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

• Published in: Nature (London) Vol. 565; no. 7739; pp. 337 - 342
• Main Authors: 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
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 01.01.2019; Nature Publishing Group
• Subjects: 639/301/119/995; 639/301/357/1018; 639/766/1130/2798; 639/925/927/1007; Aircraft; Analysis; Current voltage characteristics; Curvature; Dipole moments; Electric currents; Electric fields; Electromagnetic fields; Electromagnetism; Fermions; Hall effect; Humanities and Social Sciences; Letter; Magnetic fields; Magnetic materials; Magnetic properties; Magnetic studies; Magnetism; Magnetization; Magnets; Metals; multidisciplinary; Nonlinear response; Phase transitions; Quantum Hall effect; Science; Science (multidisciplinary); solar (photovoltaic), solid state lighting, photosynthesis (natural and artificial), charge transport, optics, synthesis (novel materials), synthesis (self-assembly), synthesis (scalable processing); Symmetry; Time reversal; Voltage
• ISSN: 0028-0836; 1476-4687; 1476-4687
• DOI: 10.1038/s41586-018-0807-6

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. The nonlinear Hall effect is observed in bilayer WTe 2 in the absence of a magnetic field, providing a direct measure of the dipole moment of the Berry curvature.