Local Field Effects in an Isolated Quantum Dot: Self-Consistent Microscopic Approach

A self-consistent microscopic local-field theory for an isolated arbitrary shaped quantum dot (QD) has been presented. In our approach we introduce into the Schrödinger equation a depo-larization field induced by an external electromagnetic field, and combine this idea with the second quantization technique for electron–hole pairs. As a result, we succeeded in deriving the general self-consistent nonlinear equations for the system “QD + classical electromagnetic field”. In the linear approximation, our approach reproduces microscopically the depolarization shift of the QD gain band and, in anisotropically shaped QDs, polarization dependent splitting of this band. Introduction Conventionally, local field effects are related to a difference between act-ing and mean fields in statistically large ensembles of particles like dense gases and artificial composite materials. Electromagnetic properties of such ensembles are usually modeled in the framework of the effective–medium approach. For this approach to hold, all inclusions must be electrically small, i.e., their maximal linear size must b