The Wannier Function Software Ecosystem for Materials Simulations

Abstract

Over the last two decades, following the early developments on maximally localized Wannier functions, an ecosystem of electronic-structure simulation techniques and software packages leveraging the Wannier representation has flourished. This environment includes codes to obtain Wannier functions and interfaces with first-principles simulation software, as well as an increasing number of related post-processing packages. Wannier functions can be obtained for isolated or extended systems (both crystalline and disordered), and can be used to understand chemical bonding, to characterize electric polarization, magnetization, and topology, or as an optimal basis set, providing very accurate interpolations in reciprocal space or large-scale Hamiltonians in real space. In this review, we summarize the current landscape of techniques, materials properties and simulation codes based on Wannier functions that have been made accessible to the research community, and that are now well integrated into what we term a \emph{Wannier function software ecosystem}. First, we introduce the theory and practicalities of Wannier functions, starting from their broad domains of applicability to advanced minimization methods using alternative approaches beyond maximal localization. Then we define the concept of a Wannier ecosystem and its interactions and interoperability with many quantum simulations engines and post-processing packages. We focus on some of the key properties and capabilities that are empowered by such ecosystem\textemdash from band interpolations and large-scale simulations to electronic transport, Berryology, topology, electron-phonon couplings, dynamical mean-field theory, embedding, and Koopmans functionals\textemdash concluding with the current status of interoperability and automation. [...]

Review article, revised version, 60 pages, 12 figures, references in alphabetical order. To appear in Rev. Mod. Phys. https://journals.aps.org/rmp/accepted/e3072EabZ471ee0bd0ff81e5ef7e01214bbaff57a

References in corpus (294)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Topological Insulators
• The SIESTA method for ab initio order-N materials simulation
• Efficient index handling of multidimensional periodic boundary conditions
• Phonons and related properties of extended systems from density-functional perturbation theory
• Quantum Spin Hall Effect in Graphene
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• BoltzTraP. A code for calculating band-structure dependent quantities
• Density functional method for nonequilibrium electron transport
• Berry Phase Effects on Electronic Properties
• Topological Insulators in Three Dimensions
• Weyl and Dirac Semimetals in Three Dimensional Solids
• CP2K: An Electronic Structure and Molecular Dynamics Software Package -- Quickstep: Efficient and Accurate Electronic Structure Calculations
• Wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions
• Maximally localized Wannier functions: Theory and applications
• WannierTools: An open-source software package for novel topological materials
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Maximally-localized Wannier functions for entangled energy bands
• Quantum Spin Hall Effect
• Topological Crystalline Insulators
• Wannier90 as a community code: new features and applications
• BoltzTraP2, a program for interpolating band structures and calculating semi-classical transport coefficients
• Topological quantum chemistry
• Electron-phonon interactions from first principles
• EPW: Electron-phonon coupling, transport and superconducting properties using maximally localized Wannier functions
• Kwant: a software package for quantum transport
• Recent developments in the PySCF program package
• Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
• The (High Quality) Topological Materials In The World
• Anomalous Hall Effect and Magnetic Monopoles in Momentum-Space
• First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe
• Catalogue of Topological Electronic Materials
• An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
• Frequency-dependent local interactions and low-energy effective models from electronic structure calculations
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Nonequilibrium dynamical mean-field theory and its applications
• Topological nodal line semimetals
• Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry
• Topological classification of crystalline insulators through band structure combinatorics
• AiiDA: Automated Interactive Infrastructure and Database for Computational Science
• Topological Anderson Insulator
• Dynamical Mean-Field Theory within the Full-Potential Methods: Electronic structure of Ce-115 materials
• Berry phase effect in anomalous thermoelectric transport
• Berry phase correction to electron density of states in solids
• Ab initio calculation of the anomalous Hall conductivity by Wannier interpolation
• Computing topological invariants without inversion symmetry
• Many-body perturbation theory calculations using the yambo code
• EPW: A program for calculating the electron-phonon coupling using maximally localized Wannier functions
• Theory of the topological Anderson insulator
• TRIQS: A Toolbox for Research on Interacting Quantum Systems
• Wien2wannier: From linearized augmented plane waves to maximally localized Wannier functions
• Mott transition and suppression of orbital fluctuations in orthorhombic 3$d^1$ perovskites
• Orbital magnetization in periodic insulators
• Wannier representation of Z_2 topological insulators
• Multiplet ligand-field theory using Wannier orbitals
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials
• Anharmonic free energies and phonon dispersions from the stochastic self-consistent harmonic approximation: application to platinum and palladium hydrides
• Self-consistent hybrid functional for condensed systems
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• Anisotropic Migdal-Eliashberg theory using Wannier functions
• Exponential localization of Wannier functions in insulators
• Spectral and Fermi surface properties from Wannier interpolation
• Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems
• Materials Cloud, a platform for open computational science
• i-PI 2.0: A Universal Force Engine for Advanced Molecular Simulations
• Quantum Crystal Structure in the 250 K Superconducting Lanthanum Hydride
• Fröhlich electron-phonon vertex from first principles
• First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials
• BoltzWann: A code for the evaluation of thermoelectric and electronic transport properties with a maximally-localized Wannier functions basis
• Simulation of Graphene Nanoribbon Field Effect Transistors
• Towards predictive many-body calculations of phonon-limited carrier mobilities in semiconductors
• TB2J: a python package for computing magnetic interaction parameters
• The Individual and Collective Effects of Exact Exchange and Dispersion Interactions on the Ab Initio Structure of Liquid Water
• Quantitative mappings between symmetry and topology in solids
• AiiDA 1.0, a scalable computational infrastructure for automated reproducible workflows and data provenance
• Mapping topological order in coordinate space
• Full orbital calculation scheme for materials with strongly correlated electrons
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Numerical study of the topological Anderson insulator in HgTe/CdTe quantum wells
• Perturbo: a software package for ab initio electron-phonon interactions, charge transport and ultrafast dynamics
• First-principles method for electron-phonon coupling and electron mobility: Applications to 2D materials
• Ab-initio transport properties of nanostructures from maximally-localized Wannier functions
• First-Principles Theory of Anharmonicity and the Inverse Isotope Effect in Superconducting Palladium-Hydride Compounds
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Turbo charging time-dependent density-functional theory with Lanczos chains
• Koopmans' condition for density-functional theory
• A new and efficient approach to time-dependent density-functional perturbation theory for optical spectroscopy
• Conserving GW scheme for nonequilibrium quantum transport in molecular contacts
• One-shot calculation of temperature-dependent optical spectra and phonon-induced band-gap renormalization
• Efficient implementation of the GW approximation within the all-electron FLAPW method
• Towards high-throughput superconductor discovery via machine learning
• Two-dimensional Fröhlich interaction in transition-metal dichalcogenide monolayers: Theoretical modeling and first-principles calculations
• The Stochastic Self-Consistent Harmonic Approximation: Calculating Vibrational Properties of Materials with Full Quantum and Anharmonic Effects
• Orthogonal Polynomial Representation of Imaginary-Time Green's Functions
• Dynamical mean-field theory using Wannier functions: a flexible route to electronic structure calculations of strongly correlated materials
• TRIQS/DFTTools: A TRIQS application for ab initio calculations of correlated materials
• Wannier Center Sheets in Topological Insulators
• Band Structure and Quantum Conductance of Nanostructures from Maximally-Localized Wannier Functions: The Case of Functionalized Carbon Nanotubes
• Topological Materials Discovery from Crystal Symmetry
• Order-N implementation of exact exchange in extended systems
• Phonon-assisted optical absorption in silicon from first principles
• Calculation of intrinsic spin Hall conductivity by Wannier interpolation
• Ab initio calculation of the shift photocurrent by Wannier interpolation
• Efficient implementation of the nonequilibrium Green function method for electronic transport calculations
• Symmetry Demanded Topological Nodal-line Materials
• Workflows in AiiDA: Engineering a high-throughput, event-based engine for robust and modular computational workflows
• The insulator/Chern-insulator transition in the Haldane model
• Wannier interpolation of the electron-phonon matrix elements in polar semiconductors: Polar-optical coupling in GaAs
• Theory of quasiparticle spectra for Fe, Co, and Ni: bulk and surface
• Maximally Localized Wannier Functions within the FLAPW formalism
• Fermi-surface calculation of the anomalous Hall conductivity
• High performance Wannier interpolation of Berry curvature and related quantities: WannierBerri code
• Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations
• w2dynamics: Local one- and two-particle quantities from dynamical mean field theory
• Electron localization in the insulating state: application to crystalline semiconductors
• Adiabatic and non-adiabatic phonon dispersion in a Wannier function approach
• Triviality of Bloch and Bloch-Dirac bundles
• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• GW method with the self-consistent Sternheimer equation
• Polarons from first principles, without supercells
• Momentum-resolved spectral functions of SrVO${}_3$ calculated by LDA+DMFT
• Double Counting in LDA+DMFT - The Example of NiO
• Spinless Topological Insulators without Time-Reversal Symmetry
• Electron-Phonon Coupling from $\text{Ab Initio}$ Linear-Response Theory within the $GW$ Method: Correlation-Enhanced Interactions and Superconductivity in Ba${}_{1-x}$K${}_x$BiO${}_3$
• The alpha to gamma transition in Ce: a theoretical view from optical spectroscopy
• Exciton-Phonon Interaction and Relaxation Times from First Principles
• Molecular transport calculations with Wannier functions
• First-principles predictions of Hall and drift mobilities in semiconductors
• Graph Theory Data for Topological Quantum Chemistry
• Edge modes in band topological insulators
• Why Two-Dimensional Semiconductors Generally Have Low Electron Mobility
• Theory of the special displacement method for electronic structure calculations at finite temperature
• Band gaps of crystalline solids from Wannier-localization based optimal tuning of a screened range-separated hybrid functional
• Composite Weyl nodes stabilized by screw symmetry with and without time reversal
• Electron-Phonon Beyond Fröhlich: Dynamical Quadrupoles in Polar and Covalent Solids
• RESPACK: An ab initio tool for derivation of effective low-energy model of material
• Unified understanding of superconductivity and Mott transition in alkali-doped fullerides from first principles
• Koopmans-compliant functionals and their performance against reference molecular data
• Signatures of electronic correlations in iron silicide
• Wannier-based calculation of the orbital magnetization in crystals
• Phonon-limited electron mobility in Si, GaAs and GaP with exact treatment of dynamical quadrupoles
• Chiral degeneracies and Fermi-surface Chern numbers in bcc Fe
• Symmetry-adapted Wannier functions in the maximal localization procedure
• Antiferromagnetism and the gap of a Mott insulator: Results from analytic continuation of the self-energy
• Efficient and realistic device modeling from atomic detail to the nanoscale
• Abundance of ${\mathbb{Z}}_2$ topological order in exfoliable two-dimensional insulators
• Piezoelectric Electron-Phonon Interaction from Ab Initio Dynamical Quadrupoles: Impact on Charge Transport in Wurtzite GaN
• The magnetic excitation spectra in BaFe${}_2$As${}_2$: a two-particle approach within DFT+DMFT
• Berry-phase description of Topological Crystalline Insulators
• Correlation effects in total energy of transition metals and related properties
• Forces for Structural Optimizations in Correlated Materials within DFT+Embedded DMFT Functional Approach
• How to verify the precision of density-functional-theory implementations via reproducible and universal workflows
• Efficient treatment of two-particle vertices in dynamical mean-field theory
• Effective and accurate representation of extended Bloch states on finite Hilbert spaces
• Wannier Function Approach to Realistic Coulomb Interactions in Layered Materials and Heterostructures
• Applications of DFT+DMFT in Materials Science
• Finite temperature quantum embedding theories for correlated systems
• Charge Transport in Organic Molecular Semiconductors from First Principles: The Band-Like Hole Mobility in Naphthalene Crystal
• Screened Coulomb interaction calculations: cRPA implementation and applications to dynamical screening and self-consistency in uranium dioxide and cerium
• Orbital Magnetization as a Local Property
• Partly Occupied Wannier Functions
• Green's function formulation of quantum defect embedding theory
• Anharmonic electron-phonon coupling in ultrasoft and locally disordered perovskites
• Maximally localized Wannier function within linear combination of pseudo-atomic orbital method: Implementation and applications to transition-metal-benzene complex
• Maximally-localized Wannier functions for GW quasiparticles
• Predicting charge transport in the presence of polarons: The beyond-quasiparticle regime in SrTiO${}_3$
• Quantum embedding methods for correlated excited states of point defects: Case studies and challenges
• Polarons in two-dimensional atomic crystals
• Koopmans-compliant spectral functionals for extended systems
• Long-range quadrupole electron-phonon interaction from first principles
• Dynamical Screening Effects in Correlated Electron Materials -- A Progress Report on Combined Many-Body Perturbation and Dynamical Mean Field Theory: "GW+DMFT"
• Anharmonic lattice dynamics via the special displacement method
• First-principles theory of spatial dispersion: Dynamical quadrupoles and flexoelectricity
• Dynamical screening in correlated electron systems - from lattice models to realistic materials
• Bloch bundles, Marzari-Vanderbilt functional and maximally localized Wannier functions
• Accurate polarization within a unified Wannier function formalism
• LDA+DMFT approach to core-level spectroscopy: application to 3d transition metal compounds
• WannSymm: A symmetry analysis code for Wannier orbitals
• Intrinsic Magnetoconductivity of Non-magnetic Metals
• Dynamical Mean Field Studies of Infinite Layer Nickelates: Physics Results and Methodological Implications
• Ab initio electron-phonon interactions in correlated electron systems
• Electron-phonon drag enhancement of transport properties from fully coupled \textit{ab initio} Boltzmann formalism
• Engineering polar discontinuities in honeycomb lattices
• Unified approach to polarons and phonon-induced band structure renormalization
• Automated construction of symmetrized Wannier-like tight-binding models from ab initio calculations
• Ab Initio Electron-Phonon Interactions Using Atomic Orbital Wavefunctions
• Charge self-consistent many-body corrections using optimized projected localized orbitals
• Large scale GW-BSE calculations with N3 scaling: excitonic effects in dye sensitised solar cells
• Distinctive signatures of the spin- and momentum-forbidden dark exciton states in the photo-luminescences of strained WSe${}_2$ monolayers under thermalization
• Magneto-transport phenomena in p-doped diamond from first principles
• Automated construction of maximally localized Wannier functions: Optimized projection functions method
• Long-range electrostatic contribution to the electron-phonon couplings and mobilities of two-dimensional and bulk materials
• Electron-Phonon Interactions Using the PAW Method and Wannier Functions
• First-principles Calculation of Atomic Forces and Structural Distortions in Strongly Correlated Materials
• ComDMFT: a Massively Parallel Computer Package for the Electronic Structure of Correlated-Electron Systems
• Excitonic polarons and self-trapped excitons from first-principles exciton-phonon couplings
• Phoebe: a High-Performance Framework for Solving Phonon and Electron Boltzmann Transport Equations
• Tight-binding calculations of optical matrix elements for conductivity using non-orthogonal atomic orbitals: Anomalous Hall conductivity in bcc Fe
• Theory and applications of generalized Pipek--Mezey Wannier functions
• Coupled transport of phonons and carriers in semiconductors: A case study of n-doped GaAs
• Accurate prediction of Hall mobilities in two-dimensional materials through gauge-covariant quadrupolar contributions
• Efficient lattice dynamics calculations for correlated materials with DFT+DMFT
• Zero-point Renormalization of the Band Gap of Semiconductors and Insulators Using the PAW Method
• Amorphous topological matter: theory and experiment
• Computation of intrinsic spin Hall conductivities from first principles using maximally-localized Wannier functions
• EDRIXS: An open source toolkit for simulating spectra of resonant inelastic x-ray scattering
• Consequences of local gauge symmetry in empirical tight-binding theory
• Koopmans-compliant functionals and potentials and their application to the GW100 test-set
• Gauge invariance of light-matter interactions in first-principle tight-binding models
• Ab initio complex band structure of conjugated polymers: Effects of hydrid DFT and GW schemes
• Unified ab initio description of Fröhlich electron-phonon interactions in two-dimensional and three-dimensional materials
• Theory of excitonic polarons: From models to first-principles calculations
• Giant Magnetochiral Anisotropy in Weyl-semimetal WTe2 Induced by Diverging Berry Curvature
• Dependence of DFT+DMFT Results on the Construction of the Correlated Orbitals
• DMFTwDFT: An open-source code combining Dynamical Mean Field Theory with various Density Functional Theory packages
• Full-bandwidth anisotropic Migdal-Eliashberg theory and its application to superhydrides
• Continuum Charge Excitations in High-Valence Transition-Metal Oxides Revealed by Resonant Inelastic X-ray Scattering
• Theory of $L$-edge spectroscopy of strongly correlated systems
• EDIpack: A parallel exact diagonalization package for quantum impurity problems
• Selectively Localized Wannier Functions
• Axion coupling in the hybrid Wannier representation
• Robust determination of maximally-localized Wannier functions
• Enhancement of the Na${}_x$CoO${}_2$ thermopower due to electronic correlations
• Orbital magnetization of insulating perovskite transition-metal oxides with the net ferromagnetic moment in the ground state
• Local theory of the insulating state
• The CECAM Electronic Structure Library and the modular software development paradigm
• Ab initio theory of free-carrier absorption in semiconductors
• Orbital magnetization and Chern number in a supercell framework: Single k-point formula
• Maximally-localized Wannier Functions in Antiferromagnetic MnO within the FLAPW Formalism
• Automated quantum conductance calculations using maximally-localised Wannier functions
• Koopmans Meets Bethe-Salpeter: Excitonic Optical Spectra without GW
• Phonon-limited Mobility of 2D Semiconductors: Quadrupole Scattering and Free-carrier Screening
• Hall coefficient signals orbital differentiation in the Hund's metal Sr${}_2$RuO${}_4$
• Electron-phonon interaction and longitudinal-transverse phonon splitting in doped semiconductors
• Control of interlayer delocalization in 2H transition metal dichalcogenides
• Phonon Self-Energy Corrections: To Screen, or Not to Screen
• Ab initio dipolar electron-phonon interactions in two-dimensional materials
• koopmans: an open-source package for accurately and efficiently predicting spectral properties with Koopmans functionals
• Transition state method and Wannier functions
• Assessing the role of interatomic position matrix elements in tight-binding calculations of optical properties
• Many-body renormalisation of forces in f-electron materials
• EPIq : an open-source software for the calculation of electron-phonon interaction related properties
• Exciton-phonon interaction calls for a revision of the "exciton" concept
• Dipole matrix element approach vs. Peierls approximation for optical conductivity
• Projectability disentanglement for accurate and automated electronic-structure Hamiltonians
• Multipole theory of optical spatial dispersion in crystals
• A theoretical approach for electron dynamics and ultrafast spectroscopy
• Bloch's theorem in orbital-density-dependent functionals: Band structures from Koopmans spectral functionals
• Local force method for the ab initio tight-binding model with spin-dependent hopping
• Irrelevance of the boundary on the magnetization of metals
• Woptic: optical conductivity with Wannier functions and adaptive k-mesh refinement
• Screening in orbital-density-dependent functionals
• Charge self-consistent electronic structure calculations with dynamical mean-field theory using Quantum ESPRESSO, Wannier90 and TRIQS
• Localized orbital scaling correction for periodic systems
• Electron-phonon coupling from GW perturbation theory: Practical workflow combining BerkeleyGW, ABINIT, and EPW
• Downfolding electron-phonon Hamiltonians from ab-initio calculations: application to K${}_3$Picene
• Facile ab initio approach for self-localized polarons from canonical transformations
• Wavefunctions, electronic localization and bonding properties for correlated materials beyond the Kohn-Sham formalism
• Trends in atomistic simulation software usage
• Towards high-throughput many-body perturbation theory: efficient algorithms and automated workflows
• Wannier Function Perturbation Theory: Localized Representation and Interpolation of Wavefunction Perturbation
• Local Chern Marker for Periodic Systems
• Calculating DMFT forces in ab-initio ultrasoft pseudopotential formalism
• Local embedding and effective downfolding in the auxiliary-field quantum Monte Carlo method
• Automated mixing of maximally localized Wannier functions into target manifolds
• Orbital densities functional
• Boosting the efficiency of ab initio electron-phonon coupling calculations through dual interpolation
• DCore: Integrated DMFT software for correlated electrons
• Ab initio electron dynamics in high electric fields: accurate predictions of velocity-field curves
• Prospect of high-temperature superconductivity in layered metal borocarbides
• Single-point spin Chern number in a supercell framework
• Data-driven compression of electron-phonon interactions
• Reliable methods for seamless stitching of tight-binding models based on maximally localized Wannier functions
• Band tail formation in mono and multilayered transition metal dichalcogenides: A detailed assessment and a quick-reference guide
• Theory of local ${\mathbb{Z}}_2$ topological markers for finite and periodic two-dimensional systems
• The Iterated Projected Position Algorithm for Constructing Exponentially Localized Generalized Wannier Functions for Periodic and Non-Periodic Insulators in Two Dimensions and Higher
• Phonon-assisted Auger-Meitner Recombination in Silicon from First Principles
• Maximally localized Wannier functions within the (L)APW+LO method
• Efficient anisotropic Migdal-Eliashberg calculations with the Intermediate Representation basis and Wannier interpolation
• Numerical construction of Wannier functions through homotopy
• Interface tool from Wannier90 to RESPACK: wan2respack
• Optimally Localized Wannier Functions for 2D Chern Insulators
• Spread balanced Wannier functions: Robust and automatable orbital localization
• Automatic, high-order, and adaptive algorithms for Brillouin zone integration
• LinReTraCe: The Linear Response Transport Centre
• Signatures of Hund Metal and finite-frequency nesting in Sr${}_2$RuO${}_4$ Revealed by Electronic Raman Scattering
• Symmetric Helmholtz Fermi-surface harmonics for an optimal representation of anisotropic quantities on the Fermi surface: Application to the electron-phonon problem
• Fully anisotropic superconductivity with few Helmholtz Fermi-surface harmonics
• A complementary screening for quantum spin Hall insulators in 2D exfoliable materials
• Spin-dependent interactions in orbital-density-dependent functionals: non-collinear Koopmans spectral functionals
• mkite: A distributed computing platform for high-throughput materials simulations

Cited by in corpus (11)

• High-throughput calculations of spin Hall conductivity in non-magnetic 2D materials
• Electron-phonon vertex correction effect in superconducting H3S
• Robust Wannierization including magnetization and spin-orbit coupling via projectability disentanglement
• Fluctuations and Correlations of Local Topological Order Parameters in Disordered Two-dimensional Topological Insulators
• Precise quantum-geometric electronic properties from first principles
• Making atomistic materials calculations accessible with the AiiDAlab Quantum ESPRESSO app
• First-Principles Calculation of Superconducting $T_c$ in Superhard B-C-N Metals
• Orbital-Selective Spin-Orbit Mott Insulator in Fractional Valence Iridate La${}_3$Ir${}_3$O${}_{11}$
• Exact expression for the Berry connection in the projection gauge
• Reduced Wannier representation for topological bands
• High-$T_{\mathrm{c}}$ Ag${}_x$BC and Cu${}_x$BC superconductors accessible via topochemical reactions