Ground State of an Electron Gas in a Magnetic Field

Abstract

Abstract : The ground state of an electron gas in a uniform magnetic field is found to be not the customary uniform state, but rather one in which a spin density wave exists, directed along the field. This conclusion is reached through what is essentially a Hartree-Fock calculation with a repulsive interaction, but in which no restrictive assumptions are made about either the strength or the range of the exchange interaction. Thus static screening does not eliminate the spin density wave in the presence of a magnetic field, as it does in the electron gas when no magnetic field is present. The temperature at which the transition to a spin density wave state occurs approaches zero as the field vanishes. The pertinent question is therefore not the nature of the ground state, but whether there is a range of field strengths and electronic densities for which the transition temperature is observably high. It is found that spin density wave formation is most favorable when only a few Landau levels are occupied, corresponding to large field strengths and low electronic densities. A rough calculation indicates that in InSb a transition temperature as high as 10 millidegrees can be realized. (Author)