Localized Basis for Lattice Vibrations

Abstract

For the case of electrons in a periodic lattice there exist extended basis functions (Bloch waves) and localized basis functions (Wannier functions). It is shown here that also for lattice vibrations there exists, in addition to the usual extended basis functions (normal modes), a set of localized basis functions. These are nontrivial only for lattices with several atoms per unit cell. Examples are worked out and discussed. These functions appear to be of interest for the treatment of defects and other problems calling for a localized description.