Equilibrium current distributions and W_{infinity} gauge theory in quantum Hall systems of conventional electrons and Dirac electrons

Abstract

In equilibrium planer systems of Hall electrons, such as GaAs heterostructures and graphene, support two species of current counterflowing along the system edges, as observed recently in experiment using a nanoscale magnetometer. We examine distinct origins and distinctive features of these equilibrium currents, with the Coulombic many-body effects taken into account, and derive their real-space distributions. Our basic tool of analysis is a reformulation of quantum Hall systems as a W_{infinity} gauge theory, which allows one to diagonalize the total Hamiltonian according to the resolutions of external probes. These equilibrium currents are deeply tied to the orbital magnetization in quantum Hall systems. Special attention is drawn to the case of graphene, especially the neutral (nu=0) ground state and its intrinsic diamagnetic response that combines with the equilibrium currents to govern the orbital magnetization and its oscillations with filling.