Electron-Phonon Interaction and Phonon Dispersion Relations Using the Augmented-Plane-Wave Method

Abstract

A new version of the "Schrödinger method" for treating the electron-phonon matrix element is presented. Using the Schrödinger equation, the matrix element is transformed so as to obtain the first-order perturbed charge density of the valence electrons self-consistently as the sum of two parts. The first or "bound" part corresponds to the rigid movement of the valence charge density inside a volume $V_0$ (chosen for maximum convenience) in the unit cell with the ion core, while the second or "deformation" part represents the rest of the perturbation and may be calculated as the self-consistent response to a weak effective driving potential, called the residual potential, which does not contain the deep well near the core. The screened matrix element is obtained, and the relationship to Bardeen's method and to the more recent pseudopotential methods is discussed. A certain resemblance of the residual potential to the Heine-Abarenkov model potential is pointed out. Finally, the dynamical matrix is transformed without approximation to be written as the sum of an interaction between pseudoatoms and a deformation part. The advantages of such a recasting are discussed. Explicit expressions are derived based on the APW representation of the valence wave functions, since it is intended to apply the formalism to transition metals and other more complicated solids.