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Volume 31, Issue 2
A General Algorithm for Calculating Irreducible Brillouin Zones

Jeremy J. Jorgensen, John E. Christensen, Tyler J. Jarvis & Gus L. W. Hart

DOI: 10.4208/cicp.OA-2021-0094

Commun. Comput. Phys., 31 (2022), pp. 495-515.

Published online: 2022-01

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  • Abstract

Calculations of properties of materials require performing numerical integrals over the Brillouin zone (BZ). Integration points in density functional theory codes are uniformly spread over the BZ (despite integration error being concentrated in small regions of the BZ) and preserve symmetry to improve computational efficiency. Integration points over an irreducible Brillouin zone (IBZ), a rotationally distinct region of the BZ, do not have to preserve crystal symmetry for greater efficiency. This freedom allows the use of adaptive meshes with higher concentrations of points at locations of large error, resulting in improved algorithmic efficiency. We have created an algorithm for constructing an IBZ of any crystal structure in 2D and 3D. The algorithm uses convex hull and half-space representations for the BZ and IBZ to make many aspects of construction and symmetry reduction of the BZ trivial. The algorithm is simple, general, and available as open-source software.

  • Keywords

Brillouin zone, irreducible Brillouin zone.

  • AMS Subject Headings

68U05, 20H15, 52B55, 52C07, 68W40, 57Z05, 57Z15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-31-495, author = {Jorgensen , Jeremy J.Christensen , John E.Jarvis , Tyler J. and Hart , Gus L. W.}, title = {A General Algorithm for Calculating Irreducible Brillouin Zones}, journal = {Communications in Computational Physics}, year = {2022}, volume = {31}, number = {2}, pages = {495--515}, abstract = {

Calculations of properties of materials require performing numerical integrals over the Brillouin zone (BZ). Integration points in density functional theory codes are uniformly spread over the BZ (despite integration error being concentrated in small regions of the BZ) and preserve symmetry to improve computational efficiency. Integration points over an irreducible Brillouin zone (IBZ), a rotationally distinct region of the BZ, do not have to preserve crystal symmetry for greater efficiency. This freedom allows the use of adaptive meshes with higher concentrations of points at locations of large error, resulting in improved algorithmic efficiency. We have created an algorithm for constructing an IBZ of any crystal structure in 2D and 3D. The algorithm uses convex hull and half-space representations for the BZ and IBZ to make many aspects of construction and symmetry reduction of the BZ trivial. The algorithm is simple, general, and available as open-source software.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0094}, url = {http://global-sci.org/intro/article_detail/cicp/20213.html} }
TY - JOUR T1 - A General Algorithm for Calculating Irreducible Brillouin Zones AU - Jorgensen , Jeremy J. AU - Christensen , John E. AU - Jarvis , Tyler J. AU - Hart , Gus L. W. JO - Communications in Computational Physics VL - 2 SP - 495 EP - 515 PY - 2022 DA - 2022/01 SN - 31 DO - http://doi.org/10.4208/cicp.OA-2021-0094 UR - https://global-sci.org/intro/article_detail/cicp/20213.html KW - Brillouin zone, irreducible Brillouin zone. AB -

Calculations of properties of materials require performing numerical integrals over the Brillouin zone (BZ). Integration points in density functional theory codes are uniformly spread over the BZ (despite integration error being concentrated in small regions of the BZ) and preserve symmetry to improve computational efficiency. Integration points over an irreducible Brillouin zone (IBZ), a rotationally distinct region of the BZ, do not have to preserve crystal symmetry for greater efficiency. This freedom allows the use of adaptive meshes with higher concentrations of points at locations of large error, resulting in improved algorithmic efficiency. We have created an algorithm for constructing an IBZ of any crystal structure in 2D and 3D. The algorithm uses convex hull and half-space representations for the BZ and IBZ to make many aspects of construction and symmetry reduction of the BZ trivial. The algorithm is simple, general, and available as open-source software.

Jorgensen , Jeremy J.Christensen , John E.Jarvis , Tyler J. and Hart , Gus L. W.. (2022). A General Algorithm for Calculating Irreducible Brillouin Zones. Communications in Computational Physics. 31 (2). 495-515. doi:10.4208/cicp.OA-2021-0094
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