Localization properties of fractons in percolating structures

Abstract

Scaling curves for the density of states and localization length of fractons near a percolation threshold are obtained for dilute and superconducting lattices in both two and three dimensions. These are used to verify the predictions of single-parameter scaling and to show that the energy dependence of the inverse localization length is consistent with known values of the spectral dimensionalities of these structures. The results demonstrate that eigenstates of an infinite, percolating, dilute structure exhibit superlocalization of the form ψ(r)∼${\mathit{e}}^{\mathrm{-}\mathrm{\beta }\mathit{r}\mathrm{\delta }}$ with values of δ=1.13±0.06 and 1.39±0.07 in two and three dimensions, respectively.