Revisiting the homogeneous electron gas in pursuit of the properly normed ab initio Eliashberg theory


الملخص بالإنكليزية

We address an issue of how to accurately include the self energy effect of the screened electron-electron Coulomb interaction in the phonon-mediated superconductors from first principles. In the Eliashberg theory for superconductors, self energy is usually decomposed using the $2times 2$ Pauli matrices in the electron-hole space. We examine how the diagonal ($sigma_{0}$ and $sigma_{3}$) components, which results in the quasiparticle correction to the normal state, behave in the homogeneous electron gas in order to establish a norm of treating those components in real metallic systems. Within the $G_{0}W_{0}$ approximation, we point out that these components are non-analytic near the Fermi surface but their directional derivatives and resulting corrections to the quasiparticle velocity are nevertheless well defined. In the low-energy spectrum, we observe large cancellation between effects of these components and, without the numerically more tedious $sigma_{3}$ component, the effective mass is incorrectly increased. Feasible paths to manage this cancellation in the ab initio Eliashberg calculations are discussed.

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