Pseudopotential calculation of the excitonic fine structure of million-atom self-assembled ${\mathrm{In}}_{1-x}{\mathrm{Ga}}_x\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum dots

The atomistic pseudopotential method is used to accurately predict the electron-hole exchange-induced fine structure (FS) and polarization anisotropy in million-atom ${\mathrm{In}}_{1-x}{\mathrm{Ga}}_x\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum dots of various shapes and compositions. The origin of the FS splittings is clarified using a simple model where the effects of atomistic symmetry and spin-orbit interaction are separately evident. Remarkably, polarization anisotropy and FS splittings are shown to occur, even in a cylindrically symmetric dot. Furthermore, “dark excitons” are predicted to be partially allowed. Trends in splittings among different shapes and compositions are revealed.