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, 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 resistivity ${\rho }_H^{\mathrm{N}\mathrm{L}}$ originates from carrier mobility anisotropy or the coexistence of different charges. Since ${\rho }_H^{\mathrm{N}\mathrm{L}}$ is inversely proportional to the carrier difference between electrons and holes $\mathrm{\Delta }n$, 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 ZrTe${}_5$ is comparable to the experimental values, underscoring the importance of accounting for classical contributions before attributing non-linear Hall effects to quantum mechanisms.