A statistical model of quantum dot arrays with Coulomb coupling

We present a study of a statistical model of arrays of quantum dots, in which electrons are confined by semiconductor heterojunctions in all three dimensions, with Coulomb coupling. Our model describes repulsively interacting localized electrons whose number can vary with changes in chemical potential. By means of a Monte Carlo simulation, it is shown that, at low temperatures, some stable electron densities hardly changing in certain ranges of chemical potential appear, which are associated with suppressed fluctuation and characteristic spatial electron distributions. Spin fluctuation, which gives magnetic susceptibility, exhibits essentially different behavior depending on temperature and Coulomb energies