Quantum wires in magnetic field: a comparative study of the Hartree–Fock and the spindensity functional approaches

Abstract

We present a detailed comparison of the self-consistent calculations based on theHartree–Fock and the spin density functional theory for a split-gate quantum wire inthe IQH regime. We demonstrate that both approaches provide qualitatively(and, in most cases, quantitatively) similar results for the spin-resolved electrondensity, spin polarization, spatial spin separation at the edges and the effectiveg factor. Both approaches produce the same values of the magnetic fields corresponding tothe successive subband depopulation and qualitatively similar evolution of themagnetosubbands. Quantitatively, however, the HF and the DFT subbands are different(even though the corresponding total electron densities are practically the same). Incontrast to the HF approach, the DFT calculations predict much larger spatial spinseparation near the wire edge for the low magnetic fields (when the compressible strips forspinless electrons are not formed yet). In the opposite limit of the large fields, theHartree–Fock and the DFT approaches give very similar values for the spatial spinseparation.