We study effects of randomly distributed impurities on spin polarization and electronlocalization in realistic semiconductor quantum point contacts (QPCs). To this end we usedensity functional theory in local spin-density approximation (LSDA). Previous studies (as,for example, in ) have been restricted to the Thomas-Fermi approximation, and thus theeffects of electron correlation and realistic confinement potentials were beyond the subject.Our studies have been performed for the two geometries of the gates, the first one with onlysplit gates, and the other one with an additional top gate situated over the split gates. In thelatter case there is a possibility to vary electron density within a fixed confinement whichgives an opportunity to separate the effects on conductance caused by impurities and electronelectroninteractions in a more distinct way. In both cases we recover the conventionalfluctuation free parabolic electrostatic potential when the distance between the donor layerand the two-dimensional electron gas (2DEG) exceeds ~50 nm. In the opposite case, i.e.,when the randomly distributed donors are placed more close to the 2DEG layer, there aredrastic changes like the localization of electrons in the vicinity of the confinement potentialminima which gives rise to fluctuation in conductance and resonances. At the same time theusual conductance steps vanish. By charging asymmetrically the split gates voltage wecalculate the conductance as a function of the voltage applied to the top gate. In this way wefind that resonances in conductance caused by randomly distributed donors are shifted anddescreased in amplitude while the anomalies caused by interaction effects remain unmodified.Resonance peaks in the conductance derive from localized states within the QPC due torandom fluctuations. The nature of electron localization has been discussed in our previousstudy  where we stress the crucial role of the shape of confinement potential on theformation of electron localization. In the present study we have shown that electronlocalization may be caused by randomly distributed donors and play an important role inelectron transport, especially near the pinch-off regime. The results of our numericalsimulations agree qualitatively with experimental studies [3-4]. We have also shown that fora wide QPC spin polarization appears in the form of stripes. This finding may be interesting inview of experimental study in  where it has been shown that the structure of such kind canbe responsible for the anomalous behavior of the quantized conductance of a quantum wire inthe shallow confinement limit. We also discuss the diminished effect of partially ionizedrandom donors on the electronic potentials and the appearance of short-range order among thedonors. The results of the present study is important for applications. For example,homogeneity and order of an assembly of nanostructures are crucial for their use in largescaleelectronic and optical systems. J.A. Nixon, J.H. Davies, and H.U. Baranger, Phys. Rev. B 43, 12638 (1991) I. I. Yakimenko, V. S. Tsykunov and K.-F. Berggren, J. Phys. Condens. Matter 25, 072201 (2013) L.W. Smith, K. J. Thomas, M. Pepper, D. A. Ritchie, I. Farrer, J.P. Griffiths, G.A.C. Jones, J. ofPhys.: Conf. Series 376, 012018, (2012) L. W. Smith, H. Al-Taie, F. Sfigakis, P. See, A. A. J. Lesage, B. Xu, J. P. Griffiths, H. E. Beere, G.A. C. Jones, D. A. Ritchie, M. J. Kelly, and C. G. Smith, Phys. Rev. B 90, 045426 (2014).
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