Finite cluster calculations of the conductivity tensor, with application to alkali fullerides and the Anderson impurity model

Abstract

We have developed a method, based on direct evaluation of the Kubo-Greenwood formula on finite clusters, to evaluate the zero-temperature conductivity tensor in zero and low magnetic fields for tight-binding models. We have applied this method to square-lattice Anderson impurity models, and to a class of models inspired by the alkali fullerides A3C60. Experiments on A3C60 show what appears to be a "universal" relation between Hall coefficient and lattice constant; such variations with lattice constant have usually been interpreted as indicating that that conduction bandwidth is the key physical property that is varying (everything else being nearly constant). However, our calculations are inconsistent with this standard interpretation, and we find that the data can only be accounted for within the models under consideration if one accepts the radical suggestion that the effective conduction band filling varies significantly with lattice constant. These calculations also exhibit enormous deviations from Matthiessen's rule. Our results for the Anderson impurity model appear to exhibit the universal conductance fluctuations that would be expected in this sort of finite-cluster calculation. We present evidence for unanticipated universal fluctuations in the low-field Hall conductivity.