Spin polarization in modulation-doped GaAs quantum wires

We study spin polarization in a split-gate quantum wire focussing on the effect of a realistic smooth potential due to remote donors. Electron interaction and spin effects are included within the density functional theory in the local spin density approximation. We find that depending on the electron density, the spin polarization exhibits qualitatively different features. For the case of relatively high electron density, when the Fermi energy $E_{F}$ exceeds a characteristic strength of a long-range impurity potential $V_{donors}$, the density spin polarization inside the wire is practically negligible and the wire conductance is spin-degenerate. When the density is decreased such that $E_{F}$ approaches $V_{donors}$, the electron density and conductance quickly become spin polarized. With further decrease of the density the electrons are trapped inside the lakes (droplets) formed by the impurity potential and the wire conductance approaches the pinch-off regime. We discuss the limitations of DFT-LSDA in this regime and compare the obtained results with available experimental data.