A General Algorithm for Calculating Irreducible Brillouin Zones (Communications in Computational Physics, 2022)
Calculations of properties of materials require performing numerical integrals over the Brillouin zone (BZ). Integration points in density functional theory codesare uniformly spread over the BZ (despite integration error being concentrated in smallregions of the BZ) and preserve symmetry to improve computational efficiency. Integration points over an irreducible Brillouin zone (IBZ), a rotationally distinct region ofthe BZ, do not have to preserve crystal symmetry for greater efficiency. This freedomallows the use of adaptive meshes with higher concentrations of points at locationsof 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 usesconvex hull and half-space representations for the BZ and IBZ to make many aspectsof construction and symmetry reduction of the BZ trivial. The algorithm is simple,general, and available as open-source software.