Software implementation for calculating the Chern and $Z_2$ topological invariants with WIEN2k all-electron density functional package

Abstract

We present two modules that expand functionalities of the all-electron full-potential density functional theory package WIEN2k for computation of the Chern and $Z_2$ topological invariants. Characterization of topological properties relies on two methods: computing an evolution of hybrid Wannier charge centers for $Z_2$ topological insulators (construction of maximally localized Wannier functions is not needed) and computing the Berry phase for a multitude of Wilson loops that discretize a 2D Brillouin zone for Chern insulators as well as for mapping the Berry curvature. The implementation is validated by testing on well-known materials that feature topologically non-trivial electronic states.