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

TL;DR

This study uses density functional theory to analyze how electron-electron interactions influence ground-state spin and conductance peak spacing in quantum dots, revealing that interaction strength and electron number significantly affect these properties.

Contribution

It provides a systematic comparison of isolated and realistic quantum dots, showing qualitative similarity in their statistical properties and exploring the effects of interaction strength and electron number.

Findings

Strong even/odd pairing occurs only at weak interactions.

High spin states become more probable with stronger interactions.

Distributions vary significantly with electron number, saturating near N=150.

Abstract

We use Kohn-Sham spin-density-functional theory to study the statistics of ground-state spin and the spacing between conductance peaks in the Coulomb blockade regime for both 2D isolated and realistic quantum dots. We make a systematic investigation of the effects of electron-electron interaction strength and electron number on both the peak spacing and spin distributions. A direct comparison between the distributions from isolated and realistic dots shows that, despite the difference in the boundary conditions and confining potential, the statistical properties are qualitatively the same. Strong even/odd pairing in the peak spacing distribution is observed only in the weak e-e interaction regime and vanishes for moderate interactions. The probability of high spin ground states increases for stronger e-e interaction and seems to saturate around $r_s \sim 4$. The saturated value is larger than previous theoretical predictions. Both spin and conductance peak spacing distributions show substantial variation as the electron number increases, not saturating until $N \sim 150$. To interpret our numerical results, we analyze the spin distribution in the even $N$ case using a simple two-level model.