Prediction of a new effect in localized electronic systems

Abstract

For classical systems the specific heat can be expressed in terms of the spatial energy correlation function. It is pointed out that for localized states a similar expression can be written down and leads to the prediction that the electronic specific heat has a singularity at the Anderson-Mott transition, the usual equation for the electronic specific heat not being valid below the mobility edge. The ratio of the electronic specific heat to the minimum metallic conductivity at the transition is found to be proportional to the temperature via a universal constant, k 2π 2 m/3ħ e 2.