Nonuniform grids for Brillouin zone integration and interpolation

Abstract

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.

19 pages, 9 figures

References in corpus (10)

• First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe
• Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
• The phonon dispersion of graphite by inelastic x-ray scattering
• First-Principles Prediction of Phononic Thermal Conductivity of Silicene: a Comparison with Graphene
• The temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation
• Non-uniform sampling schemes of the Brillouin zone for many-electron perturbation-theory calculations in reduced dimensionality
• Comparing electron-phonon coupling strength in diamond, silicon and silicon carbide: First-principles study
• Phoebe: a High-Performance Framework for Solving Phonon and Electron Boltzmann Transport Equations
• Anharmonic effects in MgB2? A comparative inelastic X-ray scattering and Raman study
• Phonons and electron-phonon coupling in graphene-h-BN heterostructures

Cited by in corpus (6)

• On the dynamical stability of copper-doped lead apatite
• Automatic, high-order, and adaptive algorithms for Brillouin zone integration
• Origin of competing charge density waves in kagome metal ScV${}_6$Sn${}_6$
• Temperature effects in topological insulators of transition metal dichalcogenide monolayers
• Low-temperature transport in high-conductivity correlated metals: a density-functional plus dynamical mean-field study of cubic perovskites
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$