A general algorithm for calculating irreducible Brillouin zones

TL;DR

This paper introduces a versatile algorithm for constructing irreducible Brillouin zones in 2D and 3D, enabling more efficient numerical integrations in material property calculations by allowing adaptive meshing without symmetry constraints.

Contribution

The authors present a simple, general, open-source algorithm that constructs IBZ for any crystal structure using convex hull and half-space representations.

Findings

Algorithm effectively constructs IBZ for various crystal structures.

Allows adaptive meshing with higher point density at error-prone regions.

Improves computational efficiency in density functional theory calculations.

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.