Localization and delocalization studies in one dimensional electronic disordered systems.

Abstract

In this thesis, uniform and disordered one dimensional systems of delta-potentials are studied using the Kronig-Penney Model. In this model, the continuous Schrodinger equation of the system is transformed into a finite difference equation, using the Poincare Map Technique, which simplifies the calculations. First introduced in this study is a new representation of this finite difference equation which gives a clearer insight into the problem. Based on this new representation, localization of electronic states is investigated in particular in the context of correlated and uncorrelated disorder. Also, in the context of correlated disorder, the first rigorous study of the critical behaviour of the electronic states between localized and extended states is discussed.