Correlations and Local Field Corrections for a Two-Dimensional Electronic System in an External Magnetic Field

Abstract

It is shown that the correlation effects on a two-dimensional electron gas in a uniform perpendicular magnetic field are significantly affected by a strong magnetic field. A dielectric function approach is used to go beyond the RPA by improving the effective potential. This is done by including the local field correction Gq to the mean Hartree field. Following Singwi et al. we replace the two-particle distribution function ƒ2(r, p; r′, p′; t) by a product of two equilibrium one-particle distribution functions ƒ(r, p; t)ƒ(r′, p′; t) g(r − r′), where g(r) is the static equilibrium pair correlation function. We have shown that the form of the effective potential is not altered by a uniform magnetic field. Both Gq and the pair correlation function oscillate as functions of the magnetic field. The local field correction has maxima at half-odd integer fillings and minima at integer filling factors. As a result, the effective inter-particle potential has enhanced oscillations. The effect due to correlations on the plasma excitations is also discussed.