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Theory of magneto-optical properties of neutral and charged excitons in GaAs/AlGaAs quantum dots

Detailed theoretical study of the magneto-optical properties of weakly confining GaAs/AlGaAs quantum dots is provided. We focus on the diamagnetic coefficient and the $g$-factor of the neutral and the charged excitonic states, respectively, and their evolution with various dot sizes for the magnetic fields applied along $[001]$ direction. For the calculations we utilize the combination of ${\bf k}\cdot{\bf p}$ and the configuration interaction methods. We decompose the theory into four levels of precision,~i.e., (i) single-particle electron and hole states, (ii) non-interacting electron-hole pair, (iii) electron-hole pair constructed from the ground state of both quasiparticles and interacting via the Coulomb interaction (i.e. with minimal amount of correlation), and (iv) that including the effect of correlation. The aforementioned approach allows us to pinpoint the dominant influence of various single- and multi-particle effects on the studied magneto-optical properties, allowing the characterization of experiments using models which are as simple as possible, yet retaining the detailed physical picture.