  Energy spectrum fine structure of triplet two-electron states is investigated
theoretically. Spin-orbit interaction induced terms in the effective
Hamiltonian of electron-electron interaction are derived for zinc-blende
lattice semiconductor nanostructures: quantum wells and quantum dots. The
effects of bulk and structural inversion asymmetry are taken into account.
Simple analytical expressions describing the splittings of the two-electron
states localized in a single quantum dot and in a lateral double quantum dot
are derived. The spin degeneracy of triplet states is shown to be completely
lifted by the spin-orbit interaction. An interplay of the conduction band spin
splitting and the spin-orbit terms in electron-electron interaction is
discussed. The photoluminescence spectra of hot trions and of doubly charged
excitons are calculated and are shown to reveal the fine structure of
two-electron states.
