Nonlinear anomalous Hall effect in few-layer WTe2


The Hall effect occurs only in systems with broken time-reversal symmetry, such as materials under an external magnetic field in the ordinary Hall effect and magnetic materials in the anomalous Hall effect (AHE)1. Here we show a nonlinear AHE in a non-magnetic material under zero magnetic field, in which the Hall voltage depends quadratically on the longitudinal current2,3,4,5,6. We observe the effect in few-layer Td-WTe2, a two-dimensional semimetal with broken inversion symmetry and only one mirror line in the crystal plane. Our angle-resolved electrical measurements reveal that the Hall voltage maximizes (vanishes) when the bias current is perpendicular (parallel) to the mirror line. The observed effect can be understood as an AHE induced by the bias current, which generates an out-of-plane magnetization. The temperature dependence of the Hall conductivity further suggests that both the intrinsic Berry curvature dipole and extrinsic spin-dependent scatterings contribute to the observed nonlinear AHE.

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Fig. 1: Atomic structure and basic characterization of few-layer WTe2.
Fig. 2: Nonlinear AHE.
Fig. 3: Angular dependence of the nonlinear AHE.
Fig. 4: Temperature dependence of the nonlinear AHE.

Data availability

The data supporting the plots within this paper and other findings of this study are available from the corresponding authors upon request.


  1. 1.

    Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).

    Article  Google Scholar 

  2. 2.

    Low, T., Jiang, Y. & Guinea, F. Topological currents in black phosphorus with broken inversion symmetry. Phys. Rev. B 92, 235447 (2015).

    Article  Google Scholar 

  3. 3.

    Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015).

    Article  Google Scholar 

  4. 4.

    Zhang, Y., van den Brink, J., Felser, C. & Yan, B. Electrically tuneable nonlinear anomalous Hall effect in two-dimensional transition-metal dichalcogenides WTe2 and MoTe2. 2D Mater. 5, 044001 (2018).

    Article  Google Scholar 

  5. 5.

    Shi, L.-k. & Song, J. C. W. Symmetry, spin-texture, and tunable quantum geometry in a WTe2 monolayer. Phys. Rev. B 99, 035403 (2019).

    Article  Google Scholar 

  6. 6.

    You, J.-S., Fang, S., Xu, S.-Y., Kaxiras, E. & Low, T. Berry curvature dipole current in the transition metal dichalcogenides family. Phys. Rev. B 98, 121109 (2018).

    Article  Google Scholar 

  7. 7.

    Landau, L. D., Lifshitz, E. M. & Pitaevskii, L. P. Statistical Physics (Pergamon, Oxford, 1999).

    Google Scholar 

  8. 8.

    Shen, Y. R. The Principles of Nonlinear Optics (Wiley, Hoboken, 2002).

  9. 9.

    Brown, B. E. The crystal structures of WTe2 and high-temperature MoTe2. Acta Crystallogr. 20, 268–274 (1966).

    CAS  Article  Google Scholar 

  10. 10.

    Song, Q. et al. The in-plane anisotropy of WTe2 investigated by angle-dependent and polarized Raman spectroscopy. Sci. Rep. 6, 29254 (2016).

    Article  Google Scholar 

  11. 11.

    Ali, M. N. et al. Large, non-saturating magnetoresistance in WTe2. Nature 514, 205–208 (2014).

    CAS  Article  Google Scholar 

  12. 12.

    Soluyanov, A. A. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015).

    CAS  Article  Google Scholar 

  13. 13.

    Wang, Y. et al. Gate-tunable negative longitudinal magnetoresistance in the predicted type-II Weyl semimetal WTe2. Nat. Commun. 7, 13142 (2016).

    CAS  Article  Google Scholar 

  14. 14.

    Fatemi, V. et al. Magnetoresistance and quantum oscillations of an electrostatically tuned semimetal-to-metal transition in ultrathin WTe2. Phys. Rev. B 95, 041410 (2017).

    Article  Google Scholar 

  15. 15.

    Qian, X., Liu, J., Fu, L. & Li, J. Quantum spin Hall effect in two-dimensional transition metal dichalcogenides. Science 346, 1344–1347 (2014).

    CAS  Article  Google Scholar 

  16. 16.

    Tang, S. et al. Quantum spin Hall state in monolayer 1Tʹ-WTe2. Nat. Phys. 13, 683–687 (2017).

    CAS  Article  Google Scholar 

  17. 17.

    Fei, Z. et al. Edge conduction in monolayer WTe2.Nat. Phys. 13, 677–682 (2017).

    CAS  Article  Google Scholar 

  18. 18.

    Wu, S. et al. Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal. Science 359, 76–79 (2018).

    CAS  Article  Google Scholar 

  19. 19.

    Fei, Z. et al. Ferroelectric switching of a two-dimensional metal. Nature 560, 336–339 (2018).

    CAS  Article  Google Scholar 

  20. 20.

    Sajadi, E. et al. Gate-induced superconductivity in a monolayer topological insulator. Science 362, 922–925 (2018).

    CAS  Article  Google Scholar 

  21. 21.

    Fatemi, V. et al. Electrically tunable low density superconductivity in a monolayer topological insulator. Science 362, 926–929 (2018).

    CAS  Article  Google Scholar 

  22. 22.

    Ma, Q. et al. Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565, 337–342 (2019).

    Article  Google Scholar 

  23. 23.

    Luo, Y. et al. Hall effect in the extremely large magnetoresistance semimetal WTe2. Appl. Phys. Lett. 107, 182411 (2015).

    Article  Google Scholar 

  24. 24.

    Olbrich, P. et al. Room-temperature high-frequency transport of Dirac fermions in epitaxially grown Sb2Te3- and Bi2Te3-based topological insulators. Phys. Rev. Lett. 113, 096601 (2014).

    CAS  Article  Google Scholar 

  25. 25.

    Yu, H., Wu, Y., Liu, G.-B., Xu, X. & Yao, W. Nonlinear valley and spin currents from Fermi pocket anisotropy in 2D crystals. Phys. Rev. Lett. 113, 156603 (2014).

    Article  Google Scholar 

  26. 26.

    Edelstein, V. M. Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems. Solid State Commun. 73, 233–235 (1990).

    Article  Google Scholar 

  27. 27.

    Lee, J., Wang, Z., Xie, H., Mak, K. F. & Shan, J. Valley magnetoelectricity in single-layer MoS2. Nat. Mater. 16, 887–891 (2017).

    CAS  Article  Google Scholar 

  28. 28.

    Mak, K. F., Xiao, D. & Shan, J. Light–valley interactions in 2D semiconductors. Nat. Photon. 12, 451–460 (2018).

    CAS  Article  Google Scholar 

  29. 29.

    MacNeill, D. et al. Control of spin–orbit torques through crystal symmetry in WTe2/ferromagnet bilayers. Nat. Phys. 13, 300–305 (2016).

    Article  Google Scholar 

  30. 30.

    MacNeill, D. et al. Thickness dependence of spin–orbit torques generated by WTe2. Phys. Rev. B 96, 054450 (2017).

    Article  Google Scholar 

  31. 31.

    Tian, Y., Ye, L. & Jin, X. Proper scaling of the anomalous Hall effect. Phys. Rev. Lett. 103, 087206 (2009).

    Article  Google Scholar 

  32. 32.

    Ye, L. et al. Massive Dirac fermions in a ferromagnetic kagome metal. Nature 555, 638–642 (2018).

    CAS  Article  Google Scholar 

  33. 33.

    Xu, S.-Y. et al. Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2. Nat. Phys. 14, 900–906 (2018).

    CAS  Article  Google Scholar 

  34. 34.

    Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).

    CAS  Article  Google Scholar 

  35. 35.

    Chang, T.-R. et al. Prediction of an arc-tunable Weyl Fermion metallic state in MoxW1−xTe2. Nat. Commun. 7, 10639 (2016).

    CAS  Article  Google Scholar 

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The research was supported by ARO Award W911NF-17-1-0605 for sample fabrication and transport measurements, and the US Department of Energy, Office of Basic Energy Sciences under award no. DESC0013883 for optical measurements. It was also partially supported by the Cornell Center for Materials Research with funding from the NSF MRSEC program (DMR-1719875) for the low-temperature studies. This work was performed in part at Cornell NanoScale Facility, an NNCI member supported by NSF Grant NNCI-1542081. We also thank the David and Lucille Packard Fellowship and a Sloan Fellowship (K.F.M.) for support and G. Stiehl for fruitful discussions on the crystal symmetry properties of multilayer Td-WTe2.

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K.K. and T.L. fabricated the devices. E.S., T.L. and K.K. developed the experimental set-up and performed the measurements. K.K., T.L. and K.F.M. analysed the data. J.S. and K.F.M. developed the model and wrote the paper. All the authors discussed the results and commented on the manuscript.

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Correspondence to Jie Shan or Kin Fai Mak.

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Supplementary Information

Supplementary Figures 1–7, Supplementary Tables 1,2, Supplementary Notes 1–5, Supplementary References 1–3

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Kang, K., Li, T., Sohn, E. et al. Nonlinear anomalous Hall effect in few-layer WTe2. Nat. Mater. 18, 324–328 (2019).

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