Theory of Hall Effect. I

Abstract

A gauge-invariant expression of the Hall conductivity in a weak magnetic field is derived on the basis of the Kubo formula for nearly free electron systems. In order to calculate the correlation functions systematically, diagram techniques have been employed. It is shown that the Hall coefficient is inversely proportional to the square of the density of states at the Fermi energy, which justifies the conjectures of Mott and Ziman in connection with the discussion of liquid metals.