The primary purpose of Wannier90 is to construct Maximally Localized Wannier Functions (MLWFs) and to transform the first-principles Hamiltonian from the Bloch basis into a compact Hamiltonian in the Wannier basis. Beyond Wannierization itself, the package provides several powerful built-in capabilities:
- Construction of Maximally Localized Wannier Functions (MLWFs).
- Generation of real-space tight-binding Hamiltonians $\texttt{seedname_hr.dat}$.
- Accurate interpolation of electronic band structures on arbitrary $\mathbf{k}$-point paths.
- Calculation of densities of states (DOS).
- Calculation and visualization of Fermi surfaces.
- Visualization of Wannier functions and Wannier charge centers.
- Evaluation of Wannier spreads and localization properties.
- Calculation of Berry phases and electric polarization.
- Calculation of Berry curvature using Wannier interpolation.
- Calculation of anomalous Hall conductivity.
- Calculation of orbital magnetization.
- Calculation of spin Hall conductivity (for systems with spin–orbit coupling).
- Interpolation of position and velocity matrix elements for optical-property calculations.
The Hamiltonian produced by Wannier90 also serves as the starting point for many advanced electronic-structure methods implemented in external software packages, including calculations of electron–phonon interactions, superconductivity, excitons, transport properties, and many-body effects.
WannierTools is a separate post-processing package that uses the Wannier Hamiltonian generated by Wannier90 to investigate the electronic and topological properties of materials. Its main capabilities include:
- Calculation of surface electronic band structures.
- Surface and bulk density of states.
- Fermi surfaces and spin textures.
- Surface spectral functions.
- Berry curvature and Berry phase analysis.
- Wilson loops and Wannier charge center evolution.
- Calculation of topological invariants ($\mathbb{Z}_2$, Chern numbers).
- Identification of Weyl and Dirac points.
- Visualization of Fermi arcs on material surfaces.
- Analysis of nodal-line semimetals and other topological phases.
Together, Wannier90 and WannierTools provide a powerful workflow that starts from first-principles calculations and ends with accurate tight-binding models and detailed analysis of the electronic and topological properties of crystalline materials.