Graphene and Evidence for Duality in Quantum Hall Systems

Abstract: Quantum Hall systems are characterized by a spectacular set of observations (universal low-temperature conductivity, critical behaviour and semi-circle laws for transitions between Quantum Hall states) that are more robust than would be expected from the detailed theory of underlying electron dynamics. The talk starts with a summary of these observations, and their derivation from the assumption that the important charge carriers at the low energies relevant to conductivity measurements are weakly interacting particles or vortices. This implies a large emergent duality symmetry (a level two subgroup of SL(2,Z)), whose presence underlies the robustness of the observations in question. The newly-discovered and unusual Quantum Hall properties of graphene are discussed as providing a new test of this picture.