Three-dimensional quantum Hall effect and metal–insulator transition in ZrTe5

Abstract

The discovery of the quantum Hall effect (QHE)1,2 in two-dimensional electronic systems has given topology a central role in condensed matter physics. Although the possibility of generalizing the QHE to three-dimensional (3D) electronic systems3,4 was proposed decades ago, it has not been demonstrated experimentally. Here we report the experimental realization of the 3D QHE in bulk zirconium pentatelluride (ZrTe5) crystals. We perform low-temperature electric-transport measurements on bulk ZrTe5 crystals under a magnetic field and achieve the extreme quantum limit, where only the lowest Landau level is occupied, at relatively low magnetic fields. In this regime, we observe a dissipationless longitudinal resistivity close to zero, accompanied by a well-developed Hall resistivity plateau proportional to half of the Fermi wavelength along the field direction. This response is the signature of the 3D QHE and strongly suggests a Fermi surface instability driven by enhanced interaction effects in the extreme quantum limit. By further increasing the magnetic field, both the longitudinal and Hall resistivity increase considerably and display a metal–insulator transition, which represents another magnetic-field-driven quantum phase transition. Our findings provide experimental evidence of the 3D QHE and a promising platform for further exploration of exotic quantum phases and transitions in 3D systems.

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Fig. 1: Temperature dependence of transport properties.
Fig. 2: Topology and morphology of the Fermi surface in ZrTe5.
Fig. 3: 3D QHE and transport signatures of edge states.
Fig. 4: Metal–insulator transition and phase diagrams.

Data availability

The data that support the findings of this study are available from the corresponding author on request.

References

  1. 1.

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

    ADS  Article  Google Scholar 

  2. 2.

    Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982).

    ADS  CAS  Article  Google Scholar 

  3. 3.

    Halperin, B. I. Possible states for a three-dimensional electron gas in a strong magnetic field. Jpn. J. Appl. Phys. 26, 1913–1919 (1987).

    CAS  Article  Google Scholar 

  4. 4.

    Kohmoto, M., Halperin, B. I. & Wu, Y.-S. Diophantine equation for the three-dimensional quantum Hall effect. Phys. Rev. B 45, 13488–13493 (1992).

    CAS  Article  Google Scholar 

  5. 5.

    Bernevig, A., Hughes, T., Raghu, S. & Arovas, D. Theory of the three-dimensional quantum Hall effect in graphite. Phys. Rev. Lett. 99, 146804 (2007).

    ADS  Article  Google Scholar 

  6. 6.

    Störmer, H. L., Eisenstein, J. P., Gossard, A. C., Wiegmann, W. & Baldwin, K. Quantization of the Hall effect in an anisotropic three-dimensional electronic system. Phys. Rev. Lett. 56, 85–88 (1986).

    ADS  Article  Google Scholar 

  7. 7.

    Hannahs, S. T., Brooks, J. S., Kang, W., Chiang, L. Y. & Chaikin, P. M. Quantum Hall effect in a bulk crystal. Phys. Rev. Lett. 63, 1988–1991 (1989).

    ADS  CAS  Article  Google Scholar 

  8. 8.

    Cooper, J. R. K., Auban, W., Montambaux, P. & Jérome, G. D. & Bechgaard, K. Quantized Hall effect and a new field-induced phase transition in the organic superconductor (TMTSF)2(PF)6. Phys. Rev. Lett. 63, 1984–1987 (1989).

    ADS  CAS  Article  Google Scholar 

  9. 9.

    Hill, S. et al. Bulk quantum Hall effect in η–Mo4O11. Phys. Rev. B 58, 10778–10783 (1998).

    ADS  CAS  Article  Google Scholar 

  10. 10.

    Cao, H. et al. Quantized Hall effect and Shubnikov–de Haas oscillations in highly doped Bi2Se3: evidence for layered transport of bulk carriers. Phys. Rev. Lett. 108, 216803 (2012).

    ADS  Article  Google Scholar 

  11. 11.

    Masuda, H. et al. Quantum Hall effect in a bulk antiferromagnet EuMnBi2 with magnetically confined two-dimensional Dirac fermions. Sci. Adv. 2, e1501117 (2016).

    ADS  Article  Google Scholar 

  12. 12.

    Weng, H., Dai, X. & Fang, Z. Transition-metal pentatelluride ZrTe5 and HfTe5: a paradigm for large-gap quantum spin Hall insulators. Phys. Rev. X 4, 011002 (2014).

    Google Scholar 

  13. 13.

    Jones, T. E., Fuller, W. W., Wieting, T. J. & Levy, F. Thermoelectric power of HfTe5 and ZrTe5. Solid State Commun. 42, 793–798 (1982).

    ADS  CAS  Article  Google Scholar 

  14. 14.

    Li, Q. et al. Chiral magnetic effect in ZrTe5. Nat. Phys. 12, 550–554 (2016).

    Article  Google Scholar 

  15. 15.

    Liang, T. et al. Anomalous Hall effect in ZrTe5. Nat. Phys. 14, 451–455 (2018).

    CAS  Article  Google Scholar 

  16. 16.

    Liu, Y. et al. Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5. Nat. Commun. 7, 12516 (2016).

    ADS  CAS  Article  Google Scholar 

  17. 17.

    Zheng, G. et al. Transport evidence for the three-dimensional Dirac semimetal phase in ZrTe5. Phys. Rev. B 93, 115414 (2016).

    ADS  Article  Google Scholar 

  18. 18.

    Zhang, Y. et al. Electronic evidence of temperature-induced Lifshitz transition and topological nature in ZrTe5. Nat. Commun. 8, 15512 (2017).

    ADS  CAS  Article  Google Scholar 

  19. 19.

    Bardasis, A. & Das Sarma, S. Peierls instability in degenerate semiconductors under strong external magnetic fields. Phys. Rev. B 29, 780–784 (1984).

    ADS  CAS  Article  Google Scholar 

  20. 20.

    MacDonald, A. & Bryant, G. Strong-magnetic-field states of the pure electron plasma. Phys. Rev. Lett. 58, 515–518 (1987).

    ADS  CAS  Article  Google Scholar 

  21. 21.

    Chen, R. Y. et al. Magnetoinfrared spectroscopy of Landau levels and Zeeman splitting of three-dimensional massless Dirac fermions in ZrTe5. Phys. Rev. Lett. 115, 176404 (2015).

    ADS  CAS  Article  Google Scholar 

  22. 22.

    Wilson, J. A., Di Salvo, F. J. & Mahajan, S. Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides. Adv. Phys. 24, 117 (1975).

    ADS  CAS  Article  Google Scholar 

  23. 23.

    McMillan, W. L. Theory of discommensurations and the commensurate–incommensurate charge-density-wave phase transition. Phys. Rev. B 14, 1496 (1976).

    ADS  CAS  Article  Google Scholar 

  24. 24.

    Lee, P. A. & Rice, T. M. Electric field depinning of charge density waves. Phys. Rev. B 19, 3970 (1979).

    ADS  CAS  Article  Google Scholar 

  25. 25.

    Monçeau, P., Ong, N. P., Portis, A. M., Meerschaut, A. & Rouxel, J. Electric field breakdown of charge-density-wave–induced anomalies in NbSe3. Phys. Rev. Lett. 37, 602 (1976).

    ADS  Article  Google Scholar 

  26. 26.

    Andrei, E. et al. Observation of a magnetically induced Wigner solid. Phys. Rev. Lett. 60, 2765–2768 (1988).

    ADS  CAS  Article  Google Scholar 

  27. 27.

    Zhang, C., Du, R.-R., Manfra, M. J., Pfeiffer, L. N. & West, K. W. Transport of a sliding Wigner crystal in the four flux composite fermion regime. Phys. Rev. B 92, 075434 (2015).

    ADS  Article  Google Scholar 

  28. 28.

    Yang, K., Haldane, F. D. M. & Rezayi, E. H. Wigner crystals in the lowest Landau level at low-filling factors. Phys. Rev. B 64, 081301 (2001).

    ADS  Article  Google Scholar 

  29. 29.

    Field, S. B., Reich, D. H., Rosenbaum, T. F., Littlewood, P. B. & Nelson, D. A. Electron correlation and disorder in Hg1−xCdxTe in a magnetic field. Phys. Rev. B 38, 1856–1864 (1988).

    ADS  CAS  Article  Google Scholar 

  30. 30.

    Shayegan, M., Goldman, V. J. & Drew, H. D. Magnetic-field-induced localization in narrow-gap semiconductors Hg1−xCdxTe and InSb. Phys. Rev. B 38, 5585–5602 (1988).

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank J. Mei, L. Fu, X. Dai, X. Wang, K. T. Law, D. Yu, F. Zhang, J. Wu and D. L. Deng for valuable discussions. This work was supported by the Guangdong Innovative and Entrepreneurial Research Team Program (2016ZT06D348), NNSFC (11874193), the Shenzhen Fundamental Subject Research Program (JCYJ20170817110751776) and the Innovation Commission of Shenzhen Municipality (KQTD2016022619565991). F.T. thanks the Department of Physics, Renmin University of China for visiting student support. Work at the University of Science and Technology of China, was supported by the National Key R&D Program of China (2016YFA0301700), NNSFC (11474265) and Anhui Initiative in Quantum Information Technologies (AHY170000). Work at Brookhaven is supported by the Office of Basic Energy Sciences, US Department of Energy under contract number DE-SC0012704. The work of K.Y. is supported by National Science Foundation grants DMR-1442366 and DMR-1644779. P.A.L. acknowledges support by the US Department of Energy Basic Energy Sciences grant DE-FG02-03-ER46076. S.A.Y. is supported by the Singapore Ministry of Education AcRF Tier 2 (MOE2015-T2-2-144).

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Nature thanks Alberto Crepaldi, Itamar Kimchi and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Contributions

F.T. and P.W. carried out the transport measurements. J.S., R.Z. and G.G. prepared the samples. Y.R., S.A.Y., K.Y. and P.A.L. performed the theoretical analysis. Z.Q. and L.Z. designed and supervised the work. All authors contributed to the interpretation and analysis of the data and the writing of the manuscript.

Corresponding authors

Correspondence to Shengyuan A. Yang or Zhenhua Qiao or Liyuan Zhang.

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Extended data figures and tables

Extended Data Fig. 1 3D QHE in different samples and temperature dependence of Hall resistivity.

ac, 3D QHE results for ZrTe5 samples 1 (a), 2 (b) and 4 (c) at T = 1.5 K. d, Hall resistivity of sample 2 at different temperatures ranging from 0.6 K to 20 K. Neighbouring curves are shifted by 5 mΩ cm for clarity.

Extended Data Fig. 2 Angular dependence of Hall resistivity.

ad, The dependence of the Hall resistivity on angle β (a, c) and angle α (b, d) is shown for ZrTe5 samples 1 (a), 4 (b), 2 (c) and 2 (d).

Extended Data Fig. 3 Signatures of 3D fractional QHE.

a, dρxy/dB and −d2ρxx/dB2 and versus 1/B at angles β = 0°, 15°, 30°, 60°. The vertical dashed lines indicate the N = 1/3, 1, 2, 3, 4, 5 Landau indices. b, Zoom-in of the extreme-quantum-limit region 0 < N < 1. The N = 1/3 peak can be observed. c, dρxy/dB versus 1/B at temperatures ranging from 1.5 K to 15 K.

Extended Data Fig. 4 In-plane measurements and quantum oscillations.

Measurement of SdH oscillations in ZrTe5 (sample 4) when a magnetic field is applied in the y direction. ad, Coherent transport of ρxx (a, c) and ρzz (b, d). a, b, Schematic illustration of the setup with B//y and I//x (a) and with B//y and I//z (b). c, Longitudinal resistivity ρxx and Hall resistivity ρzx measured in the xz plane, with magnetic field B//y and current I//x. c, d, ρxx and ρzz show similar oscillation patterns. Inset, zoom-in view of ρzz versus B. However, in zero magnetic field, the resistivity ρzz is about 30 times larger than ρxx.

Extended Data Table 1 Charge-transport parameters
Extended Data Table 2 Fermi wavelength λF,z and CDW period λQ for different samples

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Tables 1 and 2, Supplementary Figures 1-22 and Supplementary References – see Contents page for details.

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Tang, F., Ren, Y., Wang, P. et al. Three-dimensional quantum Hall effect and metal–insulator transition in ZrTe5. Nature 569, 537–541 (2019). https://doi.org/10.1038/s41586-019-1180-9

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