# Observation of the nonlinear Hall effect under time-reversal-symmetric conditions

## Abstract

The electrical Hall effect is the production, upon the application of an electric field, of a transverse voltage under an out-of-plane magnetic field. Studies of the Hall effect have led to important breakthroughs, including the discoveries of Berry curvature and topological Chern invariants1,2. The internal magnetization of magnets means that the electrical Hall effect can occur in the absence of an external magnetic field2; this ‘anomalous’ Hall effect is important for the study of quantum magnets2,3,4,5,6,7. The electrical Hall effect has rarely been studied in non-magnetic materials without external magnetic fields, owing to the constraint of time-reversal symmetry. However, only in the linear response regime—when the Hall voltage is linearly proportional to the external electric field—does the Hall effect identically vanish as a result of time-reversal symmetry; the Hall effect in the nonlinear response regime is not subject to such symmetry constraints8,9,10. Here we report observations of the nonlinear Hall effect10 in electrical transport in bilayers of the non-magnetic quantum material WTe2 under time-reversal-symmetric conditions. We show that an electric current in bilayer WTe2 leads to a nonlinear Hall voltage in the absence of a magnetic field. The properties of this nonlinear Hall effect are distinct from those of themore »

- Authors:
- more »

- Publication Date:

- Research Org.:
- Energy Frontier Research Centers (EFRC) (United States). Center for Excitonics (CE); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1566622

- DOE Contract Number:
- SC0001088

- Resource Type:
- Journal Article

- Journal Name:
- Nature (London)

- Additional Journal Information:
- Journal Volume: 565; Journal Issue: 7739; Journal ID: ISSN 0028-0836

- Publisher:
- Nature Publishing Group

- Country of Publication:
- United States

- Language:
- English

- Subject:
- solar (photovoltaic), solid state lighting, photosynthesis (natural and artificial), charge transport, optics, synthesis (novel materials), synthesis (self-assembly), synthesis (scalable processing)

### Citation Formats

```
Ma, Qiong, Xu, Su-Yang, Shen, Huitao, MacNeill, David, Fatemi, Valla, Chang, Tay-Rong, Mier Valdivia, Andrés M., Wu, Sanfeng, Du, Zongzheng, Hsu, Chuang-Han, Fang, Shiang, Gibson, Quinn D., Watanabe, Kenji, Taniguchi, Takashi, Cava, Robert J., Kaxiras, Efthimios, Lu, Hai-Zhou, Lin, Hsin, Fu, Liang, Gedik, Nuh, and Jarillo-Herrero, Pablo.
```*Observation of the nonlinear Hall effect under time-reversal-symmetric conditions*. United States: N. p., 2018.
Web. doi:10.1038/s41586-018-0807-6.

```
Ma, Qiong, Xu, Su-Yang, Shen, Huitao, MacNeill, David, Fatemi, Valla, Chang, Tay-Rong, Mier Valdivia, Andrés M., Wu, Sanfeng, Du, Zongzheng, Hsu, Chuang-Han, Fang, Shiang, Gibson, Quinn D., Watanabe, Kenji, Taniguchi, Takashi, Cava, Robert J., Kaxiras, Efthimios, Lu, Hai-Zhou, Lin, Hsin, Fu, Liang, Gedik, Nuh, & Jarillo-Herrero, Pablo.
```*Observation of the nonlinear Hall effect under time-reversal-symmetric conditions*. United States. doi:10.1038/s41586-018-0807-6.

```
Ma, Qiong, Xu, Su-Yang, Shen, Huitao, MacNeill, David, Fatemi, Valla, Chang, Tay-Rong, Mier Valdivia, Andrés M., Wu, Sanfeng, Du, Zongzheng, Hsu, Chuang-Han, Fang, Shiang, Gibson, Quinn D., Watanabe, Kenji, Taniguchi, Takashi, Cava, Robert J., Kaxiras, Efthimios, Lu, Hai-Zhou, Lin, Hsin, Fu, Liang, Gedik, Nuh, and Jarillo-Herrero, Pablo. Mon .
"Observation of the nonlinear Hall effect under time-reversal-symmetric conditions". United States. doi:10.1038/s41586-018-0807-6.
```

```
@article{osti_1566622,
```

title = {Observation of the nonlinear Hall effect under time-reversal-symmetric conditions},

author = {Ma, Qiong and Xu, Su-Yang and Shen, Huitao and MacNeill, David and Fatemi, Valla and Chang, Tay-Rong and Mier Valdivia, Andrés M. and Wu, Sanfeng and Du, Zongzheng and Hsu, Chuang-Han and Fang, Shiang and Gibson, Quinn D. and Watanabe, Kenji and Taniguchi, Takashi and Cava, Robert J. and Kaxiras, Efthimios and Lu, Hai-Zhou and Lin, Hsin and Fu, Liang and Gedik, Nuh and Jarillo-Herrero, Pablo},

abstractNote = {The electrical Hall effect is the production, upon the application of an electric field, of a transverse voltage under an out-of-plane magnetic field. Studies of the Hall effect have led to important breakthroughs, including the discoveries of Berry curvature and topological Chern invariants1,2. The internal magnetization of magnets means that the electrical Hall effect can occur in the absence of an external magnetic field2; this ‘anomalous’ Hall effect is important for the study of quantum magnets2,3,4,5,6,7. The electrical Hall effect has rarely been studied in non-magnetic materials without external magnetic fields, owing to the constraint of time-reversal symmetry. However, only in the linear response regime—when the Hall voltage is linearly proportional to the external electric field—does the Hall effect identically vanish as a result of time-reversal symmetry; the Hall effect in the nonlinear response regime is not subject to such symmetry constraints8,9,10. Here we report observations of the nonlinear Hall effect10 in electrical transport in bilayers of the non-magnetic quantum material WTe2 under time-reversal-symmetric conditions. We show that an electric current in bilayer WTe2 leads to a nonlinear Hall voltage in the absence of a magnetic field. The properties of this nonlinear Hall effect are distinct from those of the anomalous Hall effect in metals: the nonlinear Hall effect results in a quadratic, rather than linear, current–voltage characteristic and, in contrast to the anomalous Hall effect, the nonlinear Hall effect results in a much larger transverse than longitudinal voltage response, leading to a nonlinear Hall angle (the angle between the total voltage response and the applied electric field) of nearly 90 degrees. We further show that the nonlinear Hall effect provides a direct measure of the dipole moment10 of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe2. Our results demonstrate a new type of Hall effect and provide a way of detecting Berry curvature in non-magnetic quantum materials.},

doi = {10.1038/s41586-018-0807-6},

journal = {Nature (London)},

issn = {0028-0836},

number = 7739,

volume = 565,

place = {United States},

year = {2018},

month = {12}

}

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