Conductance Distribution in Superlocalization Regime

Abstract

The phenomenon of superlocalization has been studied by means of numerical simulations performed on two-dimensional percolation cluster at the threshold site concentration p = p c = 0.593. It is shown that superlocalization takes place also for the states inside the band. In this case the averaged logarithm of conductance scales with the size of percolation cluster L as (In g) ∼ -L do with localization exponent d o ≅ 1.14. The distribution of In g arises from the multiplication of two random variables, namely the chemical length l and inverse localization length y. The distribution of y is Gaussian with size independent average and variance which scales like var γ ∼ -1 . The distribution of l has a long tail towards large l. Its average and variance scale like ∼ L do and var l ∼ . There is a small correlation between l and y, which decreases as L do/2 as the size of the percolation cluster increases.