Third-order nonlinear Hall effect induced by the Berry-connection polarizability tensor

Nonlinear responses in transport measurements are linked to material properties not accessible at linear order¹ because they follow distinct symmetry requirements^2-5. While the linear Hall effect indicates time-reversal symmetry breaking, the second-order nonlinear Hall effect typically requires broken inversion symmetry¹. Recent experiments on ultrathin WTe₂ demonstrated this connection between crystal structure and nonlinear response^6,7. The observed second-order nonlinear Hall effect can probe the Berry curvature dipole, a band geometric property, in non-magnetic materials, just like the anomalous Hall effect probes the Berry curvature in magnetic materials^8,9. Theory predicts that another intrinsic band geometric property, the Berry-connection polarizability tensor¹⁰, gives rise to higher-order signals, but it has not been probed experimentally. Here, we report a third-order nonlinear Hall effect in thick T_d-MoTe₂ samples. The third-order signal is found to be the dominant response over both the linear- and second-order ones. Angle-resolved measurements reveal that this feature results from crystal symmetry constraints. Temperature-dependent measurement shows that the third-order Hall response agrees with the Berry-connection polarizability contribution evaluated by first-principles calculations. The third-order nonlinear Hall effect provides a valuable probe for intriguing material properties that are not accessible at lower orders and may be employed for high-order-response electronic devices.