New Method for Computing the Weak-Field Hall Coefficient. II. Some Extensions and Modifications

Abstract

An earlier paper described a simple method for computing the weak-field Hall coefficient through the use of a Fermi surface composed entirely of planar faces. That paper developed a set of rules which linked the general behavior of the Hall coefficient to two fundamental properties of transport models, Fermi-surface shape and scattering anisotropy. The present paper reformulates those rules by adding a third ingredient to the model description, shape evolution. Exceptions to the earlier rules are thereby eliminated. The present paper also extends the simple method to noncubic models. The results for "undulating cylinders" (a Fermi-surface approximation for some hexagonal metals) and toroidal Fermi surfaces (a possible model for the wurtzite lattice) are analyzed. Finally, the effect of rounding the sharp edges at which the planar Fermi-surface faces intersect is investigated. The results resolve an apparent paradox pointed out by Stern, and provide some insight into the general magnetic field dependence of the Hall coefficient.