Scaling conductance on random fractal

In the paper we use numerical simulations to show that superlocalization of electronic wave functions takes place on fractal objects also for energies E from the band. Finite size scaling of conductance g versus system size L reveals that [ln g] scales as L-d phi. The values of localization exponent d(phi) we found in 2D are 1.138(3) for the state in the middle of the band E = 0.5t, and 1.144(3) for the state near the lower band edge E = -3.5t. T hese values are in good agreement with the conjecture d(phi) = zeta (l), wh ere zeta (l) is the chemical length exponent.