Abstract
The theoretical description of transport in a wide class of novel materials is based upon quantum-percolation and related random-resistor-network (RRN) models. We examine the localization properties of electronic states of diverse two-dimensional quantum-percolation models using exact diagonalization in combination with kernel-polynomial-expansion techniques. Employing the local-distribution approach, we determine the arithmetically and geometrically averaged densities of states in order to distinguish extended, current-carrying states from localized ones. To get further insight into the nature of eigenstates of RRN models, we analyze the probability distribution of the local density of states in the whole parameter and energy range. For a recently proposed RRN representation of graphene sheets, we discuss leakage effects.
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