Duality near quantum Hall transitions

A recent experiment by Shahar et al., on the phase transitions between quantum Hall states and the insulator, found that the current-voltage characteristics in the two phases are related by symmetry. It was suggested in this work that this is evidence for charge-flux duality near quantum Hall transitions. Here we provide details of this analysis. We review some theoretical ideas on charge-flux duality in the composite boson description of the quantum Hall effect, and interpret the data as implying that this duality is a symmetry in the transition region and that the Hall response of the bosons vanishes. We observe that duality for composite bosons is equivalent to a particle-hole symmetry for composite fermions and show that a Landauer analysis of transport for the latter allows a possible understanding of the reflection symmetry and Hall response beyond the linear regime. We note that the duality interpretation supports the scenario of superuniversality for quantum Hall transitions outlined by Kivelson, Lee, and Zhang. Finally, we discuss how to search for the duality at other transitions in the quantum Hall regime.