Strong suppression of spin splitting in quantum wires due to correlations induced by edge state screening

Abstract

A modified local-density approximation is developed to treat self-consistently exchange and correlations in a quantum wire (QW) subjected to a strong perpendicular magnetic field. The influence of many-body interactions on the spin splitting between the two lowest Landau levels (LLs) is calculated within the screened Hartree-Fock approximation (SHFA), for filling factor , and the strong spatial dependence of the screening properties of electrons is taken into account. In comparison with the Hartree-Fock result, the spatial behaviour of the occupied LLs in a QW is strongly modified when correlations are included. Correlations caused by bulk screening are very weak whereas those caused by screening at the edges are very strong. The latter strongly suppress the exchange splitting and smoothen the energy dispersion at the edges. The theory is in reasonable agreement with the observed strong suppression of the spin splitting pertinent to the quantum Hall effect (QHE) state and the destruction of this state in long QWs.