Optical transitions in a single CdTe spherical quantum dot

We discuss different aspects of the optical properties in a single CdTe spherical quantum dot after performing a systematic study of the eigenvalues, wave functions, and their dominant symmetries within the $8\times 8$ $\mathbf{k}\cdot \mathbf{p}$ Kane-Weiler Hamiltonian derived from the conduction-valence band coupling and the mixing of the valence states. The analysis of the inherent symmetries in the Hamiltonian leads to basis function sets separated into two Hilbert subspaces. A detailed discussion of the symmetries associated with the electronic levels and the selection rules for optical transitions are derived by considering circular polarization for the incident light. We also calculated the optical oscillator strengths and the corresponding absorption spectra in the dipole approximation. Also, we discuss the roles of nonparabolicity, valence-band admixture, and symmetry signatures of the involved states. We compare the numerical results for the electronic dispersions in a zinc-blende based quantum dot when the spherical or the axial approximations are used inside the $8\times 8$ multiband Hamiltonian.