Statistics of closed quantum dots: Effects of disorder and interactions

We employ a fast response-function algorithm within the spin-density-functional theory to study the effects of disorder and electron-electron interactions on few-electron quantum dots. We focus on the regime between a clear shell structure and complete distortion by applying a realistic impurity model with a tunable impurity density. A drastic change in the addition-energy distribution computed from a thousand impurity configurations is observed in this regime. However, the electron-electron interactions symmetrize the distribution in accordance with the experiments. We show that the spin probabilities are sensitive to the impurities, but in the high-disorder limit the spin states stabilize and become totally independent of the corresponding single-electron level spacings.