Electron-Electron Interactions in Isolated and Realistic Quantum Dots: A Density Functional Theory Study

摘要

We use Kohn-Sham spin-density-functional theory to study the statistics ofground-state spin and the spacing between conductance peaks in the Coulombblockade regime for both 2D isolated and realistic quantum dots. We make asystematic investigation of the effects of electron-electron interactionstrength and electron number on both the peak spacing and spin distributions. Adirect comparison between the distributions from isolated and realistic dotsshows that, despite the difference in the boundary conditions and confiningpotential, the statistical properties are qualitatively the same. Strongeven/odd pairing in the peak spacing distribution is observed only in the weake-e interaction regime and vanishes for moderate interactions. The probabilityof high spin ground states increases for stronger e-e interaction and seems tosaturate around $r_s \sim 4$. The saturated value is larger than previoustheoretical predictions. Both spin and conductance peak spacing distributionsshow substantial variation as the electron number increases, not saturatinguntil $N \sim 150$. To interpret our numerical results, we analyze the spindistribution in the even $N$ case using a simple two-level model.