Local-density approximation to the energy density functionals in a magnetic field

Abstract

For an electron gas in a uniform magnetic field, explicit expressions of the electron density, current density, and the density matrix are derived as functions of the Fermi energy and the field strength, using plane waves and the Landau energy levels. The local-density approximations for the kinetic and the exchange energy functionals for an inhomogeneous many-electron system are thereby suggested using the density quantities as basic variables. A practical scheme for the density-functional calculation involving the magnetic field in the spirit of Thomas-Fermi-Dirac theory is outlined.