Mixed singlet-triplet trion states in quantum dot molecules: A spatial-dependent spin-splitting effect

Trion states in semiconductor double quantum dots can be a mix of spin-singlet and spin-triplet states. Experimental studies have invoked different mechanisms as the origin for this spin mixing, namely, (i) the electron-hole exchange interaction and (ii) the carrier spin interaction with the nuclear spins of the host semiconductor. We have investigated the effects of the spin mixing on the X+ trion (two holes and one electron) in an asymmetric double dot under applied electric field. The trion problem is solved numerically for a quasi-one-dimensional system, and the singlet-triplet mixing is treated by spatial-dependent spin splittings having the characteristics of the two mechanisms mentioned above. Our calculation reproduces many of the experimentally observed features of the trion optical spectra under applied electric field, and it shows that the mechanisms (i) and (ii) yield similar trion optical spectra, but with some differences that can be used to identify the dominant mechanism causing the singlet-triplet mixing.