On the fractal dimensionality of the extended states in disordered two-dimensional systems in a strong magnetic field

Abstract

It is argued that the extended states in two-dimensional electronic systems subject to a strong perpendicular magnetic field must not be “area-filling”. Their fractal dimensionality d ∗ is calculated from the inverse participation number for the ideal Landau model, and the Teller model. For disordered systems the fractal dimensionality is obtained in the limit of strong magnetic field from percolation theory. The result is d ∗=1.75 . The quantum mechanical Teller model with disorder is treated numerically.