Abstract
Several recent theoretical advances concerning semiconductor quantum dots are reviewed. First of all, the effect of the quantum confinement on the energy gap is revisited on the basis of GW and Bethe-Salpeter calculations, showing that the excitonic gap is practically equal to the ordinary eigenvalue gap of single-particle approximations. The second part demonstrates that it is now possible to calculate the conductance peaks for the tunnelling current through a nanostructure. Finally, we discuss in some detail the concept of a macroscopic dielectric constant for nanostructures, showing that, except for a thin surface layer, the local dielectric constant still keeps its bulk value down to pretty small nanostructures.
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