Polarized photoluminescence and g-factor in an inhomogeneous ensemble of quantum dots in magnetic fields

In this work, polarized photoluminescence caused by quasi-equilibrium spin orientation of excitons at Zeeman sublevels in an ensemble of quantum dots of different sizes is studied theoretically. The following unexpected results are found: (i) the splitting of photoluminescence bands in a magnetic field in an ensemble of quantum dots is much larger than the Zeeman splitting of exciton levels in a single dot, (ii) contrary to the Boltzmann distribution the low-energy luminescence band has a lower intensity than the high-energy band, (iii) the sign of the circular polarization of photoluminescence changes along the contour of the bands, (iv) a universal formula for the dependence of the exciton g-factor on the quantum dot size is obtained. All of the above features of the polarized luminescence spectra are explained by variations of the exciton g-factor when its quantization energy changes. The results obtained are applicable not only to ensembles of quantum dots, but also to any ensemble of localized states: excitons in quantum wells under conditions of well-width fluctuations, impurity states in quantum wells, etc. •In this work, the magnetic field induced polarized luminescence of excitons, in an ensemble of quantum dots of different sizes, has been investigated. It was found that (i) the splitting of luminescence band maxima is several orders of magnitude greater than the Zeeman splitting in each individual quantum dot. (ii) the low-energy luminescence band has a lower intensity than the high-energy band. That, at first sight, contradicts the Boltzmann distribution of excitons on Zeeman sublevels. (iii) the effects described in (i) and (ii) take place only if the exciton g-factor depends on the dot size and changes sign when the dot size changes. (iv) if the change of sign of the g-factor occurs at energies above the maximum of the emission bands, i.e., for dots of small size, the ratio of band intensities becomes “correct” (corresponding to the Boltzmann distribution). (v) the theory of the dependence of the exciton g-factor on the dot size is constructed. A universal formula for the dependence of the g-factor on the quantum dot size is obtained. This dependence is valid both for bulk material and for nanostructures of different types and sizes: quantum wells, quantum filaments and quantum dots.