The quantum percolation model of the scaling theory of the quantum Hall effect: a unifying model for plateau-to-plateau transitions

We present a unifying model of plateau-to-plateau transitions in the quantum Hall effect based on results from high resolution frequency scaling experiments. We show that as the frequency or quantum coherence length of the two-dimensional electron system is varied, one observes a crossover between classical percolation and quantum percolation in the measured values of the critical scaling exponents of the plateau-to-plateau transitions. This crossover is dependent on the relationship between certain relevant length scales of a two- dimensional system and can be explained using a quantum percolation model. The model explains why quantum criticality can be observed in some systems, but is absent from others.