The Optical Activity of the Dark Exciton

We present a phenomenological model to consider the effect of shape symmetry breaking on the optical properties of self-assembled quantum dots. We compare between quantum dots with two-fold rotational and two reflections ($C_{2v}$) symmetry and quantum dots in which this symmetry is reduced by perturbation to one reflection only ($C_{s}$). We show that this symmetry reduction drastically affects the optical activity of the dark exciton. In symmetric quantum dots, one of the dark exciton eigenstate is totally dark and the other, due to heavy- and light-hole mixing, has a small dipole moment polarized along the symmetry axis (growth direction) of the quantum dot. In non-symmetric quantum dots, the two dark excitons' eigenstates are mixed with the bright excitons' eigenstates which have cross-linearly polarized perpendicular to the growth direction dipole moments. As a result of this mixing one of the dark exciton eigenstate is dark while the other one does have dipole moment which is linearly polarized normal to the growth direction, like the lower energy bright exciton eigenstate. Our model agrees well with recently obtained experimental data.