Correlations, inhomogeneous screening, and suppression of spin splitting in quantum wires at strong magnetic fields

A self-consistent treatment of exchange and correlations in a quantum wire (QW) subject to a strong perpendicular magnetic field is presented using a modified local-density approximation. The influence of many-body interactions on the spin splitting between the two lowest Landau levels (LL's) is calculated within the screened Hartree-Fock approximation, for filling factor ν=1, and the strong spatial dependence of the screening properties of electrons is taken into account. In comparison with the Hartree-Fock result, the spatial behavior of the occupied LL in a QW is strongly modified when correlations are included. Correlations caused by screening at the edges strongly suppress the exchange splitting and smoothen the energy dispersion at the edges. The theory accounts well for the experimentally observed strong suppression of the spin splitting pertinent to the {ν}=1 quantum Hall effect state as well as the destruction of this state in long, quasiballistic GaₓAl_1-xAs/GaAs QW's.