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

N1 - Funding Information:
Odyssey cluster, which is supported by the FAS Division of Science, Research Computing Group.
Funding Information:
Acknowledgements We thank J. Checkelsky, F. Qin, Y. Iwasa, J.-S. You and I. Sodemann for discussions. Work in the PJH group was supported partly by the Center for Excitonics, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences (BES) under award number DESC0001088 (fabrication and measurement) and partly through AFOSR grant FA9550-16-1-0382 (data analysis), and by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4541 to P.J.-H. This work made use of the Materials Research Science and Engineering Center Shared Experimental Facilities supported by the National Science Foundation (NSF; grant number DMR-0819762). N.G. and S.-Y.X. acknowledge support from DOE, BES DMSE (data taking and analysis), the Gordon and Betty Moore Foundations EPiQS Initiative through grant GBMF4540 (manuscript writing) and NSF grant number DMR-1809815 (modelling). The WTe2 crystal growth performed at Princeton University was supported by NSF MRSEC grant DMR-1420541 (Q.D.G. and R.J.C.). Z.D. and H.-Z.L. were supported by the Guangdong Innovative and Entrepreneurial Research Team Program (2016ZT06D348), the National Key R&D Program (2016YFA0301700), the National Natural Science Foundation of China (11574127), and the Science, Technology, and Innovation Commission of Shenzhen Municipality (ZDSYS20170303165926217 and JCYJ20170412152620376). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan, JSPS KAKENHI grant numbers JP18K19136 and CREST (JPMJCR15F3), JST. H.S., L.F. and S.F. acknowledge support from NSF Science and Technology Center for Integrated Quantum Materials grant DMR-1231319 (theory for H.S. and L.F.; calculations for S.F.). H.L. acknowledges Academia Sinica, Taiwan, for support under Innovative Materials and Analysis Technology Exploration (AS-iMATE-107-11). T.-R.C. was supported by the Young Scholar Fellowship Program by Ministry of Science and Technology (MOST) in Taiwan, under MOST Grant for the Columbus Program MOST107-2636-M-006-004, National Cheng Kung University, Taiwan, and National Center for Theoretical Sciences (NCTS), Taiwan. E.K. acknowledges support by ARO MURI Award W911NF-14-0247. The computational work at Harvard University was performed on the
Publisher Copyright:
© 2018, Springer Nature Limited.

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 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 magnets2–7. 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 constraints8–10. 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.

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 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 magnets2–7. 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 constraints8–10. 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.

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 - Article

C2 - 30559379

AN - SCOPUS:85060176578

SN - 0028-0836

VL - 565

SP - 337

EP - 342

JO - Nature

JF - Nature

IS - 7739

ER -