Localization of relativistic electrons in a one-dimensional disordered system

Abstract

We address the question as to whether relativistic effects have any influence on localization phenomena in disordered systems. Starting from the Schradinger and Dirac equations for Kronig-Penney potentials, we derive their discrete counterparts within the framework of the linear combination of atomic orbitals and tight-binding approaches. As a specific example we subsequently focus on substitutional binary alloys. We show that taking relativity into account leads to many important differences with respect to the results obtained in the non-relativistic approximation. The predicted behaviour of localization length can be very relevant in several experimental contexts.