2.2.1Maximally Localized Wannier Orbital

Let us read the article written by Marzari, who developed the theory of the most localized Wannier orbital.

Wannier orbitals was introduced many years ago as a method to interpret a band in terms of a bond. Originally this was done by Fourtier transforming the Bloch orbitals with respect to the reciprocal vector. The degree of localization is not sufficient in many cases, requiring thereby more stronger localization method. In this context, Prof. Marzari invented an effective procedure.

Theory of Wannier orbital

MLWF=Maximally Localized Wannier Function

How to construct the Wannier orbital in practice.

How to compute gradients wrt k

These useful expressions allow us to compute the parameters required for the variational localization function (5).

For the tight-binding model, please read excellent documents in the web, e.g. the note written by Prof. Fujimori (in Japanese).