Scaling theory of the Hall effect in disordered electronic systems

Abstract

A scaling theory for the Hall effect in disordered electronic systems is developed. It is suggested that a universal scaling function for the Hall conductance exists, and the leading quantum correction to the classical value ($d-2\mathrm{}$) of this function is calculated ($d$ is the dimensionality). It is shown, by means of a scaling argument, that at the mobility edge the zero-temperature Hall conductivity approaches zero with an exponent $t_H=2t$, where $t$ is the conductivity exponent. This relation between the exponents is supported by a microscopic calculation in $2+\epsilon$ dimensions, which yields $t=1\mathrm{}$, $t_H=2\mathrm{}$.