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Theory of excitons in cubic III-V semiconductor GaAs, InAs and GaN quantum dots: fine structure and spin relaxation

Exciton fine structures in cubic III-V semiconductor GaAs, InAs and GaN quantum dots are investigated systematically and the exciton spin relaxation in GaN quantum dots is calculated by first setting up the effective exciton Hamiltonian. The electron-hole exchange interaction Hamiltonian, which consists of the long- and short-range parts, is derived within the effective-mass approximation by taking into account the conduction, heavy- and light-hole bands, and especially the split-off band. The scheme applied in this work allows the description of excitons in both the strong and weak confinement regimes. The importance of treating the direct electron-hole Coulomb interaction unperturbatively is demonstrated. We show in our calculation that the light-hole and split-off bands are negligible when considering the exciton fine structure, even for GaN quantum dots, and the short-range exchange interaction is irrelevant when considering the optically active doublet splitting. We point out that the long-range exchange interaction, which is neglected in many previous works, contributes to the energy splitting between the bright and dark states, together with the short-range exchange interaction. Strong dependence of the optically active doublet splitting on the anisotropy of dot shape is reported. Large doublet splittings up to 600 $μ$eV, and even up to several meV for small dot size with large anisotropy, is shown in GaN quantum dots. The spin relaxation between the lowest two optically active exciton states in GaN quantum dots is calculated, showing a strong dependence on the dot anisotropy. Long exciton spin relaxation time is reported in GaN quantum dots. These findings are in good agreement with the experimental results.