Hall coefficient of a holelike Fermi surface

Abstract

A holelike Fermi surface by itself can lead to a negative Hall coefficient at "low fields." This is especially true for nearly-free-electron polyvalent metals in which the local curvature of the hole sheet is predominantly electronlike. A simple analytic method for calculating the magnetoconductivity tensor and the Hall coefficient as a function of ${\omega }_c\tau$ is presented. The effects of the local curvature are included explicitly in the solution of the Boltzmann equation. In addition, only one relaxation time has been used. A general expression for the zero-field Hall coefficient of an idealized $N$-sided regular Brillouin-zone section normal to the applied magnetic field is also given. The results are useful for a proper understanding of the magnetotransport properties in the polyvalent metals. A dynamic-two-carrier model that mimics the exact theoretical results is proposed for the hole sheet of these metals.