Electronic Phase Diagrams of Carriers in Self-Assembled Quantum Dots: Violation of Hund’s Rule and the Aufbau Principle for Holes

We study the ground-state orbital and spin configurations of up to six electrons or holes loaded into self-assembled $\mathrm{InAs}/\mathrm{GaAs}$ quantum dots. We use a general phase-diagram approach constructed from single-particle pseudopotential and many-particle configuration interaction methods. The predicted hole charging energies agree with recent charging experiments, but offer a different interpretation: we find that while the charging of electrons follows both Hund’s rule and the Aufbau principle, the charging of holes follows a nontrivial charging pattern which violates both the Aufbau principle and Hund’s rule.

Figure 1

(Left) The ground-state configurations (a) calculated from 2D parabolic model, (b) suggested by Reuter et al [15], and (c) calculated from pseudopotential-CI method. (Right) The phase-diagrams for $N=4$, 5, 6 electrons and holes (a) calculated from 2D parabolic model, (b) for electrons using realistic Coulomb and exchange integrals, and (c) for holes using realistic Coulomb and exchange integrals. For $N=6$, ${\delta }_{d_1,d_2}={\delta }_{p_1,p_2}$ is assumed. Symbols denote the stablest configurations for specific dots: circles represent electrostatic dots, while lenses represent self-assembled dots. The configurations of phases are given by Eqs. (2, 3, 4).