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A topological Dirac insulator in a quantum spin Hall phase

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-xSb x 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-xSb x 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-xSb x 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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Figure 1: Dirac-like dispersion near the L-point in the bulk Brillouin zone.
Figure 2: Dispersion along the cut in the k z -direction.
Figure 3: The topological gapless surface states in bulk insulating Bi0.9Sb0.1.

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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.

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Correspondence to M. Z. Hasan.

Supplementary information

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. (PDF 503 kb)

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Hsieh, D., Qian, D., Wray, L. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008). https://doi.org/10.1038/nature06843

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