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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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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).

Reviewer information

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

Author information

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.

Competing interests

The authors declare no competing interests.

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

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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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.
Extended Data Fig. 1: 3D QHE in different samples and temperature dependence of Hall resistivity.
Extended Data Fig. 2: Angular dependence of Hall resistivity.
Extended Data Fig. 3: Signatures of 3D fractional QHE.
Extended Data Fig. 4: In-plane measurements and quantum oscillations.

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