Two-carrier Hall coefficient ($R_H=\frac{p{\mu }_h^2-n{\mu }_e^2}{e(p{\mu }_h+n{\mu }_e{)}^2}$)

For isotropic Electrons and electron holes with positive mobilities, adding their weak-field electrical conductivity tensors and imposing zero transverse total current givesThe Hall coefficient changes sign at $p{\mu }_h^2=n{\mu }_e^2$. Carrier abundance alone does not fix the sign; mobilities enter quadratically. The formula assumes ${\mu }_{e}B\ll 1$, ${\mu }_{h}B\ll 1$, independent semiclassical carriers, and no anomalous Hall contribution.