= Two-carrier Hall coefficient
{title2=$R_H=\dfrac{p\mu_h^2-n\mu_e^2}{e(p\mu_h+n\mu_e)^2}$}
For isotropic <Electrons> and <electron holes> with positive mobilities, adding their weak-field <electrical conductivity> tensors and imposing zero transverse total current gives
$$
R_H=\frac{p\mu_h^2-n\mu_e^2}{e(p\mu_h+n\mu_e)^2},\qquad
\sigma=e(n\mu_e+p\mu_h).
$$
The <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 $\mu_e B\ll1$, $\mu_h B\ll1$, independent semiclassical carriers, and no anomalous Hall contribution.
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