A numerical method for exact diagonalization of semiconductor quantum dot model. (English) Zbl 1205.82139
Summary: 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.
MSC:
| 82D37 | Statistical mechanics of semiconductors |
| 81V65 | Quantum dots as quasi particles |
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 65F10 | Iterative numerical methods for linear systems |
| 82-08 | Computational methods (statistical mechanics) (MSC2010) |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
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