The nonlinear Hall effect, a new member of the Hall effect family, has attracted significant interest due to the rich quantum quantities it can manifest. Recent discoveries not only suggest novel nonlinear applications but also provide a powerful probe of the quantum geometry of the electron Bloch wave functions, including the Berry curvature dipole, quantum metric dipole, and beyond. These new developments, however, also bring a new challenge. The transverse transport consists of both Hall and non-Hall contributions. Unlike in the linear regime, separating the Hall and non-Hall transverse contributions in the nonlinear regime remains a significant challenge. Without the ability to discern Hall from non-Hall, the proposed novel quantum geometrical properties of the nonlinear Hall effect cannot be systematically studied and isolated. In this work, we present a unifying experimental method that can discern the Hall and non-Hall transverse currents in both the linear and nonlinear regimes. In particular, we show that this differentiation can be achieved by comparing the measured conductivities if one swaps the directions between the applied current and measured voltage, effectively probing the symmetry or antisymmetry of the conductivity tensor. We experimentally demonstrate this method in a number of novel quantum materials, including odd-layer ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, black phosphorus, two-dimensional ${\mathrm{WTe}}_2$ and even-layer ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, which allows us to verify this method in both the linear and nonlinear regimes, elucidating their distinct quantum geometrical origins. Our results offer a powerful and broadly applicable technique for disentangling transverse responses, contributing to active studies of the nonlinear electric transport of novel quantum materials.

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• Berry curvature
• Electrical properties
• Hall effect
• 2-dimensional systems
• van der Waals systems
• Electrical transport techniques