Shape Ellipticity Dependence of Exciton Fine Levels and Optical Nonlinearities in CdSe and CdTe Nanocrystal Quantum Dots

Shape ellipticity dependence of the exciton fine energy levels in CdTe and CdSe nanocrystal quantum dots were compared theoretically by considering the crystal structure and the Coulomb interaction of an electron and a hole. While quantum dot ellipticity changes from an oblate to prolate quantum dot via spherical shape, both the fine energy levels and the dipole moment in wurtzite structure of a CdSe quantum dot change linearly for ellipticity. In contrast, CdTe quantum dots were found to show a level crossing between the bright and dark exciton states with a significant change of the dipole moment due to the cubic structure. Shape ellipticity dependence of the optical nonlinearities in CdTe and CdSe nanocrystal quantum dots was also calculated by using semiconductor Bloch equations. For a spherical shape quantum dot, only $1^L$ dominates the optical nonlinearities in a CdSe quantum dot, but both $1^U$ and $0^U$ contribute in a CdTe quantum dot. As excitation pulse area becomes strong (${\sim}{\pi}$), the optical nonlinearities of both CdSe and CdTe quantum dots are mainly governed by absorption saturation. However, in the case of a prolate CdTe quantum dot, the real part of the nonlinear refractive index becomes relatively significant.