Comparison of Wannier functions resulting from different minimization schemes in gallium arsenide (larger pink spheres are Ga cation atoms and yellow spheres are As anions). Credit: Valerio Vitale @Imperial College London.

Wannier functions were first introduced by Gregory Wannier in 1937 as an alternative way of describing the electronic ground state of periodic systems. They were linked to Bloch orbitals, the standard method of describing these ground states, by families of transformations in a continuous space of unitary matrices. Unfortunately, this was linked to a large degree of arbitrariness.

In 1996, NCCR MARVEL director Nicola Marzari, then a postdoc at Rutgers University, and Prof. David Vanderbilt, also at Rutgers, developed a novel method allowing researchers to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique…

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