We propose an effective model to describe the statistical properties of exciton fine structure splitting (FSS) and polarization angle of quantum dot ensembles (QDEs). We derive the distributions of FSS and polarization angle for QDEs and show that th
eir statistical features can be fully characterized using at most three independent measurable parameters. The effective model is confirmed using atomistic pseudopotential calculations as well as experimental measurements for several rather different QDEs. The model naturally addresses three fundamental questions that are frequently encountered in theories and experiments: (I) Why the probability of finding QDs with vanishing FSS is generally very small? (II) Why FSS and polarization angle differ dramatically from QD to QD? and (III) Is there any direct connection between FSS, optical polarization and the morphology of QDs? The answers to these fundamental questions yield a completely new physical picture for understanding optical properties of QDEs.
The spin-orbit interaction generally leads to spin splitting (SS) of electron and hole energy states in solids, a splitting that is characterized by a scaling with the wavevector $bf k$. Whereas for {it 3D bulk zincblende} solids the electron (heavy
hole) SS exhibits a cubic (linear) scaling with $k$, in {it 2D quantum-wells} the electron (heavy hole) SS is currently believed to have a mostly linear (cubic) scaling. Such expectations are based on using a small 3D envelope function basis set to describe 2D physics. By treating instead the 2D system explicitly in a multi-band many-body approach we discover a large linear scaling of hole states in 2D. This scaling emerges from hole bands coupling that would be unsuspected by the standard model that judges coupling by energy proximity. This discovery of a linear Dresselhaus k-scaling for holes in 2D implies a different understanding of hole-physics in low-dimensions.
