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## Wannier 2022

#### International Centre for Theoretical Physics (ICTP) - Trieste, Italy

#### Organisers

The last two decades have witnessed a tremendous growth in the use of Wannier functions (WFs) for first-principles electronic structure calculations. Beyond providing fundamental insights on several aspects of the electronic structure, from chemical bonding to electrical polarisation, topological invariants, Berry curvature and more, WFs have found applications in a plethora of different domains. On the one hand, WFs provide a tool to bridge length scales by accurately embedding information from the atomistic scale to mesoscopic scales, allowing for instance first-principles modelling of nano-devices. This can be achieved by first performing density-functional theory or many-body perturbation theory calculations, and then employing WFs to construct a tight-binding Hamiltonian in a Wannier basis that reproduces the first-principles band structure. On the other hand, advanced materials properties that require dense sampling of the Brillouin zone (BZ) can be computed at a much lower computational cost, without any loss of accuracy, via Wannier interpolation [1].

In principle, multiple options are possibile to construct Wannier functions from first-principles calculations. Maximally-localised Wannier functions [1,2] (MLWFs) have emerged as the leading approach in the electronic structure community, as testified by more than 3000 citations for the original work by Marzari and Vanderbilt [2] and more than 1700 citations for the MLWFs review article [1].

The software package WANNIER90 has become a reference for calculating MLWFs and related properties [2,3,4]. As Wannier functions are independent from the basis sets used to represent the electronic structure in the underlying first-principles calculations, WANNIER90 can be interfaced to virtually any electronic-structure code. Indeed, most of the major electronic-structure packages have already an interface to WANNIER90, including Quantum ESPRESSO, ABINIT, VASP, Siesta, Wien2k, Fleur and Octopus.

The availability of a robust MLWF code that is connected to several ab-initio engines has acted as a fertiliser for the birth of independent computational efforts aimed at calculating complex materials properties by leveraging WFs. Several independent packages exploiting MLWFs and WANNIER90 exist nowadays targeting a number of properties, from electron-phonon coupling [5] (EPW) to topological invariants [6] (Z2Pack), surface spectral densities [7] (WannierTools), Berry-phase related properties [8] (Wannier Berri), tight-binding models (PythTB, TBModels), high-throughput calculations [9] (AiiDA-Wannier90), and more.

Wannier 2022 is an event that recognises the existence of such community of symbiotic packages that form a research and software ecosystem built upon the concept of MLWFs. The workshop will serve the two-fold objective of teaching the Wannier-function technologies to young researchers and fostering an integration between all the packages composing the Wannier ecosystem, contrasting fragmentation and duplication of efforts. About 2/3 of the workshop is dedicated to methods and standalone codes that exploit Wannier functions but are not included in WANNIER90. Code developers will have the opportunity to lecture about their Wannier-based technologies, and cooperate with other developers to integrate and interconnect different packages into an organic ecosystem.

## References

**Italy**

Antimo Marrazzo (University of Trieste) - Organiser

**Switzerland**

Giovanni Pizzi (EPFL) - Organiser

Stepan Tsirkin (University of Zurich) - Organiser

**United States**

Sinisa Coh (University of California, Riverside) - Organiser

Roxana Margine (Binghamton University - State University of New York) - Organiser