Characterization of the Metal-Insulator Transition in the Anderson Model of Localization

Summary

In this chapter we discuss three different methods in statistical physics which have been successfully implemented to determine the metal-insulator transition and to characterize the electronic states in disordered systems described by the Ander­son model of localization. First, we study the spatial decay of electronic states of the Anderson Hamiltonian along quasi-one-dimensional bars and use finite-size scaling to analyze the data and the transition in infinite three-dimensional samples. Second, we calculate the eigenfunctions and describe their spatial distribution by means of multi-fractal analysis. Third, we compute the eigenvalue spectrum and study the energy level statistics to determine the transition. Emphasis is laid on programming tricks to save computer time or to increase accuracy. As an example, some results of large-scale nu­merical investigations for anisotropic materials are presented, demonstrating that the three methods yield coinciding results. Several related topics of current research on the electronic properties of disordered materials are mentioned in which these statistical methods have been successfully applied.