The nonlinear anomalous Hall effect can reveal various aspects of the quantum geometry of Bloch electrons and disorder scattering that are not accessible in its linear counterpart, such as Berry curvature multipole and Berry connection polarizability. Here we study the nonlinear transport in a unique heterodimensional superlattice of ${\mathrm{V}}_5{\mathrm{S}}_8$. Strong third-order nonlinear Hall and longitudinal resistances persisting up to room temperature are observed. Moreover, the nonlinear resistances exhibit a marked magnetic field dependence. By using a special measurement method and a transformation formula to avoid issues largely overlooked in nonlinear transport experiments, we obtain nonlinear conductivity coefficients and their temperature and magnetic field dependences. First-principles calculations suggest that disorder-induced extrinsic contributions dominate the nonlinear transport at zero magnetic field, while the Berry connection polarizability can contribute a giant magnetic field dependence. The exceptionally strong nonlinear effects may stimulate further theoretical development in the nonlinear anomalous transport.

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• Anomalous Hall effect
• Berry curvature
• Geometric & topological phases
• Transport phenomena
• Metals
• Hall bar
• Resistivity measurements
• Transport techniques