Variational method for the generation of localized Wannier functions on the basis of Bloch functions

A simple and universal variational method for constructing localized Wannier functions from Bloch functions is proposed. The variational procedure is preceded by a symmetry analysis based on the induced representation theory and succeeded by a suitable orthogonalization procedure. The reliability of the method is demonstrated by computations of localized displacements in a one-dimensional diatomic lattice and it germanium lattice, of localized electronic states in a one-dimensional Kronig-Penney model, for the tipper valence bands of Si and MgO crystals.