Level statistics for electronic states in a disordered fractal

Abstract

We present results for the density of states and the statistics of the energy levels in a random tight binding matrix ensemble defined on a disordered two-dimensional Sierpinski gasket. In the absence of disorder the nearest level spacing distribution function P(S) is shown to follow the inverse power law , which defines the fractal dimension of the corresponding spectrum. In the random case P(S) approaches, instead, the Poisson law , which is consistent with localization of the corresponding eigenstates. In the presence of a random magnetic flux our results also scale towards the Poisson statistics.