Wannier-Function-Based Translation-Invariant Computation of Orbital Magnetization and Spin Hall Conductivity

Wannier interpolation is the technique that uses Wannier functions to compute various physical quantities represented as Brillouin zone integrals. Thanks to the localized nature of the Wannier function, we can interpolate many quantities rapidly varying in momentum space from a coarse ab initio grid to a fine interpolation grid. However, due to numerical approximations such as the finite-difference formula, the convergence rate with respect to the ab initio grid in Wannier interpolation is often slow. Also, the translation invariance is violated when using the naive finite-difference formula, that is, the results change significantly when the system is translated as a whole.

In this talk, we will extend the translation-invariant finite-difference formula presented in [1] to Wannier matrix elements needed for the Wannier interpolation of orbital magnetization and spin Hall conductivity. We will show that while the derivation and implementation are straightforward, the improvement in the convergence rate is substantial. We thus demonstrate that the use of our formalism is essential for an accurate and efficient Wannier interpolation.

[1] J.-M. Lihm, M. Ghim, and C.-H. Park, "Accurate calculation of position matrix elements for Wannier interpolation, Part 1: translational invariance", Wanner 2022 Developers Meeting, Trieste, Italy (2022). https://indico.ictp.it/event/9851/0