  The role of electron-electron interaction in transport properties of open
quantum dots is studied. The self-consistent full quantum mechanical
magnetotransport calculations within the Hartree, Density Functional Theory and
Thomas-Fermi approximations were performed where a whole device, including the
semi-infinitive leads, is treated on the same footing (i.e. the
electron-electron interaction is accounted for both in the leads as well as in
the dot region). The main finding of the present paper is the effect of pinning
of the resonant levels to the Fermi energy due to the enhanced screening. Our
results represent a significant departure from a conventional picture where a
variation of external parameters (such as a gate voltage, magnetic field, etc.)
causes the successive dot states to sweep past the Fermi level in a linear
fashion. We instead demonstrate highly nonlinear behavior of the resonant
levels in the vicinity of the Fermi energy. The pinning of the resonant levels
in open quantum dots leads to the broadening of the conduction oscillations in
comparison to the one electron picture. The effect of pinning becomes much more
pronounced in the presence of the perpendicular magnetic field. This can be
attributed to the enhanced screening efficiency because of the increased
localization of the wave function. The strong pinning of the resonant energy
levels in the presence of magnetic field can have a profound effect on
transport properties of various devices operating in the edge state transport
regime. We also critically examine an approximation often used in transport
calculations where an inherently open system is replaced by a corresponding
closed one.
