Matrix elements of the electron‐phonon interaction in the fourier‐based representation of a crystal potential

Abstract

A method for electron-phonon matrix element calculations based on a Fourier representation of the crystal potential is presented. This method is free from a number of drawbacks inherent to the rigid muffin-tin approximation. At the same time it is much easier realizable as compared with the first-principle frozen-phonon technique. The long-range interactions, the collective character of ion displacements in phonon modes, and effects due to in-sphere electron-ion potential anisotropy can be easily taken into account. Non-muffin-tin corrections are shown to cause electron-ion scattering selection rule variations. Interband transitions due to absorption or emission of optical phonons with q = 0 (e.g. Raman-active A, modes) require the inclusion of nonlinear ion displacement contributions to the matrix elements.

Matrix elements of the electron‐phonon interaction in the rigid electron density displacement approximation

“…In a previous paper [3] we proposed a method capable to account for the non-muffin-tin corrections to the matrix elenients of the electron-phonon interaction (EPI). Unfortunately, Fourier representation of the crystal potential used in [3] results in a slow convergence of the perturbing potential, especially near nuclei. Here we present a new formulation of the problem free from the drawback mentioned and allowing one to make ii direct comparison with the RMTA.…”

“…IF? L. A f 0 x F'fi,(k, G,, T ' ) ( T ' )~ dr' ,(18)where MI(kk'; p i j ) is the first-order contribution of ion ( p , i, j ) , G(lm, L M , l'm') are Gaunt numbers, and F,(z) are combinations of standard LAPM' characteristics[3].…”