Effect of finite spin-orbit splitting on the electron-hole exchange interaction in excitons confined in semiconductor nanocrystals

We derive an effective spin-Hamiltonian accounting for the exciton fine structure in quasi-spherical zincblende semiconductor nanocrystals within the k center dot p formalism explicitly taking into account the spin-orbit split off valence band. It is shown that, for excitons in nanocrystals made of III-V and II-VI semiconductors with fairly small spin-orbit splitting, the scaling of the electron-hole exchange interaction with the nanocrystal size insignificantly differs from the inverse nanocrystal volume law predicted within the model neglecting the spin orbit split-off band. Numerical calculations are performed for InP nanocrystals.