Quantum Hall criticality, superconductor-insulator transition, and quantum percolation

A model consisting of a mixture of superconducting and quantum links is proposed to describe the integer quantum Hall transition. The quantum links correspond to tunneling of electrons between trajectories trapped in adjacent potential valleys, while the superconducting links mimic the merging of these trajectories once the Fermi energy exceeds the saddle point energy separating the two valleys. The quantum Hall transition in this model corresponds to percolation of the superconducting links. Numerical calculations and scaling analysis using two different approaches yield the critical exponent ν≈2.4 and a two-peak conductance distribution at the critical point. The role of quantum coherence is discussed, allowing an interpretation of ν≈1.3, found in some experiments, in terms of the percolation critical exponent. The model suggests that the critical behavior of the superconductor-insulator transition (on the insulating side) is in the same universality class as the quantum Hall transition.