Quantum percolation and plateau transitions in the quantum Hall effect

Abstract

We introduce a simple model of quantum percolation and analyze it numerically using transfer matrix methods. A central point of this paper is that 3 both integer and fractional plateau transitions in the quantum Hall effect are due to quantum percolation. Within this model, we obtained the localization length exponent ν=2.4±0.2, the dynamical exponent z=1, and the scaling functions for the conductivity tensor for both the integer and the fractional transitions. We show that our results agree extremely well with the experimental results for the integer plateau transition obtained by McEuen et al.