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

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

Research output: Contribution to journalLetter

29 Citations (Scopus)

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 languageEnglish
Pages (from-to)337-342
Number of pages6
JournalNature
Volume565
Issue number7739
DOIs
Publication statusPublished - 2019 Jan 17

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Magnetic Fields
Observation
Fruit
Magnets
Metals

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Cite this

Ma, Q., Xu, S. Y., Shen, H., MacNeill, D., Fatemi, V., Chang, T. R., ... Jarillo-Herrero, P. (2019). Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature, 565(7739), 337-342. https://doi.org/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. In: Nature. 2019 ; Vol. 565, No. 7739. pp. 337-342.
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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.",
author = "Qiong Ma and Xu, {Su Yang} and Huitao Shen and David MacNeill and Valla Fatemi and Chang, {Tay Rong} and {Mier Valdivia}, {Andr{\'e}s M.} and Sanfeng Wu and Zongzheng Du and Hsu, {Chuang Han} and Shiang Fang and Gibson, {Quinn D.} and Kenji Watanabe and Takashi Taniguchi and Cava, {Robert J.} and Efthimios Kaxiras and Lu, {Hai Zhou} and Hsin Lin and Liang Fu and Nuh Gedik and Pablo Jarillo-Herrero",
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Ma, Q, Xu, SY, Shen, H, MacNeill, D, Fatemi, V, Chang, TR, Mier Valdivia, AM, Wu, S, Du, Z, Hsu, CH, Fang, S, Gibson, QD, Watanabe, K, Taniguchi, T, Cava, RJ, Kaxiras, E, Lu, HZ, Lin, H, Fu, L, Gedik, N & Jarillo-Herrero, P 2019, 'Observation of the nonlinear Hall effect under time-reversal-symmetric conditions', 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.

In: Nature, Vol. 565, No. 7739, 17.01.2019, p. 337-342.

Research output: Contribution to journalLetter

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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.

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U2 - 10.1038/s41586-018-0807-6

DO - 10.1038/s41586-018-0807-6

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