Pseudo anomalous Hall effect in semiconductors and semimetals: a classical perspective

We demonstrate that the non-linear field dependence in the Hall effect, often indistinguishable from the anomalous Hall effect (AHE), can be realized entirely within the classical mechanism due to the Lorentz force by analyzing multi-valley models for semiconductors and semimetals. The non-linear component in the Hall resistivityρHNL, which is purely classical in origin and referred to here as the pseudo AHE, originates from carrier mobility anisotropy or the coexistence of different charges. SinceρHNLis inversely proportional to the carrier difference between electrons and holes Δn, it exceeds its zero-field value near charge neutrality. As a practical example, we show that the magnitude of the classical non-linear Hall response in ZrTe₅is comparable to the experimental values, underscoring the importance of accounting for classical contributions before attributing non-linear Hall effects to quantum mechanisms.