A numerical method for exact diagonalization of semiconductor quantum dot model

An approach to the exact diagonalization of many-electron Hamiltonian in semiconductor quantum dot (QD) structures is proposed. The QD model is based on 3D finite hard-wall confinement potential and nonparabolic effective-mass approximation (EMA) that render analytical basis functions such as Laguerre polynomials inaccessible for the numerical treatment of this kind of models. 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 EMA which results in a cubic eigenvalue problem from a finite difference discretization. The nonlinear eigenvalue problem is solved by using the Jacobi–Davidson method. The Coulomb matrix elements in the many-electron Hamiltonian are obtained by solving Poisson's problems via GMRES. Numerical results reveal that a good convergence can be achieved by means of a few single-electron basis states.