Topological insulators (TIs) are new states of quantum materials with an insulating bulk and metallic surface or edge states.


Edge State Topological Insulator Dirac Point Anomalous Hall Effect Topological Field Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Moore JE. The birth of topological insulators. Nature. 2010;464:194–8.ADSCrossRefGoogle Scholar
  2. 2.
    Hasan MZ, Kane CL. Colloquium: topological insulators. Rev Mod Phys. 2010;82:3045–67.ADSCrossRefGoogle Scholar
  3. 3.
    Qi X-L, Zhang S-C. The quantum spin Hall effect and topological insulators. Phys Today. 2010;63:33–8.ADSCrossRefGoogle Scholar
  4. 4.
    Qi X-L, Zhang S-C. Topological insulators and superconductors. Rev Mod Phys. 2011;83:1057–110.ADSCrossRefGoogle Scholar
  5. 5.
    Zhang T, Cheng P, Chen X, et al. Experimental demonstration of topological surface states protected by time-reversal symmetry. Phys Rev Lett. 2009;103:266803.ADSCrossRefGoogle Scholar
  6. 6.
    Alpichshev Z, Analytis JG, Chu JH, et al. STM imaging of electronic waves on the surface of Bi2Te3: topologically protected surface states and hexagonal warping effects. Phys Rev Lett. 2010;104:016401.ADSCrossRefGoogle Scholar
  7. 7.
    Fu L, Kane CL. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys Rev Lett. 2008;100:096407.ADSCrossRefGoogle Scholar
  8. 8.
    Qi XL, Li R, Zang J, et al. Inducing a magnetic monopole with topological surface states. Science. 2009;323:1184–7.ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Yu R, Zhang W, Zhang HJ, et al. Quantized anomalous Hall effect in magnetic topological insulators. Science. 2010;329:61–4.ADSCrossRefGoogle Scholar
  10. 10.
    Bernevig BA, Hughes TL, Zhang S-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science. 2006;314:1757–61.ADSCrossRefGoogle Scholar
  11. 11.
    König M, Wiedmann S, Brüne C, et al. Quantum spin Hall insulator state in HgTe quantum wells. Science. 2007;318:766–70.ADSCrossRefGoogle Scholar
  12. 12.
    Fu L, Kane CL. Topological insulators with inversion symmetry. Phys Rev B. 2007;76:045302.ADSCrossRefGoogle Scholar
  13. 13.
    Hsieh D, Qian D, Wray L, et al. A topological Dirac insulator in a quantum spin Hall phase. Nature. 2008;452:970–4.ADSCrossRefGoogle Scholar
  14. 14.
    Zhang H, Liu C-X, Qi X-L, et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nat Phys. 2009;5:438–42.CrossRefGoogle Scholar
  15. 15.
    Xia Y, Qian D, Hsieh D, et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nat Phys. 2009;5:398–402.CrossRefGoogle Scholar
  16. 16.
    Chen YL, Analytis JG, Chu J-H, et al. Experimental realization of a three-dimensional topological insulator, Bi2Te3. Science. 2009;325:178–81.ADSCrossRefGoogle Scholar
  17. 17.
    Hsieh D, Xia Y, Qian D, et al. Observation of time-reversal-protected single-Dirac-cone topological-insulator states in Bi2Te3 and Sb2Te3. Phys Rev Lett. 2009;103:146401.ADSCrossRefGoogle Scholar
  18. 18.
    Anderson PW. Basic notions of condensed matter physics. Boulder, CO: Westview Press; 1997.Google Scholar
  19. 19.
    Landau LD, Lifshitz EM. Statistical physics. Oxford: Pergamon Press; 1980.zbMATHGoogle Scholar
  20. 20.
    Klitzing K, Dorda G, Pepper M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys Rev Lett. 1980;45:494–7.ADSCrossRefGoogle Scholar
  21. 21.
    Thouless DJ, Kohmoto M, Nightingale MP, et al. Quantized Hall conductance in a two-dimensional periodic potential. Phys Rev Lett. 1982;49:405–8.ADSCrossRefGoogle Scholar
  22. 22.
    Berry MV. Quantal phase-factors accompanying adiabatic changes. P Roy Soc Lond A Mat. 1984;392:45–57.ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Haldane FDM. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “parity anomaly”. Phys Rev Lett. 1988;61:2015–8.ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Volovik GE. Quantized Hall-effect in superfluid He-3 Film. Phys Lett A. 1988;128:277–9.ADSCrossRefGoogle Scholar
  25. 25.
    Wolf SA, Awschalom DD, Buhrman RA, et al. Spintronics: a spin-based electronics vision for the future. Science. 2001;294:1488–95.ADSCrossRefGoogle Scholar
  26. 26.
    Nagaosa N, Sinova J, Onoda S, et al. Anomalous Hall effect. Rev Mod Phys. 2010;82:1539–92.ADSCrossRefGoogle Scholar
  27. 27.
    Murakami S, Nagaosa N, Zhang S-C. Dissipationless quantum spin current at room temperature. Science. 2003;301:1348–51.ADSCrossRefGoogle Scholar
  28. 28.
    Sinova J, Culcer D, Niu Q, et al. Universal intrinsic spin Hall effect. Phys Rev Lett. 2004;92:126603.ADSCrossRefGoogle Scholar
  29. 29.
    Murakami S, Nagaosa N, Zhang S-C. Spin-Hall insulator. Phys Rev Lett. 2004;93:156804.ADSCrossRefGoogle Scholar
  30. 30.
    Kane CL, Mele EJ. Quantum spin Hall effect in graphene. Phys Rev Lett. 2005;95:226801.ADSCrossRefGoogle Scholar
  31. 31.
    Bernevig BA, Zhang S-C. Quantum spin Hall effect. Phys Rev Lett. 2006;96:106802.ADSCrossRefGoogle Scholar
  32. 32.
    Min H, Hill JE, Sinitsyn NA, et al. Intrinsic and Rashba spin-orbit interactions in graphene sheets. Phys Rev B. 2006;74:165310.ADSCrossRefGoogle Scholar
  33. 33.
    Yao Y, Ye F, Qi X-L, et al. Spin-orbit gap of graphene: first-principles calculations. Phys Rev B. 2007;75:041401.ADSCrossRefGoogle Scholar
  34. 34.
    Roth A, Brüne C, Buhmann H, et al. Nonlocal transport in the quantum spin Hall state. Science. 2009;325:294–7.ADSCrossRefGoogle Scholar
  35. 35.
    Kane CL, Mele EJ. Z 2 topological order and the quantum spin Hall effect. Phys Rev Lett. 2005;95:146802.ADSCrossRefGoogle Scholar
  36. 36.
    Fu L, Kane CL, Mele EJ. Topological insulators in three dimensions. Phys Rev Lett. 2007;98:106803.ADSCrossRefGoogle Scholar
  37. 37.
    Moore JE, Balents L. Topological invariants of time-reversal-invariant band structures. Phys Rev B. 2007;75:121306.ADSCrossRefGoogle Scholar
  38. 38.
    Roy R. Z 2 classification of quantum spin Hall systems: an approach using time-reversal invariance. Phys Rev B. 2009;79:195321.ADSCrossRefGoogle Scholar
  39. 39.
    Fu L, Kane CL. Time reversal polarization and a Z 2 adiabatic spin pump. Phys Rev B. 2006;74:195312.ADSCrossRefGoogle Scholar
  40. 40.
    Qi X-L, Hughes TL, Zhang S-C. Topological field theory of time-reversal invariant insulators. Phys Rev B. 2008;78:195424.ADSCrossRefGoogle Scholar
  41. 41.
    Wu C, Bernevig BA, Zhang S-C. Helical liquid and the edge of quantum spin Hall systems. Phys Rev Lett. 2006;96:106401.ADSCrossRefGoogle Scholar
  42. 42.
    Xu C, Moore JE. Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z 2 topology. Phys Rev B. 2006;73:045322.ADSCrossRefGoogle Scholar
  43. 43.
    Nomura K, Koshino M, Ryu S. Topological delocalization of two-dimensional massless Dirac fermions. Phys Rev Lett. 2007;99:146806.ADSCrossRefGoogle Scholar
  44. 44.
    Sheng DN, Weng ZY, Sheng L, et al. Quantum spin-Hall effect and topologically invariant Chern numbers. Phys Rev Lett. 2006;97:036808.ADSCrossRefGoogle Scholar
  45. 45.
    Fukui T, Hatsugai Y. Topological aspects of the quantum spin-Hall effect in graphene: Z 2 topological order and spin Chern number. Phys Rev B. 2007;75:121403.ADSCrossRefGoogle Scholar
  46. 46.
    Prodan E. Robustness of the spin-Chern number. Phys Rev B. 2009;80:125327.ADSCrossRefGoogle Scholar
  47. 47.
    Zhang SC. The Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall-effect. Int J Mod Phys B. 1992;6:25–58.ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    Zhang S-C, Hu J. A four-dimensional generalization of the quantum Hall effect. Science. 2001;294:823–8.ADSCrossRefGoogle Scholar
  49. 49.
    Knez I, Du R-R, Sullivan G. Evidence for helical edge modes in inverted InAs/GaSb quantum wells. Phys Rev Lett. 2011;107:136603.ADSCrossRefGoogle Scholar
  50. 50.
    Hsieh D, Xia Y, Wray L, et al. Observation of unconventional quantum spin textures in topological insulators. Science. 2009;323:919–22.ADSCrossRefGoogle Scholar
  51. 51.
    Yang F, Miao L, Wang ZF, et al. Spatial and energy distribution of topological Edge states in single Bi(111) Bilayer. Phys Rev Lett. 2012;109:016801.ADSCrossRefGoogle Scholar
  52. 52.
    Ren Z, Taskin AA, Sasaki S, et al. Large bulk resistivity and surface quantum oscillations in the topological insulator Bi2Te2Se. Phys Rev B. 2010;82:241306.ADSCrossRefGoogle Scholar
  53. 53.
    Ren Z, Taskin AA, Sasaki S, et al. Optimizing Bi2−xSbxTe3−ySey solid solutions to approach the intrinsic topological insulator regime. Phys Rev B. 2011;84:165311.ADSCrossRefGoogle Scholar
  54. 54.
    Ji H, Allred JM, Fuccillo MK, et al. Bi2Te1.6S1.4: a topological insulator in the tetradymite family. Phys Rev B. 2012;85:201103.ADSCrossRefGoogle Scholar
  55. 55.
    Taskin AA, Ren Z, Sasaki S, et al. Observation of Dirac holes and electrons in a topological insulator. Phys Rev Lett. 2011;107:016801.ADSCrossRefGoogle Scholar
  56. 56.
    Sato T, Segawa K, Guo H, et al. Direct evidence for the Dirac-cone topological surface states in the ternary chalcogenide TlBiSe2. Phys Rev Lett. 2010;105:136802.ADSCrossRefGoogle Scholar
  57. 57.
    Chen YL, Liu ZK, Analytis JG, et al. Single Dirac cone topological surface state and unusual thermoelectric property of compounds from a new topological insulator family. Phys Rev Lett. 2010;105:266401.ADSCrossRefGoogle Scholar
  58. 58.
    Xu S-Y, Xia Y, Wray LA, et al. Topological phase transition and texture inversion in a tunable topological insulator. Science. 2011;332:560–4.ADSCrossRefGoogle Scholar
  59. 59.
    Souma S, Eto K, Nomura M, et al. Topological surface states in lead-based ternary telluride Pb(Bi1−xSbx)2Te4. Phys Rev Lett. 2012;108:116801.ADSCrossRefGoogle Scholar
  60. 60.
    Okamoto K, Kuroda K, Miyahara H, et al. Observation of a highly spin-polarized topological surface state in GeBi2Te4. Phys Rev B. 2012;86:195304.ADSCrossRefGoogle Scholar
  61. 61.
    Eremeev SV, Landolt G, Menshchikova TV, et al. Atom-specific spin mapping and buried topological states in a homologous series of topological insulators. Nat Commun. 2012;3:635.ADSCrossRefGoogle Scholar
  62. 62.
    Valla T, Ji H, Schoop LM, et al. Topological semimetal in a Bi-Bi2Se3 infinitely adaptive superlattice phase. Phys Rev B. 2012;86:241101.ADSCrossRefGoogle Scholar
  63. 63.
    Nakayama K, Eto K, Tanaka Y, et al. Manipulation of topological states and the bulk band gap using natural heterostructures of a topological insulator. Phys Rev Lett. 2012;109:236804.ADSCrossRefGoogle Scholar
  64. 64.
    Hsieh D, Xia Y, Qian D, et al. A tunable topological insulator in the spin helical Dirac transport regime. Nature. 2009;460:1101–5.ADSCrossRefGoogle Scholar
  65. 65.
    Zhang Y, He K, Chang C-Z, et al. Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit. Nat Phys. 2010;6:584–8.CrossRefGoogle Scholar
  66. 66.
    Cheng P, Song C, Zhang T, et al. Landau quantization of topological surface states in Bi2Se3. Phys Rev Lett. 2010;105:076801.ADSCrossRefGoogle Scholar
  67. 67.
    Hanaguri T, Igarashi K, Kawamura M, et al. Momentum-resolved Landau-level spectroscopy of Dirac surface state in Bi2Se3. Phys Rev B. 2010;82:081305.ADSCrossRefGoogle Scholar
  68. 68.
    Checkelsky JG, Hor YS, Liu MH, et al. Quantum interference in macroscopic crystals of nonmetallic Bi2Se3. Phys Rev Lett. 2009;103:246601.ADSCrossRefGoogle Scholar
  69. 69.
    Analytis JG, McDonald RD, Riggs SC, et al. Two-dimensional surface state in the quantum limit of a topological insulator. Nat Phys. 2010;6:960–4.CrossRefGoogle Scholar
  70. 70.
    Xiong J, Petersen AC, Qu D, et al. Quantum oscillations in a topological insulator Bi2Te2Se with large bulk resistivity (6 Ω cm). Physica E. 2012;44:917–20.ADSCrossRefGoogle Scholar
  71. 71.
    Zhang Y, Tan Y-W, Stormer HL, et al. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature. 2005;438:201–4.ADSCrossRefGoogle Scholar
  72. 72.
    Xiong J, Khoo Y, Jia S, et al. Tuning the quantum oscillations of surface Dirac electrons in the topological insulator Bi2Te2Se by liquid gating. Phys Rev B. 2013;88:035128.ADSCrossRefGoogle Scholar
  73. 73.
    Peng H, Lai K, Kong D, et al. Aharonov-Bohm interference in topological insulator nanoribbons. Nat Mater. 2010;9:225–9.ADSGoogle Scholar
  74. 74.
    Hong SS, Zhang Y, Cha JJ, et al. One-dimensional helical transport in topological insulator nanowire interferometers. Nano Lett. 2014;14:2815–21.ADSCrossRefGoogle Scholar
  75. 75.
    Chen J, Qin HJ, Yang F, et al. Gate-voltage control of chemical potential and weak antilocalization in Bi2Se3. Phys Rev Lett. 2010;105:176602.ADSCrossRefGoogle Scholar
  76. 76.
    Checkelsky JG, Hor YS, Cava RJ, et al. Bulk band gap and surface state conduction observed in voltage-tuned crystals of the topological insulator Bi2Se3. Phys Rev Lett. 2011;106:196801.ADSCrossRefGoogle Scholar
  77. 77.
    Bardarson JH, Brouwer PW, Moore JE. Aharonov-Bohm oscillations in disordered topological insulator nanowires. Phys Rev Lett. 2010;105:156803.ADSCrossRefGoogle Scholar
  78. 78.
    Zhang Y, Vishwanath A. Anomalous Aharonov-Bohm conductance oscillations from topological insulator surface states. Phys Rev Lett. 2010;105:206601.ADSCrossRefGoogle Scholar
  79. 79.
    Checkelsky JG, Ye J, Onose Y, et al. Dirac-fermion-mediated ferromagnetism in a topological insulator. Nat Phys. 2012;8:729–33.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Tsinghua UniversityBeijingChina

Personalised recommendations