Magneto-optical response of CdSe nanostructures

We present theoretical calculations of the Lande g factors of semiconductor nanostructures using a time-dependent empirical tight-binding method that allows a nonperturbative treatment of both the spin-orbit interaction and an external magnetic field. The electromagnetic field is incorporated into the tight-binding Hamiltonian in a gauge-invariant form. Eigenenergies and eigenfunctions of the band edge states are calculated as a function of the external magnetic field, and the g factors are then extracted from the field-induced energy splitting of the eigenstates. The size and aspect ratio dependence of both electron and hole g factors are investigated for CdSe nanostructures. We find that the electron g factors for single nanocrystals are weakly dependent on nanocrystal size and are strongly anisotropic, where the extent of anisotropy depends on the aspect ratio of the nanocrystal. The hole g factors are also anisotropic and are found to show more complex, oscillatory behavior as a function of size, due to a size-dependent mixing between the heavy hole-light hole components of the valence band edge states. The calculated electron g factor values are seen to be in good quantitative agreement with experimental measurements, suggesting that the multiple g factor values extracted from time resolved Faraday rotation experiments may be due to distinguishable components of the electron g factor tensor. Extension to the calculation of exciton g factors appears feasible with this approach.