A numerical method for exact diagonalization of semiconductor quantum dot model
Resource
Computer Physics Communications, 181(5), 937-946
Journal
Computer Physics Communications
Pages
937-946
Date Issued
2010
Date
2010
Author(s)
Chen, Jen-Hao
Liu, Jinn-Liang
Abstract
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. © 2010 Elsevier B.V. All rights reserved.
Type
journal article
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