Equilibrium current distributions and W∞ gauge theory in quantum Hall systems of conventional electrons and Dirac electrons

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.

Automated summary

In equilibrium planer systems of Hall electrons, two species of current counterflowing along the system edges are observed, as recently observed in experiments using a nanoscale magnetometer. The origins and features of these equilibrium currents are examined, considering the Coulombic many-body effects, and their real-space distributions are derived. The analysis is based on a reformulation of quantum Hall systems as a W-infinity gauge theory, allowing for diagonalization of the total Hamiltonian based onexternal probes' resolutions. These equilibrium currents are closely related to the orbital magnetization in quantum Hall systems, with a special focus on the case of graphene and its neutral (nu = 0) ground state and intrinsic diamagnetic response.