= Compensated two-carrier magnetoresistance
{title2=$\rho_{xx}=[1+(\mu B)^2]/(2\sigma_0)$}
Consider isotropic <Electrons> and <electron holes> with equal density $n$, charges $\mp e$, equal positive <charge carrier mobility> $\mu$, and single-species zero-field <electrical conductivity> $\sigma_0=ne\mu$. In a transverse magnetic field, opposite Hall conductivity components cancel, while diagonal components add to $2\sigma_0/[1+(\mu B)^2]$. Inverting gives $\rho_{xy}=0$ and $\rho_{xx}=\rho_{yy}=[1+(\mu B)^2]/(2\sigma_0)$. Its large-field growth is $\sigma_0B^2/(2n^2e^2)$. The total zero-field resistivity is $1/(2\sigma_0)$, half the single-species resistivity; confusing these quantities introduces a factor-of-two normalization error.
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