Coarse-grained tight-binding models
(2022) In Journal of Physics Condensed Matter 34(12).- Abstract
Calculating the electronic structure of systems involving very different length scales presents a challenge. Empirical atomistic descriptions such as pseudopotentials or tight-binding models allow one to calculate the effects of atomic placements, but the computational burden increases rapidly with the size of the system, limiting the ability to treat weakly bound extended electronic states. Here we propose a new method to connect atomistic and quasi-continuous models, thus speeding up tight-binding calculations for large systems. We divide a structure into blocks consisting of several unit cells which we diagonalize individually. We then construct a tight-binding Hamiltonian for the full structure using a truncated basis for the... (More)
Calculating the electronic structure of systems involving very different length scales presents a challenge. Empirical atomistic descriptions such as pseudopotentials or tight-binding models allow one to calculate the effects of atomic placements, but the computational burden increases rapidly with the size of the system, limiting the ability to treat weakly bound extended electronic states. Here we propose a new method to connect atomistic and quasi-continuous models, thus speeding up tight-binding calculations for large systems. We divide a structure into blocks consisting of several unit cells which we diagonalize individually. We then construct a tight-binding Hamiltonian for the full structure using a truncated basis for the blocks, ignoring states having large energy eigenvalues and retaining states with energies close to the band edge energies. A numerical test using a GaAs/AlAs quantum well shows the computation time can be decreased to less than 5% of the full calculation with errors of less than 1%. We give data for the trade-offs between computing time and loss of accuracy. We also tested calculations of the density of states for a GaAs/AlAs quantum well and find a ten times speedup without much loss in accuracy.
(Less)
- author
- Liu, Tian Xiang ; Mao, Li ; Pistol, Mats Erik LU and Pryor, Craig
- organization
- publishing date
- 2022-03-23
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- coarse-grained, semiconductors, tight-binding models
- in
- Journal of Physics Condensed Matter
- volume
- 34
- issue
- 12
- article number
- 125901
- publisher
- IOP Publishing
- external identifiers
-
- pmid:34920442
- scopus:85123392319
- ISSN
- 0953-8984
- DOI
- 10.1088/1361-648X/ac443f
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2022 The Author(s). Published by IOP Publishing Ltd.
- id
- f1b9a891-37d0-4088-941a-115633b231f1
- date added to LUP
- 2022-02-15 16:53:52
- date last changed
- 2024-09-19 19:55:25
@article{f1b9a891-37d0-4088-941a-115633b231f1,
abstract = {{<p>Calculating the electronic structure of systems involving very different length scales presents a challenge. Empirical atomistic descriptions such as pseudopotentials or tight-binding models allow one to calculate the effects of atomic placements, but the computational burden increases rapidly with the size of the system, limiting the ability to treat weakly bound extended electronic states. Here we propose a new method to connect atomistic and quasi-continuous models, thus speeding up tight-binding calculations for large systems. We divide a structure into blocks consisting of several unit cells which we diagonalize individually. We then construct a tight-binding Hamiltonian for the full structure using a truncated basis for the blocks, ignoring states having large energy eigenvalues and retaining states with energies close to the band edge energies. A numerical test using a GaAs/AlAs quantum well shows the computation time can be decreased to less than 5% of the full calculation with errors of less than 1%. We give data for the trade-offs between computing time and loss of accuracy. We also tested calculations of the density of states for a GaAs/AlAs quantum well and find a ten times speedup without much loss in accuracy. </p>}},
author = {{Liu, Tian Xiang and Mao, Li and Pistol, Mats Erik and Pryor, Craig}},
issn = {{0953-8984}},
keywords = {{coarse-grained; semiconductors; tight-binding models}},
language = {{eng}},
month = {{03}},
number = {{12}},
publisher = {{IOP Publishing}},
series = {{Journal of Physics Condensed Matter}},
title = {{Coarse-grained tight-binding models}},
url = {{http://dx.doi.org/10.1088/1361-648X/ac443f}},
doi = {{10.1088/1361-648X/ac443f}},
volume = {{34}},
year = {{2022}},
}