Maximally-localized Wannier Functions: Theory and Applications

By Nicola Marzari, Arash A. Mostofi, Jonathan R. Yates, Ivo Souza, D. Vanderbilt. 2011

2,224 citations recorded by the source corpus.

The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or "Boys orbitals" as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/cbb1f4407396d916b9f2401790e79a285c2b348d

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Solvation and Dynamics of Sodium and Potassium in Ethylene Carbonate from Ab Initio Molecular Dynamics Simulations (2017, positive): “We employ maximally localized Wannier function (MLWF) analysis 47,48 as a convenient way to examine the ion–solvent interaction.”
Colloquium: Strong-field phenomena in periodic systems (2017, background): “This is possible in the hybrid representation (Argyres, 1962; Marzari et al., 2012; Sgiarovello et al., 2001) where the wavefunctions and operators are transformed to the coordinate space only over the component of crystal momentum pointing along the field polarization.”
Tilted spin current generated by the collinear antiferromagnet ruthenium dioxide (2021, methodology): “We used the tight-binding Hamiltonians obtained from the maximally-localized Wannier functions [15] within the Wannier90 code [16].”
Quantization of fractional corner charge in Cn -symmetric higher-order topological crystalline insulators (2018, background): “By comparing these representations with those of our primitive generators, we verify that all of our generators are Wannier-representable.”
Low-Frequency Divergence and Quantum Geometry of the Bulk Photovoltaic Effect in Topological Semimetals (2020, methodology): “Since a large number of kpoints are needed to get accurate NLO responses [75, 76], we use the efficient Wannier function interpolation method based on maximally localized Wannier functions (MLWFs) [77–79].”