Dimensionality-dependent self-energy corrections and exchange-correlation potential in semiconductor nanostructures

We study the quasiparticle gap in semiconductor nanostructures versus dimensionality and compare it to the value obtained in the local density approximation. We first develop general arguments based on the GW approach which we then substantiate numerically by a tight binding version of this theory. We show that the gap correction is dominated by a macroscopic surface self-polarization term and point out its nonmonotonic behavior versus dimensionality.