The Hamiltonian generated by Wannier90 is not only useful inside Wannier90 itself. It is also widely used as an input for many external programs that perform more advanced calculations. In this sense, Wannier90 often serves as a bridge between first-principles electronic-structure calculations and specialized simulation tools.
Typical Wannier90 output files, such as seedname_hr.dat, seedname_centres.xyz, seedname_tb.dat, contain the real-space tight-binding Hamiltonian, Wannier centers, and related matrix elements. These files can be used by many post-processing programs.
Topological Materials and Surface States
Several programs use Wannier Hamiltonians to study topological properties of materials:
- WannierTools — surface band structures, surface density of states, Fermi arcs, Weyl points, Dirac points, nodal lines, Berry curvature, Wilson loops, Chern numbers, and $\mathbb{Z}_2$ topological invariants.
- Z2Pack — calculation of $\mathbb{Z}_2$ invariants and topological indices from Wannier-based tight-binding models.
- TBmodels — construction, manipulation, and symmetrization of tight-binding models derived from Wannier90.
- PythTB — simple Python-based tight-binding modeling, including models imported from Wannier90.
- WannierBerri — Berry curvature, anomalous Hall conductivity, orbital magnetization, nonlinear Hall response, and other Berry-related quantities.
Electron–Phonon Coupling and Superconductivity
Wannier functions are also essential for interpolating electron–phonon matrix elements:
- EPW — electron–phonon coupling, phonon-limited carrier mobility, superconductivity, Eliashberg spectral functions, and superconducting critical temperatures.
- Perturbo — electron–phonon interactions, carrier dynamics, ultrafast relaxation, and transport properties.
Transport Calculations
Wannier Hamiltonians are widely used to calculate electronic transport:
- BoltzTraP2 — semiclassical Boltzmann transport, electrical conductivity, Seebeck coefficient, thermal conductivity, and thermoelectric properties.
- Kwant — quantum transport in tight-binding systems, nanostructures, and devices.
- NanoDCAL — quantum transport and device simulations based on localized basis representations.
- OpenMX post-processing tools — transport and tight-binding analysis using localized orbitals and Wannier-like Hamiltonians.
Optical and Nonlinear Response
Wannier interpolation is very useful for optical calculations because it allows dense $\mathbf{k}$-space sampling at low computational cost:
- WannierBerri — optical conductivity, Berry curvature dipoles, anomalous Hall effects, nonlinear Hall effects, and related geometric response functions.
- Yambo-based workflows — many-body optical spectra, GW, BSE, and excitonic effects can be combined with Wannier-based interpolation in advanced workflows.
- WanTiBexos, WTB, Xatu, PyMEX — many research groups use Wannier90 Hamiltonians as compact input for Bethe–Salpeter equation calculations, exciton dispersion, exciton transport, and excitonic quantum geometry.
Magnetic Interactions and Spin Models
Wannier Hamiltonians can also be used to derive effective magnetic models:
- TB2J — exchange interactions, Dzyaloshinskii–Moriya interactions, magnetic anisotropy, and construction of spin Hamiltonians from Wannier-based tight-binding models.
- WannierBerri — spin Berry curvature, spin Hall conductivity, orbital magnetization, and related spin-orbit effects.
Moiré Materials and Large-Scale Tight-Binding Models
Wannier-based Hamiltonians are especially useful when the system is too large for direct first-principles calculations:
- MoireStudio, TWISTER — construction of twisted bilayers and moiré supercells combined with Wannier tight-binding models.
- PythTB — educational and research-level tight-binding models for large supercells.
- TBmodels — construction and manipulation of large tight-binding Hamiltonians.
- KITE — large-scale tight-binding simulations, density of states, conductivity, and quantum transport in large systems.
- Kwant — quantum transport in finite systems, ribbons, defects, and nanodevices.
- PyMEX - solving the Bethe–Salpeter equation in moiré exciton systems.
Many-Body and Model Hamiltonian Methods
Wannier Hamiltonians are often used as a starting point for correlated-electron calculations:
- TRIQS/DFTTools — DFT+DMFT calculations using localized correlated subspaces.
- ComDMFT — charge self-consistent DFT+DMFT workflows.
- RESPACK — construction of low-energy effective Hamiltonians, screened Coulomb interactions, and Hubbard parameters.
- ALPS-based workflows — model Hamiltonian simulations derived from Wannier tight-binding parameters.
- Custom Hubbard-model and exact-diagonalization codes (TRIQS, divERGe, HPhi, PythTB) — construction of effective models using Wannier hopping parameters.
Visualization and Analysis Tools
Wannier90 output can also be used for visualization and post-processing:
- FermiSurfer — visualization of Fermi surfaces and momentum-dependent quantities.
- XCrySDen — visualization of Wannier functions and real-space orbitals.
- VESTA — visualization of Wannier functions, charge densities, and orbital shapes.
- ParaView — visualization of large real-space volumetric data.
- Python/NumPy/SciPy workflows — custom analysis of Wannier Hamiltonians, band structures, density of states, Berry curvature, and real-space hopping amplitudes.
Ab Initio Codes Interfaced with Wannier90
Many first-principles electronic-structure codes can generate the input files required by Wannier90:
These programs provide Bloch wave functions, band energies, and overlap matrices, which Wannier90 then transforms into localized Wannier functions and compact tight-binding Hamiltonians.
In summary, Wannier90 is not only a program for constructing Wannier functions. It is a central component of a much larger computational ecosystem. Once a reliable Wannier Hamiltonian is obtained, it can be used to study band structures, topology, transport, optical response, superconductivity, electron–phonon coupling, magnetism, moiré materials, excitons, and correlated-electron physics.