Fine structure splitting cancellation in highly asymmetric InAs/InP droplet epitaxy quantum dots

We find the fine structure splitting (FSS) of a single exciton, which splits its degenerate ground-state manifold into singlets, nearly vanishes in highly asymmetric quantum dots (QDs) due to the cancellation of splitting effects with markedly different origin. The dots simulated are those that emerge on top of etch pits through the droplet epitaxy growth process; these etch pit dots break square ($C_{4v}$) spatial symmetry, which has been previously associated with small FSS. Configuration interaction calculations predict a vanishing FSS at a specific finite etch pit displacement from the center of the dot, for a structure far from square symmetry. We thus predict that highly asymmetric QDs may still display negligible FSS, providing avenues for high-fidelity generation of indistinguishable, polarization entangled photon pairs on demand.

Figure 1

Schematic diagram of the quantum dot (green) and etch pit (blue). Both structures are discretized on a grid with grid spacings of $1\times 1\times 1{\mathrm{nm}}^3$.

Figure 2

The fine structure splitting (FSS) between the bright excitons for a droplet epitaxy quantum dot. The FSS is defined as ${\text{FSS}}_{\text{bright}}=E_{\text{brightest}}-E_{\text{bright}}$. The black line indicates the calculated FSS for the total exchange interaction. The blue line indicates the calculated FSS when solely including the band mixing terms of the exchange interaction; these are ${\mathcal{K}}_{\text{LR},\mathrm{BM}}^{\left(0\right)}$, ${\mathcal{K}}_{\text{LR},\mathrm{BM}}^{\left(1\right)}$, and ${\mathcal{K}}_{\text{LR},\mathrm{BM}}^{\left(2\right)}$. The red line indicates the calculated FSS when solely including the short-range (${\mathcal{K}}_{\text{SR}}$) and dipole (${\mathcal{K}}_{\text{LR},\mathrm{DD}}^{\left(2\right)}$) interactions.

Figure 3

The contributions of each part of the exchange interaction to the fine structure splitting of both the bright (red) and the dark (gray) excitons. It is evident from all plots that the bright states are predominantly affected by the exchange interaction, whereas the dark states are not.

Figure 4

Oscillator strengths for the bright (red) and dark (gray) excitons as a function of the etch pit position. With a centered etch pit, the bright excitons have equal oscillator strengths, but as the pit shifts, one ($X_B$) becomes slightly brighter than the other ($X_b$). For zero etch pit shift, the dark excitons have zero oscillator strength to within the numerical accuracy of the calculations. As the pit shifts, the dark excitons become merely dim ($X_D$ and $X_d$).

Figure 5

Energies of an exciton in a quantum dot which has a varying etch pit position, relative to the ground-state exciton. The top figure shows the two bright excitons ($X_b$, $X_B$), which are always higher in energy. The lowest-energy exciton can be either the dark exciton ($X_D$) or the dim exciton ($X_d$). The bottom figure shows the splitting between these two and indicates which is the ground-state exciton.

Figure 6

Single-particle electron (red) and hole (blue) states for two different etch pit positions. Above the states, the quantum dot (QD) and etch pit geometries are depicted schematically (not to scale of the states). The states on the left correspond to a QD with a centered etch pit, while the states on the right correspond to a QD with its etch pit shifted along the diagonal by 8.49 nm, whose FSS is 2.35 $\mu \mathrm{eV}$. The innermost isosurfaces are set at 30% of the maximum probability density, with each subsequent isosurface at 30% probability density of the previous isosurface. Lines along symmetry axes intersect at the dot center; fixed positions are labeled with black points and their positions relative to the center in units of nm.