New Method for Computing the Weak-Field Hall Coefficient

Abstract

The factor $r$ in the expression $R_0=\frac{r}{\mathrm{ne}}$ for the weak-field Hall coefficient is computed for a wide variety of metallic band models. The technique employs a planar-faced approximation to the true Fermi surface, and this greatly simplifies the mathematics. Strongly distorted Fermi surfaces, multivalley models, anisotropic scattering, and band-filling effects are studied, and the results are used to develop a general theory of the behavior of the factor $r$. The effects of shape and scattering anisotropies, the question of their equivalence, and the reason why a Hall coefficient changes sign are discussed. Finally, the results are applied to the model of Cooper and Raimes, to lead-pipe models, and to experimental Hall data on the noble metals.