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Third-order nonlinear Hall effect induced by the Berry-connection polarizability tensor

Nature Nanotechnology volume 16, pages 869–873 (2021)Cite this article

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Abstract

Nonlinear responses in transport measurements are linked to material properties not accessible at linear order1 because they follow distinct symmetry requirements2,3,4,5. While the linear Hall effect indicates time-reversal symmetry breaking, the second-order nonlinear Hall effect typically requires broken inversion symmetry1. Recent experiments on ultrathin WTe2 demonstrated this connection between crystal structure and nonlinear response6,7. The observed second-order nonlinear Hall effect can probe the Berry curvature dipole, a band geometric property, in non-magnetic materials, just like the anomalous Hall effect probes the Berry curvature in magnetic materials8,9. Theory predicts that another intrinsic band geometric property, the Berry-connection polarizability tensor10, gives rise to higher-order signals, but it has not been probed experimentally. Here, we report a third-order nonlinear Hall effect in thick Td-MoTe2 samples. The third-order signal is found to be the dominant response over both the linear- and second-order ones. Angle-resolved measurements reveal that this feature results from crystal symmetry constraints. Temperature-dependent measurement shows that the third-order Hall response agrees with the Berry-connection polarizability contribution evaluated by first-principles calculations. The third-order nonlinear Hall effect provides a valuable probe for intriguing material properties that are not accessible at lower orders and may be employed for high-order-response electronic devices.

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Fig. 1: Illustration of the BPT.
Fig. 2: Lattice structure, device configuration and nonlinear Hall effect of Td-MoTe2 at 5 K.
Fig. 3: Angle-dependence properties of Td-MoTe2 at 5 K.
Fig. 4: Temperature-dependence measurement and first-principles results for the BPT.

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Data availability

The data supporting the findings of this study are available within the paper and the Supplementary Information. Other relevant data are available from the corresponding authors upon request. Source data are provided with this paper.

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Acknowledgements

We acknowledge financial support from the Singapore National Research Foundation through its Competitive Research Program (CRP award numbers NRF-CRP21-2018-0007, NRF-CRP22-2019-0004 and NRF-CRP23-2019-0002), the Singapore Ministry of Education (grant number MOE2016-T3-1-006 (S)) and the A*Star QTE programme.

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Authors and Affiliations

  1. Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Shen Lai, Zhaowei Zhang, Naizhou Wang, Chaolong Tang, Yuanda Liu & Wei-bo Gao

  2. Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore, Singapore

    Huiying Liu, Jianzhou Zhao, Xiaolong Feng & Shengyuan A. Yang

  3. Department of Material Science & Engineering, National University of Singapore, Singapore, Singapore

    K. S. Novoselov

  4. The Photonics Institute and Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore, Singapore

    Wei-bo Gao

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  1. Shen Lai
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Contributions

S.L. and W.G. conceived the project and designed the experiments. S.L. and Z.Z. constructed the measurement set-up and performed the transport experiments. H.L., J.Z., X.F. and S.A.Y. built the theoretical simulation model. N.W., C.T. and Y.L. conducted materials characterization and plasma etching experiments. K.S.N., S.A.Y. and W.G. supervised the project. All authors contributed extensively to the final manuscript.

Corresponding authors

Correspondence to K. S. Novoselov, Shengyuan A. Yang or Wei-bo Gao.

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The authors declare no competing interests.

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Peer review information Nature Nanotechnology thanks Su-Yang Xu, Binghai Yan and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

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Supplementary Figs. 1–22 and Discussion.

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Lai, S., Liu, H., Zhang, Z. et al. Third-order nonlinear Hall effect induced by the Berry-connection polarizability tensor. Nat. Nanotechnol. 16, 869–873 (2021). https://doi.org/10.1038/s41565-021-00917-0

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