Statistical properties of exciton fine structure splitting and polarization angles in quantum dot ensembles

We develop an effective model to describe the statistical properties of exciton fine structure splitting (FSS) and polarization angle in quantum dot ensembles (QDEs) using only a few symmetry-related parameters. The connection between the effective model and the random matrix theory is established. Such effective model is verified both theoretically and experimentally using several rather different types of QDEs, each of which contains hundreds to thousands of QDs. The model naturally addresses three fundamental issues regarding the FSS and polarization angels of QDEs, which are frequently encountered in both theories and experiments. The answers to these fundamental questions yield an approach to characterize the optical properties of QDEs. Potential applications of the effective model are also discussed.

Figure 1

(a)–(d) distributions of $\delta$ ($•$) and $\kappa$ ($\blacksquare$) for several different QDEs. The solid lines and dashed lines are the best fit to Gaussian distribution functions (see Table 1). The exciton energy dependence of $\delta$ and $\kappa$ is plotted in (e) and (f), respectively.

Figure 2

Distributions of FSS for several different QDEs. In each panel, the folded line represents numerical and experimental data, the dashed line is the best fit using Eq. (6), and the dotted-dashed line is from direct calculation using Eq. (5) with the three parameters from Table 1. The solid line is the Poisson distribution with the mean FSS equal to $\langle \Delta \rangle$.

Figure 3

Distributions of polarization angle for several different QDEs. In each panel, the symbols represent the numerical and experimental data, the solid line is the best fit using Eq. (8), and the dashed line is direct calculation using Eq. (5) with the three parameters from Table 1.