Exciton fine structure in CdSe nanoclusters

The fine structure in the CdSe nanocrystal absorption spectrum is computed by incorporating two-particle electron-hole interactions and spin-orbit coupling into a tight-binding model, with an expansion in electron-hole single-particle states. The exchange interaction and spin-orbit coupling give rise to dark, low-lying states that are predominantly triplet in character, as well as to a manifold of exciton states that are sensitive to the nanocrystal shape. Near the band gap, the exciton degeneracies are in qualitative agreement with the effective mass approximation (EMA). However, instead of the infinite lifetimes for dark states characteristic of the EMA, we obtain finite radiative lifetimes for the dark states. In particular, for the lowest, predominantly triplet, states we obtain radiative lifetimes of microseconds, in qualitative agreement with the experimental measured lifetimes. The resonant Stokes shifts obtained from the splitting between the lowest dark and bright states are also in good agreement with experimental values for larger crystallites. Higher-lying states exhibit significantly more complex behavior than predicted by EMA, due to extensive mixing of electron-hole pair states.