Fine structure of the quantum-dot trion

A theory of the fine structure of the excited state of the quantum-dot trion, which is due to spin-spin interactions, is presented. In particular, it is shown that the fine structure is universal for both positive (two holes, one electron) and negative (two electrons, one hole) trions. It consists of four doublets, three of them forming a compact group of levels separated from the remaining doublet by the energy of the exchange interaction between identical particles (i.e. between two electrons or two holes). The energy separation between the adjacent doublets in the six-level group is of the order of the much smaller energy of the exchange interaction between particles belonging to different bands, i.e. of the exciton exchange energy.