Current Density Functional Theory and Orbital Magnetism

Abstract

The basic motivations and ideas underlying the formulation of the current and spin density functional theory for electronic systems in a magnetic field are reviewed. We emphasize the advantages of using the canonical current as a basic variable, the fundamental constraints imposed by gauge symmetry on the structure of the exchange-correlation energy functional, and the role played by this symmetry in enforcing the conservation laws for the particle density and spin density. Next, we focus on the local density approximation to the exact theory. A generalized Thomas-Fermi theory for density and current is derived. Using this theory, a universal relation between density and current distributions of electronic systems, valid in the limit of large magnetic field, is obtained. The usefulness of this relation is demonstrated in some exactly solvable examples of electrons in parabolic confining potentials. Finally, we present a selection of results from some recent applications of the current-density functional theory: the surface structure of an electron-hole droplet, the current and density distributions of harmonically confined systems, and the ground-state energy of the two-dimensional Wigner crystal.KeywordsMagnetic FieldRandom Phase ApproximationLower Landau LevelMagnetic LengthLarge Magnetic FieldThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.