Letter | Published:

A topological Dirac insulator in a quantum spin Hall phase

Nature volume 452, pages 970974 (24 April 2008) | Download Citation

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Abstract

When electrons are subject to a large external magnetic field, the conventional charge quantum Hall effect1,2 dictates that an electronic excitation gap is generated in the sample bulk, but metallic conduction is permitted at the boundary. Recent theoretical models suggest that certain bulk insulators with large spin–orbit interactions may also naturally support conducting topological boundary states in the quantum limit3,4,5, which opens up the possibility for studying unusual quantum Hall-like phenomena in zero external magnetic fields6. Bulk Bi1-xSbx single crystals are predicted to be prime candidates7,8 for one such unusual Hall phase of matter known as the topological insulator9,10,11. The hallmark of a topological insulator is the existence of metallic surface states that are higher-dimensional analogues of the edge states that characterize a quantum spin Hall insulator3,4,5,6,7,8,9,10,11,12,13. In addition to its interesting boundary states, the bulk of Bi1-xSbx is predicted to exhibit three-dimensional Dirac particles14,15,16,17, another topic of heightened current interest following the new findings in two-dimensional graphene18,19,20 and charge quantum Hall fractionalization observed in pure bismuth21. However, despite numerous transport and magnetic measurements on the Bi1-xSbx family since the 1960s17, no direct evidence of either topological Hall states or bulk Dirac particles has been found. Here, using incident-photon-energy-modulated angle-resolved photoemission spectroscopy (IPEM-ARPES), we report the direct observation of massive Dirac particles in the bulk of Bi0.9Sb0.1, locate the Kramers points at the sample’s boundary and provide a comprehensive mapping of the Dirac insulator’s gapless surface electron bands. These findings taken together suggest that the observed surface state on the boundary of the bulk insulator is a realization of the ‘topological metal’9,10,11. They also suggest that this material has potential application in developing next-generation quantum computing devices that may incorporate ‘light-like’ bulk carriers and spin-textured surface currents.

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References

  1. 1.

    , & New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980)

  2. 2.

    , & Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982)

  3. 3.

    & Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005)

  4. 4.

    & Quantum spin Hall effect. Phys. Rev. Lett. 96, 106802 (2006)

  5. 5.

    , , & Quantum spin-Hall effect and topological Chern numbers. Phys. Rev. Lett. 97, 036808 (2006)

  6. 6.

    Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the ‘parity anomaly’. Phys. Rev. Lett. 61, 2015–2018 (1988)

  7. 7.

    & Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007)

  8. 8.

    Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase. New J. Phys. 9, 356 (2007)

  9. 9.

    , & Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007)

  10. 10.

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

  11. 11.

    Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect. 〈〉 (2006)

  12. 12.

    , & Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006)

  13. 13.

    et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007)

  14. 14.

    Matrix elements and selection rules for the two-band model of bismuth. J. Phys. Chem. Solids 25, 1057–1068 (1964)

  15. 15.

    & Interband effects of magnetic susceptibility. II. Diamagnetism of bismuth. J. Phys. Soc. Jpn 28, 570–581 (1970)

  16. 16.

    Weyl transformation and the magnetic susceptibility of a relativistic Dirac electron gas. Phys. Rev. A 8, 1570–1581 (1973)

  17. 17.

    et al. in Fifteenth International Conference on Thermoelectrics (Pasadena, California) 1–13 (IEEE, New York, 1996)

  18. 18.

    , , & Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 438, 201–204 (2005)

  19. 19.

    et al. Room-temperature quantum Hall effect in graphene. Science 315, 1379 (2007)

  20. 20.

    et al. Substrate-induced bandgap opening in epitaxial graphene. Nature Mater. 6, 770–775 (2007)

  21. 21.

    , & Signatures of electron fractionalization in ultraquantum bismuth. Science 317, 1729–1731 (2007)

  22. 22.

    & Electronic structure of semimetals Bi and Sb. Phys. Rev. B 52, 1566–1577 (1995)

  23. 23.

    & Interband transitions and band structure of a BiSb alloy. Phys. Lett. 10, 273–275 (1964)

  24. 24.

    & Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005)

  25. 25.

    & Fermi surface of Bi(111) measured by photoemission spectroscopy. Phys. Rev. Lett. 87, 177602 (2001)

  26. 26.

    & Lack of electron-phonon coupling along two-dimensional bands in Bi1 - xSbx single crystal alloys. J. Elect. Spectrosc. Relat. Phenom. 144, 351–355 (2005)

  27. 27.

    The surfaces of bismuth: Structural and electronic properties. Prog. Surf. Sci. 81, 191–245 (2006)

  28. 28.

    et al. Direct observation of spin splitting in bismuth surface states. Phys. Rev. B 76, 153305 (2007)

  29. 29.

    et al. Photoemission study of the carrier bands in Bi(111). Eur. Phys. J. B 17, 603–608 (2000)

  30. 30.

    & Electronic structure of a bismuth bilayer. Phys. Rev. B 67, 113102 (2003)

  31. 31.

    et al. Universal magnetic-field-driven metal-insulator-metal transformations in graphite and bismuth. Phys. Rev. B 73, 165128 (2006)

  32. 32.

    Photoelectron Spectroscopy (Springer, Berlin, 1995)

  33. 33.

    et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005)

  34. 34.

    , , , & Quasiparticle dynamics in graphene. Nature Phys. 3, 36–40 (2007)

  35. 35.

    , & Experimental band structure of semimetal bismuth. Phys. Rev. B 56, 6620–6626 (1997)

  36. 36.

    & High-resolution mapping of the three-dimensional band structure of Bi(111). Phys. Rev. B 70, 245122 (2004)

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Acknowledgements

We thank P. W. Anderson, B. A. Bernevig, L. Balents, E. Demler, A. Fedorov, F. D. M. Haldane, D. A. Huse, C. L. Kane, R. B. Laughlin, J. E. Moore, N. P. Ong, A. N. Pasupathy, D. C. Tsui and S.-C. Zhang for discussions. The synchrotron experiments are supported by the DOE-BES and materials synthesis is supported by the NSF-MRSEC at Princeton Center for Complex Materials.

Author information

Affiliations

  1. Joseph Henry Laboratories of Physics, Department of Physics,

    • D. Hsieh
    • , D. Qian
    • , L. Wray
    • , Y. Xia
    •  & M. Z. Hasan
  2. Department of Chemistry,

    • Y. S. Hor
    •  & R. J. Cava
  3. Princeton Center for Complex Materials, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA

    • M. Z. Hasan

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Correspondence to M. Z. Hasan.

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  1. 1.

    This file contains Supplementary Methods, Supplementary Notes, Supplementary Figures S1-S4 with Legends and additional references.

    The Supplementary Information (SI) describes our method of comparing experimentally measured deeper lying bands of Bi0.9Sb0.1 with theoretical calculations of bulk Bi as further evidence of their bulk origin, and as an alternate way of extracting the kz values from ARPES measurements. The SI also provides further theoretical justification that spin-orbit coupling is essential to account for the 3D bulk Dirac point, and provides further experimental evidence for an odd number of surface state Fermi crossings.

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https://doi.org/10.1038/nature06843

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