From the zero-field metal-insulator transition in two dimensions to the quantum Hall transition: a percolation-effective-medium theory

Effective-medium theory is applied to the percolation description of the metal-insulator transition in two dimensions with emphasis on the continuous connection between the zero-magnetic-field transition and the quantum Hall transition. In this model the system consists of puddles connected via saddle points, and there is loss of quantum coherence inside the puddles. The effective conductance of the network is calculated using appropriate integration over the distribution of conductances, leading to a determination of the magnetic field dependence of the critical density. Excellent quantitative agreement is obtained with the experimental data, which allows an estimate of the puddle physical parameters.