Electron-electron interactions in square quantum dots

We investigate the electronic structure of quasi-two-dimensional square quantum dots by using the spin-density functional theory. In the weak interacting regime, we identify shell fillings due to Hund’s rule and calculate the electron-number-dependent addition energies of the dots. To understand the interplay between the kinetic energy and Coulomb energy we examine the ground-state spin and charge configurations by varying size of the dot. We estimate the existence of the Wigner-molecule-like state at a critical mean distance parameter $r_s\sim {6a}_B^{*}.$