Nonlinear responses in transport measurements are linked to material properties not accessible at linear order¹ because they follow distinct symmetry requirements^2,3,4,5. 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.

^{传输测量中的非线性响应与线性顺序1}无法访问的材料属性相关联，因为它们遵循不同的对称要求^2,3,4,5。虽然线性霍尔效应表明时间反演对称性破坏，但二阶非线性霍尔效应通常需要破坏反演对称性¹。最近对超薄 WTe ₂的实验证明了晶体结构和非线性响应^6,7之间的这种联系。观察到的二阶非线性霍尔效应可以探测非磁性材料中的贝里曲率偶极子，一种带几何特性，就像异常霍尔效应探测磁性材料中的贝里曲率一样^8,9. 理论预测另一种固有的带几何特性，即贝里连接极化率张量¹⁰，会产生高阶信号，但尚未通过实验进行探索。在这里，我们报告了厚T _d -MoTe ₂中的三阶非线性霍尔效应样品。发现三阶信号是线性和二阶信号的主要响应。角度分辨测量表明，该特征是由晶体对称性约束引起的。与温度相关的测量表明，三阶霍尔响应与通过第一性原理计算评估的贝里连接极化率贡献一致。三阶非线性霍尔效应为有趣的材料特性提供了有价值的探针，这些特性在低阶时无法访问，并且可用于高阶响应电子设备。