Nonuniform grids for Brillouin zone integration and interpolation

Article

关键词: SPECIAL POINTS;    TEMPERATURE-DEPENDENCE;    ELECTRONIC-STRUCTURE;    PHONON-DISPERSION;    DIRECT-GAP;    SEMICONDUCTORS;    MAGNONS;    SUPERCONDUCTIVITY;    ERROR;    MODES;   

DOI  :  10.1103/PhysRevB.106.155102

来源: SCIE

【 摘 要 】

We present two developments for the numerical integration of a function over the Brillouin zone. First, we introduce a nonuniform grid, which we refer to as the Farey grid, that generalizes regular grids. Second, we introduce symmetry-adapted Voronoi tessellation, a general technique to assign weights to the points in an arbitrary grid. Combining these two developments, we propose a strategy to perform Brillouin zone integration and interpolation that provides a significant computational advantage compared to the usual approach based on regular uniform grids. We demonstrate our methodology in the context of first-principles calculations with the study of Kohn anomalies in the phonon dispersions of graphene and MgB2, and in the evaluation of the electron-phonon driven renormalization of the band gaps of diamond and bismuthene. In the phonon calculations, we find speedups by a factor of 3 to 4 when using density-functional perturbation theory, and by a factor of 6 to 7 when using finite differences in conjunction with supercells. As a result, the computational expense between density functional perturbation theory and finite differences becomes comparable. For electron-phonon coupling calculations, we find even larger speedups. Finally, we also demonstrate that the Farey grid can be expressed as a combination of the widely used regular grids, which should facilitate the adoption of this methodology.

【 授权许可】

Free