### 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 invariants ^{1,2} . The internal magnetization of magnets means that the electrical Hall effect can occur in the absence of an external magnetic field ^{2} ; this ‘anomalous’ Hall effect is important for the study of quantum magnets ^{2–7} . 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 constraints ^{8–10} . Here we report observations of the nonlinear Hall effect ^{10} in electrical transport in bilayers of the non-magnetic quantum material WTe _{2} under time-reversal-symmetric conditions. We show that an electric current in bilayer WTe _{2} 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 moment ^{10} of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe _{2} . Our results demonstrate a new type of Hall effect and provide a way of detecting Berry curvature in non-magnetic quantum materials.

Original language | English |
---|---|

Pages (from-to) | 337-342 |

Number of pages | 6 |

Journal | Nature |

Volume | 565 |

Issue number | 7739 |

DOIs | |

Publication status | Published - 2019 Jan 17 |

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### All Science Journal Classification (ASJC) codes

- General

### Cite this

*Nature*,

*565*(7739), 337-342. https://doi.org/10.1038/s41586-018-0807-6

}

*Nature*, vol. 565, no. 7739, pp. 337-342. https://doi.org/10.1038/s41586-018-0807-6

**Observation of the nonlinear Hall effect under time-reversal-symmetric conditions.** / 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.

Research output: Contribution to journal › Letter

TY - JOUR

T1 - Observation of the nonlinear Hall effect under time-reversal-symmetric conditions

AU - Ma, Qiong

AU - Xu, Su Yang

AU - Shen, Huitao

AU - MacNeill, David

AU - Fatemi, Valla

AU - Chang, Tay Rong

AU - Mier Valdivia, Andrés M.

AU - Wu, Sanfeng

AU - Du, Zongzheng

AU - Hsu, Chuang Han

AU - Fang, Shiang

AU - Gibson, Quinn D.

AU - Watanabe, Kenji

AU - Taniguchi, Takashi

AU - Cava, Robert J.

AU - Kaxiras, Efthimios

AU - Lu, Hai Zhou

AU - Lin, Hsin

AU - Fu, Liang

AU - Gedik, Nuh

AU - Jarillo-Herrero, Pablo

PY - 2019/1/17

Y1 - 2019/1/17

N2 - 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 invariants 1,2 . The internal magnetization of magnets means that the electrical Hall effect can occur in the absence of an external magnetic field 2 ; this ‘anomalous’ Hall effect is important for the study of quantum magnets 2–7 . 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 constraints 8–10 . Here we report observations of the nonlinear Hall effect 10 in electrical transport in bilayers of the non-magnetic quantum material WTe 2 under time-reversal-symmetric conditions. We show that an electric current in bilayer WTe 2 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 moment 10 of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe 2 . Our results demonstrate a new type of Hall effect and provide a way of detecting Berry curvature in non-magnetic quantum materials.

AB - 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 invariants 1,2 . The internal magnetization of magnets means that the electrical Hall effect can occur in the absence of an external magnetic field 2 ; this ‘anomalous’ Hall effect is important for the study of quantum magnets 2–7 . 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 constraints 8–10 . Here we report observations of the nonlinear Hall effect 10 in electrical transport in bilayers of the non-magnetic quantum material WTe 2 under time-reversal-symmetric conditions. We show that an electric current in bilayer WTe 2 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 moment 10 of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe 2 . Our results demonstrate a new type of Hall effect and provide a way of detecting Berry curvature in non-magnetic quantum materials.

UR - http://www.scopus.com/inward/record.url?scp=85060176578&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85060176578&partnerID=8YFLogxK

U2 - 10.1038/s41586-018-0807-6

DO - 10.1038/s41586-018-0807-6

M3 - Letter

C2 - 30559379

AN - SCOPUS:85060176578

VL - 565

SP - 337

EP - 342

JO - Nature

JF - Nature

SN - 0028-0836

IS - 7739

ER -