Lower Bound for the Excitonic Fine Structure Splitting in Self-Assembled Quantum Dots

The excitonic fine structure splitting describes the splitting of the bright excitons as a consequence of the atomistic symmetry of the lattice and the electron-hole exchange interaction. Efforts are underway to eliminate this natural splitting by external constraints in order to use quantum dots in quantum optics. We show by million atom empirical pseudopotential calculations that for realistic structures a lower bound for this splitting exists. We underpin our numerical calculations by an insightful symmetry analysis.

Figure 1

Symmetry analysis for four different point groups. The single-particle levels for the highest occupied and the lowest unoccupied states are shown as black lines. The ensuing exciton states with their corresponding irreducible representation are shown as thick (dashed) lines for the bright (dark) states. The pictogram for the $C_1$ point group illustrates a random alloy structure.

Figure 2

Crossing and anticrossing of excitonic lines in In(Ga)As QDs elongated along the [110] direction under uniaxial stress along the [110] direction. The insets in red in Fig. 2b show a polar plot in the (001) plane of the oscillator strength of the lowest excitonic transition.

Figure 3

Tuning of FSS in cylindrically symmetric (a–h) and elongated (i–j) $\mathrm{InAs}/\mathrm{GaAs}$ and ${\mathrm{In}}_{0.6}{\mathrm{Ga}}_{0.4}\mathrm{As}/\mathrm{GaAs}$ QDs by external uniaxial stress along the $[1\overline{1}0]$ (c,d), [110] (a,b,e,f,i,j), [100] (g,h) crystallographic directions.