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

TL;DR

This paper introduces WannierBerri, a Python code that significantly accelerates Wannier interpolation for Berry curvature calculations, enabling more efficient and accurate Brillouin zone integrations for various physical properties.

Contribution

The paper presents new methods and a Python implementation that drastically improve the speed and efficiency of Wannier interpolation for Berry curvature and related quantities.

Findings

Achieved several orders of magnitude speedup in Wannier interpolation

Implemented symmetry exploitation and adaptive grid refinement techniques

Provided a versatile Python platform for future interpolation developments

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.