Electronic structures in coupled two quantum dots by 3D-mesh Hartree-Fock-Kohn-Sham calculation

To study the electronic structures of quantum dots in the framework of self -interaction-free including three dimensional effects, we adopt the theory of nonlocal effective potential introduced by Kohn and Sham [1]. For utiliz ing the advantageous point of the real space (3D) mesh method to solve the original nonlinear and nonlocal Hartree-Fock-Kohn-Sham (HFKS)-equation, we introduce a linearization of the equation in the local form by introducing the local Coulomb potentials which depend on explicitly the two single part icle states. In practice, for solving the local form HFKS-equation, we use the Car-Parrinello-like relaxation method and the Coulomb potentials are ob tained by solving the Poisson equation under proper boundary conditions. Fi rstly the observed energy gap between triplet- and singlet-states of N = 4 in DBS [7] is discussed to reproduce the addition energies and chemical pot entials depending the magnetic field. Next the coupling between two-quantum dots in TBS [8] is studied by adding the square barrier between two dots. The spin-degeneracy [8] measured in gate-voltage depending oil magnetic fie ld is well reproduced in the limit of small mismatch. Finally, the electron ic states in the ring structure are calculated and discussed how the ring s ize and magnetic field affect to the structures.