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 - <p style="text-align: justify;">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.</p>