Fu and C. L. Kane, Phys. Rev. Lett., 2009, 102(21): 216403
CrossRef
ADS
Google scholar
|
[29] |
A. R. Akhmerov, J. Nilsson, and C. W. J. Beenakker, Phys. Rev. Lett., 2009, 102(21): 216404
CrossRef
ADS
Google scholar
|
[30] |
Y. S. Hor, A. Richardella, P. Roushan, Y. Xia, J. G. Checkelsky, A. Yazdani, M. Z. Hasan, N. P. Ong, and R. J. Cava, Phys. Rev. B, 2009, 79(19): 195208
CrossRef
ADS
Google scholar
|
[31] |
Y. L. Chen, J.-H. Chu, J. G. Analytis, Z. K. Liu, K. Igarashi, H.-H. Kuo, X. L. Qi, S. K. Mo, R. G. Moore, D. H. Lu, M. Hashimoto, T. Sasagawa, S.-C. Zhang, I. R. Fisher, Z. Hussain, and Z. X. Shen, Science, 2010, 329(5992): 659, and also online supporting materials
CrossRef
ADS
Google scholar
|
[32] |
N. P. Butch, K. Kirshenbaum, P. Syers, A. B. Sushkov, G. S. Jenkins, H. D. Drew, and J.Paglione, Phys. Rev. B, 2010, 81(24): 241301
CrossRef
ADS
Google scholar
|
[33] |
J. G. Analytis, R. D. McDonald, S. C. Riggs, J. H. Chu, G. S. Boebinger, and I. R. Fisher, Nat. Phys., 2010, 6(12): 960
CrossRef
ADS
Google scholar
|
[34] |
M. Bianchi, D. Guan, S. Bao, J. L. Mi, B. B. Iversen, P. D. C. King, and Ph. Hofmann, Nat. Commun., 2010, 1(8): 128
CrossRef
ADS
Google scholar
|
[35] |
J. G. Analytis, J.-H. Chu, Y. L. Chen, F. Corredor, R. D. McDonald, Z. X. Shen, and I. R. Fisher, Phys. Rev. B, 2010, 81(20): 205407
CrossRef
ADS
Google scholar
|
[36] |
D. X. Qu, Y. S. Hor, J. Xiong, R. J. Cava, and N. P. Ong, Science, 2010, 329(5993): 821
CrossRef
ADS
Google scholar
|
[37] |
F. Xiu, L. He, Y. Wang, L. Cheng, L.-T. Chang, M. Lang, G. Huang, X. Kou, Y. Zhou, X. Jiang, Z. Chen, J. Zou, A. Shailos, and K. L. Wang, Nat. Nano.,
CrossRef
ADS
Google scholar
|
[38] |
Z. Ren, A. A. Taskin, S. Sasaki, K. Segawa, and Y. Ando, Phys. Rev. B, 2010, 82(24): 241306
CrossRef
ADS
Google scholar
|
[39] |
J. Xiong, A. C. Petersen, Dongxia Qu, R. J. Cava, and N. P. Ong, arXiv:1101.1315, 2011
|
[40] |
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature (London), 2005, 438(7065): 197
CrossRef
ADS
Google scholar
|
[41] |
Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, Nature (London), 2005, 438(7065): 201
CrossRef
ADS
Google scholar
|
[42] |
A. A. Taskin and Y. Ando, arXiv:1103.3096, 2011
|
[43] |
B. L. Altshuler, A. G. Aronov, and B. Z. Spivak, JETP Lett., 1981, 33: 94
|
[44] |
Y. Aharonov and D. Bohm, Phys. Rev., 1959, 115(3): 485
CrossRef
ADS
Google scholar
|
[45] |
D. Y. Sharvin and Y. V. Sharvin, JETP Lett., 1981, 34: 272
|
[46] |
C. Schönenberger, A. Bachtold, C. Strunk, J.-P. Salvetat, J.- M. Bonard, L. Forró, and T. Nussbaumer, Nature (London), 1999, 397(6721): 673
CrossRef
ADS
Google scholar
|
[47] |
H. L. Peng, K. Lai, D. Kong, S. Meister, Y. Chen, X. L. Qi, S.-C. Zhang, Z.-X. Shen, and Y. Cui, Nat. Mater., 2010, 9(3): 225
|
[48] |
J. H. Bardarson, P. W. Brouwer, and J. E. Moore, Phys. Rev. Lett., 2010, 105(15): 156803
CrossRef
ADS
Google scholar
|
[49] |
Y. Zhang and A. Vishwanath, Phys. Rev. Lett., 2010, 105(20): 206601
CrossRef
ADS
Google scholar
|
[50] |
Y. Y. Qin, Z. G. Li, Z. Qu, Q. H. Wang, W. F. Ding, B. G. Wang, X. F. Wang, C. Van Haesondonck, F. Q. Song, M. Han, Y. H. Zhang, G. H. Wang, and J. G. Wan, arXiv:1012.0104, 2010
|
[51] |
D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Science, 2009, 323(5916): 919
CrossRef
ADS
Google scholar
|
[52] |
T. Ihn, Nat. Mater., 2010, 9(3): 187
CrossRef
ADS
Google scholar
|
[53] |
H. Z. Lu, W. Y. Shan, W. Yao, Q. Niu, and S. Q. Shen, Phys. Rev. B, 2010, 81: 115407
CrossRef
ADS
Google scholar
|
[54] |
C. X. Liu, H. J. Zhang, B. H. Yan, X. L. Qi, T. Frauenheim, X. Dai, Z. Fang, and S.-C. Zhang, Phys. Rev. B., 2010, 81(4): 041307(R)
CrossRef
ADS
Google scholar
|
[55] |
G. H. Zhang, H. J. Qin, J. Teng, J. D. Guo, Q. Guo, X. Dai, Z. Fang, and K. H. Wu, Appl. Phys. Lett., 2009, 95: 053114
CrossRef
ADS
Google scholar
|
[56] |
K. He, Y. Zhang, C. Z. Chang, C. L. Song, L. L. Wang, X. Chen, J. F. Jia, Z. Fang, X. Dai, W. Y. Shan, S. Q. Shen, Q. Niu, X. L. Qi, S.-C. Zhang, X. C. Ma, and Q. K. Xue, Nat. Phys., 2010, 6(8): 584
CrossRef
ADS
Google scholar
|
[57] |
Y. Zhang, C. Z. Chang, K. He, L. L. Wang, X. Chen, J. F. Jia, X. C. Ma, and Q. K. Xue, . Appl Phys. Lett., 2010, 97(19): 194102
CrossRef
ADS
Google scholar
|
[58] |
C. L. Song, Y. L. Wang, Y. P. Jiang, Y. Zhang, C. Z. Chang, L. Wang, K. He, X. Chen, J. F. Jia, Y. Wang, Z. Fang, X. Dai, X. C. Xie, X. L. Qi, S.-C. Zhang, Q. K. Xue, and X. C. Ma, Appl. Phys. Lett., 2010, 97(14): 143118
CrossRef
ADS
Google scholar
|
[59] |
J. Chen, H. J. Qin, F. Yang, J. Liu, T. Guan, F. M. Qu, G. H. Zhang, J. R. Shi, X. C. Xie, C. L. Yang, K. H. Wu, Y. Q. Li, and L. Lu, Phys. Rev. Lett., 2010, 105(17): 176602
CrossRef
ADS
Google scholar
|
[60] |
G. H. Zhang, H. J. Qin, J. Chen, X. Y. He, L. Lu, Y. Q. Li, and K. H. Wu, Adv. Func. Mater., 2011
CrossRef
ADS
Google scholar
|
[61] |
H. D. Li, Z. Y. Wang, X. Guo, T. L. Wong, N. Wang, and M. H. Xie, Appl. Phys. Lett., 2011, 98(4): 043104
CrossRef
ADS
Google scholar
|
[62] |
C. Z. Chang, K. He, L. L. Wang, X. C. Ma, M. H. Liu, Z. C. Zhang, X. Chen, Y. Y. Wang, and Q. K. Xue, arXiv:1012.5716, 2010
|
[63] |
Y. Y. Li, G. Wang, X. G. Zhu, M. H. Liu, C. Ye, X. Chen, Y. Y. Wang, K. He, L. L. Wang, X. C. Ma, H. J. Zhang, X. Dai, Z. Fang, X. C. Xie, Y. Liu, X. L. Qi, J. F. Jia, S.-C. Zhang, and Q. K. Xue, Adv. Mater., 2010, 22(36): 4002
CrossRef
ADS
Google scholar
|
[64] |
H. D. Li, Z. Y. Wang, X. Kan, X. Guo, H. T. He, Z. Wang, J. N. Wang, T. L. Wong, N. Wang, and M. H. Xie, New J. Phys., 2010, 12(10): 103038
CrossRef
ADS
Google scholar
|
[65] |
A. Richardella, D. M. Zhang, J. S. Lee, A. Koser, D. W. Rench, A. L. Yeats, B. B. Buckley, D. D. Awschalom, and N. Samarth, Appl. Phys. Lett., 2010, 97(26): 262104
CrossRef
ADS
Google scholar
|
[66] |
P. Cheng, C. Song, T. Zhang, Y. Zhang, Y. Wang, J. F. Jia, J. Wang, Y. Wang, B. F. Zhu, X. Chen, X. C. Ma, K. He, L. Wang, X. Dai, Z. Fang, X. C. Xie, X. L. Qi, C. X. Liu, S.-C. Zhang, and Q. K. Xue, Phys. Rev. Lett., 2010, 105(7): 076801
CrossRef
ADS
Google scholar
|
[67] |
H. T. He, G. Wang, T. Zhang, I.-K. Sou, G. K. L. Wong, and J. N. Wang, Phys. Rev. Lett., 2011, 106(16): 166805
CrossRef
ADS
Google scholar
|
[68] |
M. H. Liu, C. Z. Chang, Z. C. Zhang, Y. Zhang, W. Ruan, K. He, L. L.Wang, X. Chen, J. F. Jia, S.-C. Zhang, Q. K. Xue, X. C. Ma, and Y. Y. Wang, Phys. Rev. B, 2011, 83(16): 165440
CrossRef
ADS
Google scholar
|
[69] |
J. Wang, A. M. DaSilva, C. Z. Chang, K. He, J. K. Jain, N. Samarth, X. C. Ma, Q.-K. Xue, and M. H. W. Chan, arXiv:1012.0271, 2010
|
[70] |
J. Chen, X. Y. He, K. H. Wu, Z. Q. Ji, L. Lu, J. R. Shi, J. H. Smet, and Y. Q. Li, arXiv:1104.0986, 2011, to appear in Phys. Rev. B (Rapid Commun.)
|
[71] |
D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder, L. Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature (London), 2009, 460(7259): 1101
CrossRef
ADS
Google scholar
|
[72] |
J. Chen, X. Y. He, K. H. Wu, and Y. Q. Li, unpublished
|
[73] |
D. S. Kong, J. J. Cha, K. J. Lai, H. L. Peng, J. G. Analytis, S. Meister, Y. L. Chen, H. J. Zhang, I. R. Fisher, Z.-X. Shen, and Y. Cui, arXiv:1102.3935, 2011
|
[74] |
D. Teweldebrhan, V. Goyal, and A. A. Balandin, Nano Lett., 2010, 10(4): 1209
CrossRef
ADS
Google scholar
|
[75] |
J. G. Checkelsky, Y. S. Hor, R. J. Cava, and N. P. Ong, Phys. Rev. Lett., 2011, 106: 196801
CrossRef
ADS
Google scholar
|
[76] |
D. Kong, W. Dang, J. J. Cha, H. Li, S. Meister, H. Peng, Z. Liu, and Y. Cui, Nano Lett., 2010, 10(6): 2245
CrossRef
ADS
Google scholar
|
[77] |
R. Yu, W. Zhang, H. J. Zhang, S.-C. Zhang, X. Dai, and Z. Fang, Science, 2010, 329(5987): 61
CrossRef
ADS
Google scholar
|
[78] |
X. L. Qi, R. D. Li, J. Zang, and S.-C. Zhang, Science, 2009, 323(5918): 1184
CrossRef
ADS
Google scholar
|
[79] |
I. Garate and M. Franz, Phys. Rev. Lett., 2010, 104(14): 146802
CrossRef
ADS
Google scholar
|
[80] |
H. Steinberg, J. Laloe, V. Fatemi, J. S. Moodera, and P. Jarillo-Herrero, arXiv:1104.1404, 2011
|
[81] |
H. Steinberg, D. R. Gardner, Y. S. Lee, and P. Jarillo-Herrero, Nano Lett., 2010, 10(12): 5032
CrossRef
ADS
Google scholar
|
[82] |
R. C. Neville, B. Hoeneisen, and C. A. Mead, J. Appl. Phys., 1972, 43(5): 2124
CrossRef
ADS
Google scholar
|
[83] |
D. Caviglia, S. Gariglio, N. Reyren, D. Jaccard, T. Schneider, M. Gabay, S. Thiel, G. Hammerl, J. Mannhart, and J.-M. Triscone, Nature (London), 2008, 456(7222): 624
CrossRef
ADS
Google scholar
|
[84] |
P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. Lett., 2010, 105: 036803
CrossRef
ADS
Google scholar
|
[85] |
E. McCann, K. Kechedzhi, V. I. Falko, H. Suzuura, T. Ando, and B. L. Altshuler, Phys. Rev. Lett., 2006, 97(14): 146805
CrossRef
ADS
Google scholar
|
[86] |
The coefficient α would be 4 × 1/2= 2 for graphene if the intervalley and chirality breaking scatterings could be neglected.
|
[87] |
G. Bergmann, Phys. Rep., 1984, 107(1): 1
CrossRef
ADS
Google scholar
|
[88] |
R. L. Kallaher and J. J. Heremans, Phys. Rev. B, 2009, 79(7): 075322
CrossRef
ADS
Google scholar
|
[89] |
S. Hikami, A. I. Larkin, and Y. N agaoka, Prog. Theor. Phys., 1980, 63(2): 707
CrossRef
ADS
Google scholar
|
[90] |
H. Hoffmann, F. Hofmann, and W. Schoepe, Phys. Rev. B, 1982, 25(8): 5563
CrossRef
ADS
Google scholar
|
[91] |
O. Rabin, K. Nielsch, and M. S. Dresselhaus, Appl. Phys. A, 2006, 82(3): 471
CrossRef
ADS
Google scholar
|
[92] |
|
[93] |
Qualitatively similar variation of α with VG was also reported in Ref. [75], in which the weak antilocalization signal is however superimposed on fluctuating background of unknown origin. The non-Hall-bar device-geometry also precluded accurate determination of α in that work.
|
[94] |
M. Kawasaki, K. Takahashi, T. Maeda, R. Tsuchiya, M. Shinohara, O. Ishiyama, T. Yonezawa, and H. K oinuma, Science, 1994, 266: 1540
CrossRef
ADS
Google scholar
|
[95] |
A. A. Abrikosov, Phys. Rev. B, 1998, 58(5): 2788
CrossRef
ADS
Google scholar
|
[96] |
M. M. Parish and P. B. Littlewood, Nature, 2003, 426(6963): 162
CrossRef
ADS
Google scholar
|
[97] |
H. Tang, D. Liang, R. L. J. Qiu, and X. P. A. Gao, arXiv:1003.6099, 2010
|
[98] |
P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys., 1985, 57(2): 287
CrossRef
ADS
Google scholar
|
[99] |
B. L. Altshuler and A. G. Aronov, in: Electron-Electron Interactions in Disordered Systems, edited by A. L. Efros and M. Pollak, Amsterdam, North-Holland, 1985
|
[100] |
B. L. Altshuler, A. G. Aronov, and A. Y. Zuzin, Solid State Commun., 1982, 44(2): 137
CrossRef
ADS
Google scholar
|
[101] |
A. Sahnoune, J. O. Strom-Olsen, and H. E. Fischer, Phys. Rev. B, 1992, 46(16): 10035
CrossRef
ADS
Google scholar
|
[102] |
A. M. Finkelstein, Sov. Sci. Rev. A, 1990, 14: 1
|
[103] |
D. Belitz and T. R. Kirkpatrick, Rev. Mod. Phys., 1994, 66(2): 261
CrossRef
ADS
Google scholar
|
[104] |
A. D. Mirlin, private communications
|
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〈 | 〉 |