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

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 field²; 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 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.