Renormalization approach for the two-dimensional Anderson model at the band edge: Scaling of the localization volume

We study the localization volumes V ( participation ratio) of electronic wave functions in the 2d-Anderson model with diagonal disorder. Using a renormalization procedure, we show that at the band edges, i.e., for energies Eapproximate to +/- 4, V is inversely proportional to the variance [epsilon(2)] of the site potentials. Using scaling arguments, we show that in the neighborhood of E= +/- 4, V scales as V= [epsilon(2)](-1)g((4- \E\)/[epsilon(2)]) with the scaling function g(x). Numerical simulations confirm this scaling ansatz.