Electron transport properties of three-dimensional topological insulators

Abstract

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.

Keywords

topological insulator / electron transport / localization / electron–electron interaction / spin–orbit coupling

References

[1] K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett., 1980, 45(6): 494

[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

[3] B. A. Bernevig, T. A. Hughes, and S.-C. Zhang, Science, 2006, 314(5806): 1757

[4] C. L. Kane and E. J. Mele, Phys. Rev. Lett., 2005, 95(22): 226801

[5] C. L. Kane and E. J. Mele, Phys. Rev. Lett., 2005, 95(14): 146802

[6] L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett., 2007, 98(10): 106803

[7] J. E. Moore and L. Balents, Phys. Rev. B, 2007, 75(12): 121306(R)

[8] R. Roy, . Phys Rev. B, 2009, 79(19): 195322

[9] L. Fu and C. L. Kane, Phys. Rev. B, 2007, 76(4): 045302

[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

[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

[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

[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

[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

[15] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys., 2010, 82(4): 3045

[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

[19] D. Schoenberg, Magnetic Oscillations in Metals, Cambridge: Cambridge University Press, 1984

[20] H. Köhler, Phys. Stat. Sol. B, 1973, 58(1): 91

[21] H. Köhler, Solid State Commun., 1973, 13(10): 1585

[22] H. Köhler and E. Wuechner, Phys. Stat. Sol. B, 1975, 67(2): 665

[23] H. Köhler, Phys. Stat. Sol. B, 1976, 73(1): 95

[24] H. Köhler, Phys. Stat. Sol. B, 1976, 75(1): 127

[25] A. A. Taskin and Y. Ando, Phys. Rev. B, 2009, 80(8): 085303

[26] H. J. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, Nat. Phys., 2009, 5(6): 438

[27] L. Fu and C. L. Kane, Phys. Rev. Lett., 2008, 100(9): 096407

[28] L. Fu and C. L. Kane, Phys. Rev. Lett., 2009, 102(21): 216403

[29] A. R. Akhmerov, J. Nilsson, and C. W. J. Beenakker, Phys. Rev. Lett., 2009, 102(21): 216404

[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

[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

[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

[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

[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

[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

[36] D. X. Qu, Y. S. Hor, J. Xiong, R. J. Cava, and N. P. Ong, Science, 2010, 329(5993): 821

[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.,

[38] Z. Ren, A. A. Taskin, S. Sasaki, K. Segawa, and Y. Ando, Phys. Rev. B, 2010, 82(24): 241306

[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

[41] Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, Nature (London), 2005, 438(7065): 201

[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

[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

[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

[49] Y. Zhang and A. Vishwanath, Phys. Rev. Lett., 2010, 105(20): 206601

[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

[52] T. Ihn, Nat. Mater., 2010, 9(3): 187

[53] H. Z. Lu, W. Y. Shan, W. Yao, Q. Niu, and S. Q. Shen, Phys. Rev. B, 2010, 81: 115407

[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)

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[75] J. G. Checkelsky, Y. S. Hor, R. J. Cava, and N. P. Ong, Phys. Rev. Lett., 2011, 106: 196801

[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

[77] R. Yu, W. Zhang, H. J. Zhang, S.-C. Zhang, X. Dai, and Z. Fang, Science, 2010, 329(5987): 61

[78] X. L. Qi, R. D. Li, J. Zang, and S.-C. Zhang, Science, 2009, 323(5918): 1184

[79] I. Garate and M. Franz, Phys. Rev. Lett., 2010, 104(14): 146802

[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

[82] R. C. Neville, B. Hoeneisen, and C. A. Mead, J. Appl. Phys., 1972, 43(5): 2124

[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

[84] P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. Lett., 2010, 105: 036803

[85] E. McCann, K. Kechedzhi, V. I. Falko, H. Suzuura, T. Ando, and B. L. Altshuler, Phys. Rev. Lett., 2006, 97(14): 146805

[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

[88] R. L. Kallaher and J. J. Heremans, Phys. Rev. B, 2009, 79(7): 075322

[89] S. Hikami, A. I. Larkin, and Y. N agaoka, Prog. Theor. Phys., 1980, 63(2): 707

[90] H. Hoffmann, F. Hofmann, and W. Schoepe, Phys. Rev. B, 1982, 25(8): 5563

[91] O. Rabin, K. Nielsch, and M. S. Dresselhaus, Appl. Phys. A, 2006, 82(3): 471

[92] α≃1/2 was also obtained previously from Bi₂Se₃ thin films on Si by F. Yang et al. (unpublished)

[93] Qualitatively similar variation of α with V_G 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

[95] A. A. Abrikosov, Phys. Rev. B, 1998, 58(5): 2788

[96] M. M. Parish and P. B. Littlewood, Nature, 2003, 426(6963): 162

[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

[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

[101] A. Sahnoune, J. O. Strom-Olsen, and H. E. Fischer, Phys. Rev. B, 1992, 46(16): 10035

[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

[104] A. D. Mirlin, private communications

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