Quasi‐one‐dimensional systems and localized defects: Some results of the Green's matrix formalism

Abstract

The application of the self‐consistent field (SCF) local‐impurity formalism to quasi‐one‐dimensional systems is discussed. We describe a general procedure for an accurate numerical determination of the Green's function matrix elements of the unperturbed system. An application to a local impurity in a model chain with two orbitals per unit cell is reported. The changes in the charge‐bond‐order matrix and in local and total density of states due to the impurity are discussed with special emphasis on the changes at the critical points (van Hove singularities) at the band edges. The Green's matrix approach is used to reexamine long‐range Friedel oscillations caused by an impurity in a strictly one‐dimensional metal. The extent of the long‐range tail of the perturbed charge density is in an inverse relation to the localization length of the impurity state: the stronger the perturbation the more localized is the bound state and the more extended are the oscillations in the charge distribution. The results for the model chain with two orbitals per unit cell indicate that the impurity‐induced change in charge distribution may be locally screened by redistribution of the population of the on‐site orbitals, therefore damping possible oscillations and leading to a faster decay than in strictly one‐dimensional systems.