Electron-Phonon Interaction in the Tight-Binding Approximation: Validity of the Bloch Formulation

Abstract

We show that the Bloch formulation of the electron-phonon interaction is valid in the tight-binding limit, correctly describes the rigid response of the tightly bound electrons to the ion motion, and introduces corrections of first order in the bandwidth to the "modified-tight-binding" approximation of Frohlich and Mitra and the "Hubbard-Hamiltonian" approximation of Barišić, Labbé, and Friedel. Expressions are derived for the Bloch tight-binding electron-phonon matrix elements.