Magneto-optics of a charge-tunable quantum dot: Observation of a negative diamagnetic shift

We present magneto-optical studies of a self-assembled semiconductor quantum dot in neutral and positively charged states. The diamagnetic shifts and Zeeman splitting of many well-identified optical transitions are precisely measured. Remarkably, a pronounced negative diamagnetic shift is observed for spectral lines resulting from a doubly positively charged excitonic complex. We use the Hartree-Fock approximation for describing the direct Coulomb and exchange interactions between the quantum dot confined carriers in various configurations. A simple harmonic potential model, which we extend to capture the influence of an externally applied magnetic field in Faraday configuration, is then used to quantitatively account for all the measured diamagnetic shifts. We show that the negative shift is due to the change in the hole-hole exchange interaction energy induced by the magnetic field. Using this model and the measured shifts we extract the dielectric constant of the quantum dot material and get a decent estimate of the quantum dot dimensions. Further, the measured Zeeman splitting of the various spectral lines are also explained by a simple model using algebraic sums and differences of the $g$ factors of the confined charge carriers in their respective first and second discrete energy levels. Finally, the obtained values of the electronic $g$ factor and that of the dielectric constant are independently used to determine the effective composition $(x)$ of the ternary ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum dot. Both agree to within the experimental uncertainties.