Magnetic field induced circular polarization of the exciton luminescence of (In,Al)As/AlAs quantum dots with indirect band gap and type-I band alignment

The circularly polarized photoluminescence (PL) of excitons induced by application of a magnetic field is investigated experimentally and theoretically for an inhomogeneous ensemble of (In,Al)As/AlAs quantum dots with indirect band gap and type-I band alignment. We demonstrate that the circular polarization degree of the PL shows a nonmonotonic dependence on the dot size and the splitting of the oppositely polarized emission bands is significantly larger than the Zeeman splitting of the excitons in individual dots. The low-energy polarized luminescence band has lower intensity than the high-energy one. The polarization sign of the exciton emission coincides in large dots and the wetting layer, while it is opposite in small dots. A model description of this phenomenon that takes into account the equilibrium populations of long-lived exciton states is developed. The dependence of the exciton $g$ factor on the size of the quantum dot is obtained. Good agreement of the modeled spectra with the experimentally observed ones is achieved without any fitting parameters.