History

The research and development of maximally-localised Wannier functions [REF] has been supported during the years by the National Science Foundation, especially its Division of Materials Research, and more recently by DARPA.

It all started with a NSF CISE Postdoctoral Fellowship for Nicola Marzari to work with David Vanderbilt at Rutgers University in 1996-98. The original Fortran77 code was restructured on Thanksgiving Day 1996, and hence for many years known as turkey.f . In this incarnation, it was interfaced directly to the all-bands ensemble-DFT CASTEP code [REF] of the Cambridge-Keele collaboration.

In those early days, maximally-localised Wannier functions were used by the American Physical Society in the announcement of Walter Kohn's Nobel Prize for the development of density-functional theory (see here and here).

In 1998 the algorithm was implemented in CPMD by Pierluigi Silvestrelli, in the group of Michele Parrinello at MPI-Stuttgart [REF]. Public availability spurred its early popularity, leading to many applications in which Wannier functions were used to study the electronic-structure of complex systems, thanks to their connection with our intuitive understanding of chemical bonding. There is also a formal connection to the dielectric theory of solids, via the Berry phase formulation of macroscopic polarisation (King-Smith and Vanderbilt [REF], Resta [REF]), and Wannier functions centers represent a mapping onto classical charges of quantum dielectric properties [REF].

Ivo Souza (then a PhD student with Richard Martin, UIUC) became involved in the project in 1999, first in an application to compressed hydrogen, and then during his postdoctoral days at Rutgers, leading to the Souza-Marzari-Vanderbilt disentanglement extension [REF].

Several visits of Nicola Marzari to Michel Posternak and Alfonso Baldereschi, at the Ecole Polytechnique Federale de Lausanne, brought the interface to FLAPW and to any generic electronic-structure code [REF].

Yudong Wu and Manu Sharma (working with Nicola Marzari and Roberto Car at Princeton University) implemented the algorithm in CP90/Quantum-Espresso, Francois Gygi (LLNL) in JEEP/QBox [REF], Leonardo Bernasconi (University of Oxford) in CASTEP.

A collaboration with Marco Buongiorno Nardelli (NCSU) led to the Landauer transport applications, in collaboration with Arrigo Calzolari and Andrea Ferretti at the University of Modena (see here) [REF] and Young-Su Lee at MIT [REF]. Thygesen and Jacobsen (CAMP, Copenhagen) have led analogous developments centered around the DACAPO code.

In 2006 the code was rewritten in Fortran90 - restructured, extended and optimised - by Arash Mostofi and Jonathan Yates, Research Fellows at the University of Cambridge, and postdoctoral researchers in the groups of Nicola Marzari and Ivo Souza, respectively. Stefano de Gironcoli and Malgorzata Wierzbowska interfaced Wannier90 to operate seamlessly with Quantum-Espresso. Interfaces to many other electronic structure codes were written over the following years.

The v2.0 release of Wannier90 in 2013 added a large amount of new functionality built around the postw90.x executable. This performs Wannier interpolation using MPI parallelisation. In particular Boltzmann transport functionality was added by Giovanni Pizzi at EPFL, while Ivo Souza added Berry phase related properties such as the Anomalous Hall conductivity and orbital magnetisation.

The formalism has seen many and diverse applications: linear-scaling quantum Monte-Carlo (Williamson, Hood and Grossman, LLNL), photonic crystals (Whittaker and Croucher, Garcia-Martin and Wolfle), metal-insulator interfaces (Stengel and Spaldin), and as an efficient interpolator for the anomalous Hall effect (Wang, Yates, Souza and Vanderbilt) and electron-phonon couplings (Giustino, Yates and Souza), to cite only a few.

In addition, Wannier functions are playing an increasing role in bridging density-functional approaches and strongly-correlated ones, to derive model Hamiltonians or as a starting point for LDA+U or LDA+DMFT (Ku and Pickett, Georges, Vollhardt, Solovyev, Anisimov, and many others). They are also closely related to the order-N muffin-tin orbitals (NMTOs) developed by O. K. Andersen and collaborators (MPI-Stuttgart).

In 2012 a comprehensive review article on Wannier functions was published in Reviews of Modern Physics [REF]

In 2016 a developer workshop was held in San Sebastian. This co-incided with the move of the Wannier90 repository to GitHub to enable easier integration of community contributions. One of the first such contributions was the ability to compute symmetry-adapted Wannier Functions.[REF]