Contribution to the Theory of Impurity Band Conduction. II. : Hall Effect

TLDR: In this article, the effect of weak magnetic field on the impurity band conduction is taken into account on the basis of the Kubo formalism and the diagram method, and an expression for the Hall coefficient is obtained in terms of the Green's function and it is proved that this expression is reduced in a special case to the usual one derived from the Boltzmann equation method.

Abstract: In this paper we discuss the Hall coefficient of heavily doped semiconductors at very low temperatures by making use of the general method developed in previous two papers (Matsubara-Toyozawa and the first part of this series). The effect of weak magnetic field on the impurity band conduction is taken into account on the basis of the Kubo formalism and the diagram method. An expression for the Hall coefficient is obtained in terms of the Green's function and it is proved that this expression is reduced in a special case to the usual one derived from the Boltzmann equation method. Some discussion of the general feature of Hall effect in a random system is given.