N. Marzari, A. A. Mostofi, J. Yates, I. Souza and D. Vanderbilt, Maximally-localized Wannier functions: theory and applications, Rev. Mod. Phys. 84, 1419–1475 (2012) [ONLINE JOURNAL|PDF]
Arash, together with collaborators from EPFL, Rutgers, Oxford and Universidad del Pais Vasco, has published a paper in the Reviews of Modern Physics entitled “Maximally localized Wannier functions: Theory and applications”. The dichotomy between extended, or Bloch, states, and localized, or Wannier, states in solid-state physics has been known for 75 years. However, the notion of a unique, or maximally localized, Wannier function is of much more recent origin. This review explains this concept, shows how to explicitly construct maximally localized Wannier functions, and explains why they are useful for describing systems from solids to optical lattices and cold atoms.