Energy Bands in One-Dimensional Aperiodic Potentials

Abstract

By modifying the characteristic-momentum formalism of Williams and Matthews, we demonstrate the existence of two characteristic lengths of quite different magnitude. The larger, analogous to the mean free path for extended states in higher dimensions, is the distance of localization within energy bands. The smaller is that of states in the band tails. Finally, a formula for the conductivity in terms of the characteristic momentum is obtained.