Electronic structures in circular, elliptic, and triangular quantum dots

Electronic structures in circular, elliptic, and triangular shaped quantum dots containing single or a few electrons are calculated by numerically diagonalizing the $N$-electron Hamiltonian (for $N$ up to $12)$. In a circular quantum dot, the addition energy shows a clear structure as a function of $N$ due to the shell filling and the spin-polarized half filling. In an elliptic quantum dot, however, the structure is found to be diminished, which is attributed to the splitting of the degenerated single-particle states due to the asymmetric confining potential. The states with $N=3\mathrm{}$, 6, and 9 electrons in a triangular quantum dot are found to be slightly stable compared to a circular quantum dot, which is interpreted in terms of a geometrical effect.