SPATIAL MULTIFRACTALITY OF ELECTRONIC STATES AND THE METAL-INSULATOR TRANSITION IN DISORDERED SYSTEMS

Abstract

For the investigation of the spatial behavior of electronic wave functions in disordered systems, we employ the Anderson model of localization. The eigenstates of the corresponding Hamiltonian are calculated numerically by means of the Lanczos algorithm and are analyzed with respect to their spatial multifractal properties. We find that the wave functions show spatial multifractality for all parameter cases not too far away from the metal-insulator transition (MIT) which separates localized from extended states in this model. Exactly at the MIT, multifractality is expected to exist on all length scales larger than the lattice spacing. It is found that the corresponding singularity spectrum describing these multifractals is specific for the MIT and does not depend on microscopic parameters like energy or disorder, nor does it depend on the probability distribution used for the random site energies in the Anderson Hamiltonian. Therefore this calculated singularity spectrum which is characteristic for the transition can be used to identify the MIT in systems where the position of the MIT is not known a priori. We apply this idea to states near the band edge and show that the results are in agreement with other methods.