Effect of the Coupling of the Forward- and Backward-Going Electron-Hole Pairs on the Static Local Field-Factor of Jellium
A Tsolakidis, Eric L. Shirley, R M. Martin
We investigate the effect of the coupling of the forward- and backward-going electron-hole pairs on the static local-field factor of jellium with and without a gap. We calculate the static local-field factor for the two types of jellium as a function of q using the Bethe-Salpeter equation. We assume that a particle and hole interact via a statically screened Coulomb interaction. The polarization diagrams that include this interaction are summed to infinite order, leading to a matrix equation for the inverse of the polarization propagator. Employing a string of manipulations we convert the matrices into convenient forms, and then invert the resulting matrices iteratively. This allows us to use matrices of very large size, something that would have not been feasible with straightforward inversion, and therefore achieve a very high level of convergence of results with respect to sampling of electron states in the Fermi sea with relative computational ease. For the calculation of the static local-field factor, we find that the coupling of both kinds of pairs gives qualitatively different results compared to the case when there is nocoupling, and that the coupling of both kinds of electron-hole pairs is necessary for obtaining the most accurate results. Our calculations are also in qualitative agreement with recent calculations by others.
Physical Review B: Condensed Matter and Materials Physics
, Shirley, E.
and Martin, R.
Effect of the Coupling of the Forward- and Backward-Going Electron-Hole Pairs on the Static Local Field-Factor of Jellium, Physical Review B: Condensed Matter and Materials Physics
(Accessed September 23, 2023)