演講訊息 TALKS

In the talk, I will shortly introduce two approaches for semiconductor quantumdots. First, we present a theoretical model based on the current spin density functional theory for the three vertically aligned semiconductor quantum dots. This quantum dot molecule model is treated with realistic hard-wall confinement potential and external magnetic field. Using the effective-mass approximation with band nonparabolicity, the many-body Hamiltonian results in a cubic eigenvalue problem from a finite difference discretization. A self-consistent algorithm for solving the Schr¨odinger-Poisson system by using the Jacobi-Davidson method and GMRES is given to illustrate the Kohn-Sham orbitals and energies of six electrons in the molecule with some magnetic fields. It is shown that the six electrons residing in the central dot at zero magnetic field can be changed to such that each dot contains two electrons with some feasible magneticfield. Next,weintroduce the exact diagonalization of many-electron Hamiltonian in semiconductor quantum dot structures. In this approach, the many-electron wave function is expanded in a basis of Slater determinants constructed from numerical wave functions of the single-electron Hamiltonian with the nonparabolic effectivemass approximation which results in a cubic eigenvalue problem from a finite difference discretization. Numerical results reveal that a good convergence can be achieved by means of a few single-electron basis states.