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The birth of topological insulators

Abstract

Certain insulators have exotic metallic states on their surfaces. These states are formed by topological effects that also render the electrons travelling on such surfaces insensitive to scattering by impurities. Such topological insulators may provide new routes to generating novel phases and particles, possibly finding uses in technological applications in spintronics and quantum computing.

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Figure 1: Metallic states are born when a surface unties 'knotted' electron wavefunctions.
Figure 2: Topological order in two dimensions.
Figure 3: Signatures of the exotic metallic surface states in topological insulators.

References

  1. 1

    Haldane, F. D. M. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the 'parity anomaly'. Phys. Rev. Lett. 61, 2015–2018 (1988).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  2. 2

    Murakami, S., Nagaosa, N. & Zhang, S.-C. Spin-Hall insulator. Phys. Rev. Lett. 93, 156804 (2004).

    ADS  Article  Google Scholar 

  3. 3

    Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005). This paper explains the theoretical requirements for a non-magnetic material to be a 2D topological insulator, with a quantum spin Hall effect.

    ADS  CAS  Article  Google Scholar 

  4. 4

    Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).

    ADS  CAS  Article  Google Scholar 

  5. 5

    König, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007). This paper reports the first experimental observation of a 2D topological insulator that has a quantum spin Hall effect.

    ADS  Article  Google Scholar 

  6. 6

    Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007).

    ADS  Article  Google Scholar 

  7. 7

    Moore, J. E. & Balents, L. Topological invariants of time-reversal-invariant band structures. Phys. Rev. B 75, 121306(R) (2007).

    ADS  Article  Google Scholar 

  8. 8

    Roy, R. Topological phases and the quantum spin Hall effect in three dimensions. Phys. Rev. B 79, 195322 (2009).

    ADS  Article  Google Scholar 

  9. 9

    Ran, Y., Zhang, Y. & Vishwanath, A. One-dimensional topologically protected modes in topological insulators with lattice dislocations. Nature Phys. 5, 298–303 (2009).

    ADS  CAS  Article  Google Scholar 

  10. 10

    Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008). By using ARPES experiments, this study observed a 3D topological insulator, the theoretical predictions for which were made in refs 6,7,8.

    ADS  CAS  Article  Google Scholar 

  11. 11

    Hsieh, D. et al. Observation of unconventional quantum spin textures in topological insulators. Science 323, 919–922 (2009).

    ADS  CAS  Article  Google Scholar 

  12. 12

    Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nature Phys. 5, 398–402 (2009).

    ADS  CAS  Article  Google Scholar 

  13. 13

    Zhang, H. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nature Phys. 5, 438–442 (2009). References 12 and 13 report experiments and theory on next-generation topological insulator materials, which have a large bandgap and a single surface Dirac cone; these are the most promising materials for future experiments.

    ADS  CAS  Article  Google Scholar 

  14. 14

    Chen, Y. L. et al. Experimental realization of a three-dimensional topological insulator, Bi2Te3 . Science 325, 178–181 (2009).

    ADS  CAS  Article  Google Scholar 

  15. 15

    Castro Neto, A. H., Guinea, F., Peres, N. M., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–163 (2009).

    ADS  Article  Google Scholar 

  16. 16

    Roushan, P. et al. Topological surface states protected from backscattering by chiral spin texture. Nature 460, 1106–1109 (2009).

    ADS  CAS  Article  Google Scholar 

  17. 17

    Alpichshev, Z. et al. STM imaging of electronic waves on the surface of Bi2Te3: topologically protected surface states and hexagonal warping effects. Preprint at <http://arxiv.org/abs/0908.0371> (2009).

  18. 18

    Zhang, T. et al. Experimental demonstration of the topological surface states protected by the time-reversal symmetry. Preprint at <http://arxiv.org/abs/0908.4136> (2009).

    Book  Google Scholar 

  19. 19

    Nomura, K., Koshino, M. & Ryu, S. Topological delocalization of two-dimensional massless Dirac fermions. Phys. Rev. Lett. 99, 146806 (2007).

    ADS  Article  Google Scholar 

  20. 20

    Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958).

    ADS  CAS  Article  Google Scholar 

  21. 21

    Li, J. et al. Topological Anderson insulator. Phys. Rev. Lett. 102, 136806 (2009).

    ADS  Article  Google Scholar 

  22. 22

    Groth, C. W. et al. Theory of the topological Anderson insulator. Phys. Rev. Lett. 103, 196805 (2009).

    ADS  CAS  Article  Google Scholar 

  23. 23

    Hsieh, D. et al. A tunable topological insulator in the spin helical Dirac transport regime. Nature 460, 1101–1105 (2009).

    ADS  CAS  Article  Google Scholar 

  24. 24

    Seradjeh, B., Moore, J. E. & Franz, M. Exciton condensation and charge fractionalization in a topological insulator film. Phys. Rev. Lett. 103, 066402 (2009).

    ADS  CAS  Article  Google Scholar 

  25. 25

    Peng, H. et al. Aharonov–Bohm interference in topological insulator nanoribbons. Preprint at <http://arxiv.org/abs/0908.3314> (2009).

    Google Scholar 

  26. 26

    Zhang, Y. et al. Crossover of three-dimensional topological insulator of Bi2Se3 to the two-dimensional limit. Preprint at <http://arxiv.org/abs/0911.3706> (2009).

    Google Scholar 

  27. 27

    Garate, I. & Franz, M. Inverse spin-galvanic effect in a topological-insulator/ferromagnet interface. Preprint at <http://arxiv.org/abs/0911.0106> (2009).

    Google Scholar 

  28. 28

    Wilczek, F. Two applications of axion electrodynamics. Phys. Rev. Lett. 58, 1799–1802 (1987).

    ADS  CAS  Article  Google Scholar 

  29. 29

    Qi, X.-L., Hughes, T. L. & Zhang, S.-C. Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78, 195424 (2008).

    ADS  Article  Google Scholar 

  30. 30

    Qi, X.-L. et al. Inducing a magnetic monopole with topological surface states. Science 323, 1184–1187 (2009).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  31. 31

    Essin, A. M., Moore, J. E. & Vanderbilt, D. Magnetoelectric polarizability and axion electrodynamics in crystalline insulators. Phys. Rev. Lett. 102, 146805 (2009).

    ADS  Article  Google Scholar 

  32. 32

    Ramesh, R. & Spaldin, N. A. Multiferroics: progress and prospects. Nature Mater. 6, 21–27 (2007).

    ADS  CAS  Article  Google Scholar 

  33. 33

    Schnyder, A. P. et al. Classification of topological insulators and superconductors in three spatial dimensions. Phys. Rev. B 78, 195125 (2008).

    ADS  Article  Google Scholar 

  34. 34

    Kitaev, A. Periodic table for topological insulators and superconductors. Preprint at <http://arxiv.org/abs/0901.2686> (2009).

    Book  Google Scholar 

  35. 35

    Moore, J. E., Ran, Y. & Wen, X.-G. Topological surface states in three-dimensional magnetic insulators. Phys. Rev. Lett. 101, 186805 (2008).

    ADS  Article  Google Scholar 

  36. 36

    Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).

    ADS  Article  Google Scholar 

  37. 37

    Jackiw, R. & Rossi, P. Zero modes of the vortex-fermion system. Nucl. Phys. B 190, 681–691 (1980).

    ADS  Article  Google Scholar 

  38. 38

    Wilczek, F. Majorana returns. Nature Physics 5, 614–618 (2009).

    ADS  CAS  Article  Google Scholar 

  39. 39

    Nilsson, J., Akhmerov, A. R. & Beenakker, C. W. Splitting of a Cooper pair by a pair of Majorana bound states. Phys. Rev. Lett. 101, 120403 (2008).

    ADS  Article  Google Scholar 

  40. 40

    Collins, G. P. Computing with quantum knots. Sci. Am. 294, 57–63 (2006).

    Google Scholar 

  41. 41

    Teo, J. & Kane, C. L. Majorana fermions and non-Abelian statistics in three dimensions. Phys. Rev. Lett. 104, 046401 (2009).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

I have benefited from conversations about topological insulators with L. Balents, B. A. Bernevig, A. Essin, M. Franz, D. Haldane, Z. Hasan, C. Kane, D.-H. Lee, A. Ludwig, L. Molenkamp, S. Ryu, D. Vanderbilt, A. Vishwanath, X.-G. Wen, C. Xu and S.-C. Zhang. My work on topological insulators is supported by the US National Science Foundation.

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Moore, J. The birth of topological insulators. Nature 464, 194–198 (2010). https://doi.org/10.1038/nature08916

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