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Title: On optimizing Jacobi–Davidson method for calculating eigenvalues in low dimensional structures using eight band k · p model

Abstract

The paper presents two ways of improving the Jacobi–Davidson method for calculating the eigenvalues and eigenvectors described by eight-band k · p model for quantum dots and other low dimensional structures. First, the method is extended by the application of time reversal symmetry operator. This extension allows efficient calculations of the twofold degeneracy present in the multiband k · p model and other interior eigenvalues. Second, the preconditioner for the indefinite matrix which comes from the discretization of the eight band k · p Hamiltonian is presented. The construction of this preconditioner is based on physical considerations about energy band structure in the k · p model. On the basis of two real examples, it is shown that the preconditioner can significantly shorten the time needed to calculate the interior eigenvalues, despite the fact that the memory usage of the preconditioner and Hamiltionian is comparable. Finally, some technical details for implementing the eight band k · p Hamiltonian and the eigensolver are provided.

Authors:
Publication Date:
OSTI Identifier:
22230790
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 249; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 77 NANOSCIENCE AND NANOTECHNOLOGY; COMPARATIVE EVALUATIONS; EIGENVALUES; EIGENVECTORS; ELECTRONIC STRUCTURE; HAMILTONIANS; MATRICES; OPTIMIZATION; QUANTUM DOTS; SYMMETRY

Citation Formats

Andrzejewski, Janusz. On optimizing Jacobi–Davidson method for calculating eigenvalues in low dimensional structures using eight band k · p model. United States: N. p., 2013. Web. doi:10.1016/J.JCP.2013.04.003.
Andrzejewski, Janusz. On optimizing Jacobi–Davidson method for calculating eigenvalues in low dimensional structures using eight band k · p model. United States. https://doi.org/10.1016/J.JCP.2013.04.003
Andrzejewski, Janusz. 2013. "On optimizing Jacobi–Davidson method for calculating eigenvalues in low dimensional structures using eight band k · p model". United States. https://doi.org/10.1016/J.JCP.2013.04.003.
@article{osti_22230790,
title = {On optimizing Jacobi–Davidson method for calculating eigenvalues in low dimensional structures using eight band k · p model},
author = {Andrzejewski, Janusz},
abstractNote = {The paper presents two ways of improving the Jacobi–Davidson method for calculating the eigenvalues and eigenvectors described by eight-band k · p model for quantum dots and other low dimensional structures. First, the method is extended by the application of time reversal symmetry operator. This extension allows efficient calculations of the twofold degeneracy present in the multiband k · p model and other interior eigenvalues. Second, the preconditioner for the indefinite matrix which comes from the discretization of the eight band k · p Hamiltonian is presented. The construction of this preconditioner is based on physical considerations about energy band structure in the k · p model. On the basis of two real examples, it is shown that the preconditioner can significantly shorten the time needed to calculate the interior eigenvalues, despite the fact that the memory usage of the preconditioner and Hamiltionian is comparable. Finally, some technical details for implementing the eight band k · p Hamiltonian and the eigensolver are provided.},
doi = {10.1016/J.JCP.2013.04.003},
url = {https://www.osti.gov/biblio/22230790}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = ,
volume = 249,
place = {United States},
year = {Sun Sep 15 00:00:00 EDT 2013},
month = {Sun Sep 15 00:00:00 EDT 2013}
}