Generalisation of the Frohlich-Mitra modified tight-binding approximation toward the description of the electron-phonon coupling in solids

Abstract

In order to describe the electron motion in deformed lattices, the Frohlich-Mitra modified tight-binding approximation (1968) has been generalised. The unperturbed electronic wavefunction is written as a Bloch sum of displaced and suitably orthonormalised Wannier functions so as to take partly into account the adiabatic followup of the electron upon deformation of the lattice. It is then shown that the electron-phonon interaction matrix elements in this scheme are identical with those given by the ordinary Bloch theory.