Wannier functions are used far beyond the Wannier90 code itself. The Hamiltonian generated by Wannier90 is not only useful inside Wannier90, but is also widely used as an input for 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, and 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 for calculations of electronic transport, topology, electron–phonon coupling, optical properties, many-body effects, and other physical phenomena.
This page has two related goals. First, it provides examples of external programs that interface directly with Wannier90 or use data generated by it. Second, it introduces alternative methods for constructing Wannier functions or related localized orbitals without using Wannier90.
Programs That Use Wannier90
The programs in this section either interface directly with Wannier90 or use Wannier90 output files, such as the real-space Hamiltonian seedname_hr.dat.
Wannier90 is normally used to transform Bloch states obtained from a first-principles calculation into a compact localized basis. External programs then use this basis to calculate physical properties that may not be available directly in the original DFT code.
These applications include:
- electronic transport;
- topological properties;
- electron–phonon interactions;
- optical and nonlinear optical response;
- dynamical mean-field theory;
- excitonic calculations;
- model Hamiltonians and many-body simulations.
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, WannierBSE, and Xatu use Wannier-based tight-binding representations as an efficient starting point for Bethe–Salpeter equation calculations, enabling studies of exciton energies and wavefunctions, optical spectra, exciton dispersion and transport, and excitonic quantum geometry.
- PyMEX is specialized for excitonic calculations in moiré materials, where Wannier-based models provide an efficient description of large supercells and spatially varying excitonic states.
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.
- DMFTwDFT3 — DFT+DMFT calculations of strongly correlated materials using orbital-dependent many-body self-energies.
- ComDMFT — charge self-consistent DFT+DMFT workflows.
- 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.
Independent Methods for Constructing Wannier Functions
Wannier90 is one of the most widely used implementations of Wannier functions, but it is not the only possible approach. Several electronic-structure packages contain their own algorithms for constructing Wannier functions or related localized orbitals.
These implementations can be divided into three broad groups.
1. Iterative Construction of Maximally Localized Wannier Functions
In this approach, a unitary transformation among the Bloch states is optimized by minimizing the spatial spread of the resulting Wannier functions. For entangled bands, an additional disentanglement procedure is used to identify an optimal low-energy subspace.
This is conceptually closest to the standard method implemented in Wannier90.
Examples include:
- RESPACK — construction of low-energy effective Hamiltonians, screened Coulomb interactions, and Hubbard parameters. RESPACK contains its own independent implementation of disentanglement and spread minimization and does not use Wannier90. The resulting Wannier basis is used to calculate hopping parameters, screened Coulomb interactions, and low-energy effective Hamiltonians.
- JDFTx — contains an internal Wannier module that constructs localized functions and treats both isolated and entangled groups of bands.
- OpenMX — provides an internal implementation of maximally localized Wannier functions, while also offering a separate interface to the external Wannier90 program.
2. Direct Projection and Algebraic Wannier Constructions
These methods construct a localized basis directly from projections, singular-value decompositions, density matrices, or selected localized trial orbitals. They may avoid the iterative spread-minimization procedure used for MLWFs.
Such approaches are often faster and more automatic, although the resulting functions are not necessarily maximally localized according to the Marzari–Vanderbilt spread functional.
Examples include:
- VASP LOCPROJ — constructs Wannier orbitals from projections onto localized orbitals using a single-step singular-value decomposition.
- VASP SCDM — uses selected columns of the density matrix to automatically construct a Wannier basis.
- OpenMX Closest Wannier Functions (CWFs) — constructs Wannier functions that remain as close as possible to physically selected pseudo-atomic, hybrid, or molecular guiding orbitals while also allowing disentanglement.
3. Localization of Occupied or Partially Occupied Orbitals
A third group of methods localizes occupied or selected partially occupied orbitals using criteria such as Boys localization, Berry-phase localization, Pipek–Mezey localization, or related spread measures.
These localized orbitals are often used to analyze chemical bonding, polarization, molecular dynamics, charge transfer, and local electronic structure. They are closely related to Wannier functions, although they are not always intended for band interpolation or the construction of a complete low-energy tight-binding Hamiltonian.
Examples include:
- CP2K — contains internal localization methods for occupied and partially occupied orbitals, including Wannier-type localization and gradient-ascent localization for partially occupied states.
- ASE/GPAW — provides an independent Wannier localization procedure that can construct localized orbitals from GPAW wave functions.
CP2K also provides a separate interface to Wannier90, so its internal orbital-localization methods and its Wannier90 workflow should be regarded as distinct options.
These three groups should not be viewed as completely separate definitions of Wannier functions. All of them construct localized combinations of extended electronic states, but they differ in the localization criterion, treatment of entangled bands, level of automation, and intended physical application.
Wannier90 remains particularly important because it provides a general and transferable framework for constructing maximally localized Wannier functions and exporting the resulting Hamiltonians and matrix elements to a large ecosystem of external simulation programs.