High performance Wannier interpolation of Berry curvature and related quantities: WannierBerri code

Abstract

Wannier interpolation is a powerful tool for performing Brillouin zone integrals over dense grids of $\mathbf{k}$ points, which are essential to evaluate such quantities as the intrinsic anomalous Hall conductivity or Boltzmann transport coefficients. However, new physical problems and new materials create new numerical challenges, and computations with the existing codes become very expensive, which often prevents reaching the desired accuracy. In this article, I present a series of methods that boost the speed of Wannier interpolation by several orders of magnitude. They include a combination of fast and slow Fourier transforms, explicit use of symmetries and recursive adaptive grid refinement among others. The proposed methodology has been implemented in the new python code WannierBerri, which also aims to serve as a convenient platform for the future development of interpolation schemes for novel phenomena.

13 pages, 5 figures, Latex, added references, fixed typos, clarified explanations, added fig 5

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• Quantum ESPRESSO toward the exascale
• First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe
• Berry phase effect in anomalous thermoelectric transport
• Computing topological invariants without inversion symmetry
• Orbital magnetization in periodic insulators
• Spectral and Fermi surface properties from Wannier interpolation
• Magnetism and anomalous transport in the Weyl semimetal PrAlGe: Possible route to axial gauge fields
• Computation of intrinsic spin Hall conductivities from first principles using maximally-localized Wannier functions
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