Numerical studies on level statistics of electrons in disordered systems

The spectral fluctuation of electrons in disordered systems are investigated using numerical calculations on the Anderson model in two (2d) and three (3d) dimensions as well as on the random flux model. We study the dependence of the critical statistics on the dimension and on the universality class. At the Anderson transition in 3d we study the influence of a broken time reversal symmetry. We find a universal, scale invariant critical unitary statistics, which is distinguished from the critical orthogonal one. In an Aharonov-Bohm geometry we find a scale invariant, flux tuned crossover between the two critical ensembles. For the quantum Hall system we provide evidence for the existence of a critical level statistics at the localization-delocalization transition. As an application of the level statistics we use the finite size scaling properties of the spectral fluctuation to determine the localization length of electronic wavefunctions. For the two-dimensional orthogonal Anderson model we find a crossover from weak to strong localization in finite lattices. The localization length of electrons due to a random magnetic flux in 2d grows very fast from the band edges. In the center of the band the latter is so large that the level statistics shows no size dependence. Like in a model with additional potential disorder we find no indication of a metal-insulator transition. However, for small potential disorder the localization length becomes too large to exlude completely the existence of a mobility edge. The random flux strongly suppresses localization. (orig.)136 refs.Available from TIB Hannover: RO 1745(8) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman