SCALING OF THE STATIC CONDUCTIVITY IN THE QUANTUM HALL-EFFECT

We performed a numerical study of the static diagonal conductivity σxx in the lowest Landau level for a disordered two-dimensional system in a magnetic field with short range impurity potentials. We find scaling of the conductivity peak at a single critical energy which is governed by both the localization length exponent ν=2.37±0.05 and an exponent η′=1.63±0.03. We argue that η1 can be identified with the fractal dimension D(2). For the value of the critical conductivity we obtained (0.5±0.02)e2h in agreement with the hypothesis of universality. © 1994 The American Physical Society.