Phonon self-energy effects due to superconductivity: A real-axis formulation.

Abstract

The self-energy of q=0 phonons is calculated in both the superconducting and normal states, with use of a real-axis formulation, valid for arbitrary temperature, impurity scattering rate, and electron-phonon coupling strength. The calculations are performed within the Eliashberg framework. We qualitatively confirm much of the previous work done using Pade\ifmmode\acute\else\textasciiacute\fi{} approximants. Besides providing quantitative corrections, we also predict an observable effect with low-frequency phonons.