Weak-Field Galvanomagnetic Properties of a New Type of Metallic Model

Abstract

The weak-field Hall coefficient and magnetoresistance are computed for a metallic model in which the Fermi surface has the form of a cube with rounded edges and corners. Exact and relatively simple results are obtained as a function of a parameter which allows the shape of the Fermi surface to evolve continuously from a sphere to a cube with sharp edges and corners. In going from the one extreme to the other, the Hall coefficient decreases monotonically from $\frac{1}{\mathrm{ne}}$ to $\frac{\frac{1}{4}\pi }{\mathrm{ne}}$, while the Seitz magnetoresistance coefficients $b$, $c$, and $d$ increase monotonically from zero to infinity (for $b$ and $d$) and to $1-\left(\frac{8}{3\pi }\right)$ (for $c$). The results are interpreted and compared with the galvanomagnetic properties of other types of models.