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 order because they follow distinct symmetry requirements. While the linear Hall effect indicates time-reversal symmetry breaking, the second-order nonlinear Hall effect typically requires broken inversion symmetry. Recent experiments on ultrathin WTe demonstrated this connection between crystal structure and nonlinear response. 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. Theory predicts that another intrinsic band geometric property, the Berry-connection polarizability tensor, 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-MoTe 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.