Electrical conductivity in a one-dimensional aperiodic solid

Abstract

Although there has been much interest in the energy bands and the localization of electronic states in one-dimensional systems, and although there has been some discussion of the relation between characteristic momentum and conductivity, there has as yet appeared no direct calculation of the electrical conductivity. We present here the first direct numerical computation of the (frequency dependent) electrical conductivity of one electron in an aperiodic one-dimensional chain of delta-function potentials. Results are obtained for chains of various lengths and various degrees of disorder. They show that although the ground state binding energy and the density of states converge rapidly to an ensemble average for long chains, the conductivity spectrum varies with the particular chain chosen and does not converge to the ensemble average. This disagrees with the popular view of low frequency conductivity in amorphous solids, but is generally in accord with the recent theoretical work of Landauer.