Spintronics of Topological Insulators

  • Kang L. WangEmail author
  • Murong Lang
  • Xufeng Kou


Topological insulators (TIs) are an emerging group of materials with new states of quantum matter. Owing to a nontrivial band topology and strong spin–orbit coupling, gapless Dirac surface states protected by time-reversal symmetry are formed, and surface conductions exhibit unusual spin-momentum locking features. As a result, TIs are regarded as one of the most intriguing 2D materials, which arises broad interest among condensed matter physics, material science, nanoelectronics, spintronics, and energy harvesting applications. In this chapter, several important concepts that preceded the discovery of TIs have been discussed, and the roadmap of the topological-bonded quantum Hall trio has been outlined. In addition, an overview has been provided on the progress with regard to the realization of the quantum spin Hall effect in 2D CdTe/HgTe quantum wells, the extension of TIs into the 3D regime, and the experimental approaches to manipulate the surface states via both the surface-sensitive spectroscopy and electrical detections.


Topological Insulator Dirac Point Reflection High Energy Electron Diffraction Berry Phase Scanning Tunneling Spectroscopy 
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.

List of Abbreviations


Angle-resolved photoemission spectroscopy


Density of states


Full width at half maximum




Integer quantum Hall effect


Landau level




Quantum anomalous Hall effect


Quantum Hall effect


Quintuple layers


Quantum spin Hall


Shubnikov–de Haas


Spin–orbit coupling


Surface states


Scanning tunneling microscopy


Scanning tunneling spectroscopy


Topological insulator


Thouless, Kohmoto, Nightingale, and den Nijs


Time-reversal symmetry


Vapor–liquid–solid method


Weak antilocalization


Weak localization


  1. 1.
    Qi X-L, Zhang S-C (2011) Topological insulators and superconductors. Rev Mod Phys 83:1057–1110CrossRefADSGoogle Scholar
  2. 2.
    Moore JE (2010) The birth of topological insulators. Nature 464:194–198CrossRefADSGoogle Scholar
  3. 3.
    Hasan MZ, Kane CL (2010) Colloquium: topological insulators. Rev Mod Phys 82:3045CrossRefADSGoogle Scholar
  4. 4.
    Zhang Y et al (2010) Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit. Nat Phys 6:584–588CrossRefGoogle Scholar
  5. 5.
    Zhang T et al (2009) Experimental demonstration of topological surface states protected by time-reversal symmetry. Phys Rev Lett 103:266803CrossRefADSGoogle Scholar
  6. 6.
    Qi X-L, Hughes TL, Zhang S-C (2008) Topological field theory of time-reversal invariant insulators. Phys Rev B 78:195424CrossRefADSGoogle Scholar
  7. 7.
    Zhang H et al (2009) Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nat Phys 5:438–442CrossRefGoogle Scholar
  8. 8.
    Kane CL, Mele EJ (2005) Z2 topological order and the quantum spin hall effect. Phys Rev Lett 95:146802CrossRefADSGoogle Scholar
  9. 9.
    Moore JE, Balents L (2007) Topological invariants of time-reversal-invariant band structures. Phys Rev B 75:121306CrossRefADSGoogle Scholar
  10. 10.
    Ando T, Matsumoto Y, Uemura Y (1975) Theory of Hall effect in a two-dimensional electron system. J Physical Soc Japan 39:279–288CrossRefADSGoogle Scholar
  11. 11.
    Klitzing KV, Dorda G, Pepper M (1980) New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys Rev Lett 45:494–497CrossRefADSGoogle Scholar
  12. 12.
    Roth LM (1966) Semiclassical theory of magnetic energy levels and magnetic susceptibility of Bloch electrons. Phys Rev 145:434CrossRefADSGoogle Scholar
  13. 13.
    Laughlin RB (1981) Quantized Hall conductivity in two dimensions. Phys Rev B 23:5632–5633CrossRefADSGoogle Scholar
  14. 14.
    Stormer HL (1999) Nobel Lecture: the fractional quantum Hall effect. Rev Mod Phys 71:875–889MathSciNetCrossRefADSzbMATHGoogle Scholar
  15. 15.
    Novoselov KS et al (2007) Room-temperature quantum Hall effect in graphene. Science 315:1379CrossRefADSGoogle Scholar
  16. 16.
    Thouless DJ, Kohmoto M, Nightingale MP, den Nijs M (1982) Quantized Hall conductance in a two-dimensional periodic potential. Phys Rev Lett 49:405–408CrossRefADSGoogle Scholar
  17. 17.
    König M et al (2007) Quantum spin Hall insulator state in HgTe quantum wells. Science 318:766–770CrossRefADSGoogle Scholar
  18. 18.
    Qi X-L, Zhang S-C (2010) The quantum spin Hall effect and topological insulators. Phys Today 63:33–38CrossRefADSGoogle Scholar
  19. 19.
    Bernevig BA, Hughes TL, Zhang S-C (2006) Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314:1757–1761CrossRefADSGoogle Scholar
  20. 20.
    Bernevig BA, Zhang S-C (2006) Quantum spin Hall effect. Phys Rev Lett 96:106802CrossRefADSGoogle Scholar
  21. 21.
    Berry MV (1984) Quantal phase factors accompanying adiabatic changes. Proc R Soc Lond A Math Phys Sci 392:45–57CrossRefADSzbMATHGoogle Scholar
  22. 22.
    Ando T, Nakanishi T, Saito R (1998) Berry’s phase and absence of back scattering in carbon nanotubes. J Physical Soc Japan 67:2857–2862CrossRefADSGoogle Scholar
  23. 23.
    Kane CL, Mele EJ (2005) Quantum spin Hall effect in graphene. Phys Rev Lett 95:226801CrossRefADSGoogle Scholar
  24. 24.
    Du LJ, Knez I, Sullivan G, Du RR (2015) Robust helical edge transport in gated InAs/GaSb bilayers. Phys Rev Lett 114:096802CrossRefADSGoogle Scholar
  25. 25.
    Xu Y et al (2013) Large-gap quantum spin Hall insulators in tin films. Phys Rev Lett 111:136804CrossRefADSGoogle Scholar
  26. 26.
    Yu R et al (2010) Quantized anomalous Hall effect in magnetic topological insulators. Science 329:61–64CrossRefADSGoogle Scholar
  27. 27.
    He K, Wang Y, Xue Q-K (2013) Quantum anomalous Hall effect. Natl Sci Rev 1:38–48CrossRefGoogle Scholar
  28. 28.
    Liu C-X, Qi X-L, Dai X, Fang Z, Zhang S-C (2008) Quantum anomalous Hall effect in Hg1-yMnyTe quantum wells. Phys Rev Lett 101:146802CrossRefADSGoogle Scholar
  29. 29.
    Buhmann H (2012) Towards the quantum anomalous Hall effect in HgMnTe. Bull Am Phys Soc 57Google Scholar
  30. 30.
    Chang C-Z et al (2013) Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science 340:167–170CrossRefADSGoogle Scholar
  31. 31.
    Datta S (1997) Electronic transport in mesoscopic systems. Cambridge University PressGoogle Scholar
  32. 32.
    Kou XF et al (2013) Manipulating surface-related ferromagnetism in modulation-doped topological insulators. Nano Lett 13:4587–4593CrossRefADSGoogle Scholar
  33. 33.
    Roth A et al (2009) Nonlocal transport in the quantum spin Hall state. Science 325:294–297CrossRefADSGoogle Scholar
  34. 34.
    Checkelsky JG, Ye J, Onose Y, Iwasa Y, Tokura Y (2012) Dirac-fermion-mediated ferromagnetism in a topological insulator. Nat Phys 8:729–733CrossRefGoogle Scholar
  35. 35.
    Hsieh D et al (2008) A topological Dirac insulator in a quantum spin Hall phase. Nature 452:970–974CrossRefADSGoogle Scholar
  36. 36.
    Fu L, Kane CL (2007) Topological insulators with inversion symmetry. Phys Rev B 76:045302CrossRefADSGoogle Scholar
  37. 37.
    Chen YL et al (2009) Experimental realization of a three-dimensional topological insulator, Bi2Te3. Science 325:178–181CrossRefADSGoogle Scholar
  38. 38.
    Hor YS et al (2009) p-type Bi2Se3 for topological insulator and low-temperature thermoelectric applications. Phys Rev B 79:195208Google Scholar
  39. 39.
    Hsieh D et al (2009) Observation of time-reversal-protected single-dirac-cone topological-insulator states in Bi2Te3 and Sb2Te3. Phys Rev Lett 103:146401CrossRefADSGoogle Scholar
  40. 40.
    Hsieh D et al (2009) A tunable topological insulator in the spin helical Dirac transport regime. Nature 460:1101–1105CrossRefADSGoogle Scholar
  41. 41.
    Park SR et al (2010) Quasiparticle scattering and the protected nature of the topological states in a parent topological insulator Bi2Se3. Phys Rev B 81:041405CrossRefADSGoogle Scholar
  42. 42.
    Xia Y et al (2009) Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nat Phys 5:398–402CrossRefGoogle Scholar
  43. 43.
    Alpichshev Z et al (2010) STM imaging of electronic waves on the surface of Bi2Te3: topologically protected surface states and hexagonal warping effects. Phys Rev Lett 104:016401CrossRefADSGoogle Scholar
  44. 44.
    He L et al (2011) Epitaxial growth of Bi2Se3 topological insulator thin films on Si (111). J Appl Phys 109:103702CrossRefADSGoogle Scholar
  45. 45.
    Lang M et al (2011) Revelation of topological surface states in Bi2Se3 thin films by In Situ Al passivation. ACS Nano 6:295–302CrossRefGoogle Scholar
  46. 46.
    He L et al (2012) Surface-dominated conduction in a 6 nm thick Bi2Se3 thin film. Nano Lett 12:1486–1490CrossRefADSGoogle Scholar
  47. 47.
    Yu X et al (2013) Separation of top and bottom surface conduction in Bi2Te3 thin films. Nanotechnology 24:015705CrossRefADSGoogle Scholar
  48. 48.
    Lang M et al (2012) Competing weak localization and weak antilocalization in ultrathin topological insulators. Nano Lett 13:48–53CrossRefADSGoogle Scholar
  49. 49.
    He L et al (2013) Evidence of the two surface states of (Bi0.53Sb0.47)2Te3 films grown by van der Waals epitaxy. Sci Rep 3:3406Google Scholar
  50. 50.
    Kou XF et al (2012) Magnetically doped semiconducting topological insulators. J Appl Phys 112:063912–063916CrossRefADSGoogle Scholar
  51. 51.
    Kou X et al (2013) Interplay between different magnetisms in Cr-doped topological insulators. ACS NanoGoogle Scholar
  52. 52.
    Kou XF et al (2011) Epitaxial growth of high mobility Bi2Se3 thin films on CdS. Appl Phys Lett 98:242102CrossRefADSGoogle Scholar
  53. 53.
    Lang M et al (2014) Proximity induced high-temperature magnetic order in topological insulator - ferrimagnetic insulator heterostructure. Nano Lett 14:3459–3465CrossRefADSGoogle Scholar
  54. 54.
    Wang M-X et al (2012) The coexistence of superconductivity and topological order in the Bi2Se3 thin films. ScienceGoogle Scholar
  55. 55.
    Liu M et al (2012) Crossover between weak antilocalization and weak localization in a magnetically doped topological insulator. Phys Rev Lett 108:036805CrossRefADSGoogle Scholar
  56. 56.
    Chang C-Z et al (2013) Thin films of magnetically doped topological insulator with carrier-independent long-range ferromagnetic order. Adv Mater 25:1065–1070CrossRefADSGoogle Scholar
  57. 57.
    Zhang D et al (2012) Interplay between ferromagnetism, surface states, and quantum corrections in a magnetically doped topological insulator. Phys Rev B 86:205127CrossRefADSGoogle Scholar
  58. 58.
    Richardella A et al (2010) Coherent heteroepitaxy of Bi2Se3 on GaAs (111)B. Appl Phys Lett 97:262104–262103CrossRefADSGoogle Scholar
  59. 59.
    Kandala A et al (2013) Growth and characterization of hybrid insulating ferromagnet-topological insulator heterostructure devices. Appl Phys Lett 103:202409CrossRefADSGoogle Scholar
  60. 60.
    Taskin AA, Sasaki S, Segawa K, Ando Y (2012) Manifestation of topological protection in transport properties of epitaxial Bi2Se3 thin films. Phys Rev Lett 109:066803CrossRefADSGoogle Scholar
  61. 61.
    Taskin AA, Sasaki S, Segawa K, Ando Y (2012) Achieving surface quantum oscillations in topological insulator thin films of Bi2Se3. Adv Mater 24:5581–5585CrossRefGoogle Scholar
  62. 62.
    Zhang G et al (2009) Quintuple-layer epitaxy of thin films of topological insulator Bi2Se3. Appl Phys Lett 95:053114CrossRefADSGoogle Scholar
  63. 63.
    Kim YS et al (2011) Thickness-dependent bulk properties and weak antilocalization effect in topological insulator Bi2Se3. Phys Rev B 84:073109CrossRefADSGoogle Scholar
  64. 64.
    Chen J et al (2010) Gate-voltage control of chemical potential and weak antilocalization in Bi2Se3. Phys Rev Lett 105:176602CrossRefADSGoogle Scholar
  65. 65.
    Schreyeck S et al (2013) Molecular beam epitaxy of high structural quality Bi2Se3 on lattice matched InP(111) substrates. Appl Phys Lett 102:041914CrossRefADSGoogle Scholar
  66. 66.
    Teweldebrhan D, Goyal V, Balandin AA (2010) Exfoliation and characterization of bismuth telluride atomic quintuples and quasi-two-dimensional crystals. Nano Lett 10:1209–1218CrossRefADSGoogle Scholar
  67. 67.
    Shahil KM (2010) Crystal symmetry breaking in few-quintuple Bi2Te3 films: applications in nanometrology of topological insulators. Appl Phys Lett 96:153103CrossRefADSGoogle Scholar
  68. 68.
    Kong D et al (2009) Topological insulator nanowires and nanoribbons. Nano Lett 10:329–333CrossRefADSGoogle Scholar
  69. 69.
    Cha JJ, Koski, KJ, Cui Y (2013) Topological insulator nanostructures. phys status solidi (RRL) 7:15–25Google Scholar
  70. 70.
    Hong SS, Cha JJ, Kong D, Cui Y (2012) Ultra-low carrier concentration and surface-dominant transport in antimony-doped Bi2Se3 topological insulator nanoribbons. Nat Commun 3:757CrossRefADSGoogle Scholar
  71. 71.
    Kong D et al (2011) Ambipolar field effect in the ternary topological insulator (BixSb1-x)2Te3 by composition tuning. Nat Nano 6:705–709CrossRefGoogle Scholar
  72. 72.
    Kong D et al (2010) Few-layer nanoplates of Bi2Se3 and Bi2Te3 with highly tunable chemical potential. Nano Lett 10:2245–2250CrossRefADSGoogle Scholar
  73. 73.
    McClure JW (1956) Diamagnetism of graphite. Phys Rev 104:666–671CrossRefADSGoogle Scholar
  74. 74.
    Ando Y (2013) Topological insulator materials. J Physical Soc Japan 82:102001CrossRefADSGoogle Scholar
  75. 75.
    Onsager L (1952) Interpretation of the de Haas-van Alphen effect. Philos Mag 43:1006–1008CrossRefGoogle Scholar
  76. 76.
    Butch NP et al (2010) Strong surface scattering in ultrahigh-mobility Bi2Se3 topological insulator crystals. Phys Rev B 81:241301CrossRefADSGoogle Scholar
  77. 77.
    Analytis JG et al (2010) Two-dimensional surface state in the quantum limit of a topological insulator. Nat Phys 6:960–964CrossRefGoogle Scholar
  78. 78.
    Liu M et al (2011) Electron interaction-driven insulating ground state in Bi2Se3 topological insulators in the two-dimensional limit. Phys Rev B 83:165440CrossRefADSGoogle Scholar
  79. 79.
    Steinberg H, Laloe JB, Fatemi V, Moodera JS, Jarillo-Herrero P (2011) Electrically tunable surface-to-bulk coherent coupling in topological insulator thin films. Phys Rev B 84:233101CrossRefADSGoogle Scholar
  80. 80.
    Chen J et al (2011) Tunable surface conductivity in Bi2Se3 revealed in diffusive electron transport. Phys Rev B 83:241304CrossRefADSGoogle Scholar
  81. 81.
    Xiu F et al (2011) Manipulating surface states in topological insulator nanoribbons. Nat Nanotechnol 6:216–221CrossRefADSGoogle Scholar
  82. 82.
    Ren Z, Taskin AA, Sasaki S, Segawa K, Ando Y (2010) Large bulk resistivity and surface quantum oscillations in the topological insulator Bi2Te2Se. Phys Rev B 82:241306CrossRefADSGoogle Scholar
  83. 83.
    Wang Y et al (2012) Gate-controlled surface conduction in Na-doped Bi2Te3 topological insulator nanoplates. Nano Lett 12:1170–1175CrossRefADSGoogle Scholar
  84. 84.
    Analytis JG et al (2010) Bulk Fermi surface coexistence with Dirac surface state in Bi2Se3: a comparison of photoemission and Shubnikov-de Haas measurements. Phys Rev B 81:205407CrossRefADSGoogle Scholar
  85. 85.
    Peng H et al (2010) Aharonov-Bohm interference in topological insulator nanoribbons. Nat Mater 9:225–229ADSGoogle Scholar
  86. 86.
    Hikami S, Larkin AI, Nagaoka Y (1980) Spin-orbit interaction of magnetoresistance in the two dimensional random aystem. Prog Theor Phys 63:707–710CrossRefADSGoogle Scholar
  87. 87.
    Lu H-Z, Shi J, Shen S-Q (2011) Competition between weak localization and antilocalization in topological surface states. Phys Rev Lett 107:076801CrossRefADSGoogle Scholar
  88. 88.
    Bergmann G (1984) Weak localization in thin films: a time-of-flight experiment with conduction electrons. Phys Rep 107:1–58CrossRefADSGoogle Scholar
  89. 89.
    Kou XF et al (2014) Scale-invariant quantum anomalous Hall effect in magnetic topological insulators beyond the two-dimensional limit. Phys Rev Lett 113:137201CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Electrical EngineeringUniversity of CaliforniaLos AngelesUSA
  2. 2.Engineering Electrical DepartmentUniversity of CaliforniaLos AngelesUSA

Personalised recommendations