PHONON-SELF-ENERGY EFFECTS DUE TO AN ELECTRONIC MECHANISM IN HIGH-TC SUPERCONDUCTORS

The phonon self-energy at q=0 and zero temperature is calculated for a conventional electron-phonon superconductor, Pb, and for an equivalent high-T(c) superconductor, assuming an electronic mechanism for the superconductivity (to be specific and as a convenient illustrative example, we use the marginal-Fermi-liquid phenomenology). Comparison between the results demonstrates that for an s-wave strong-coupling superconductor, phonon shifts and widths exhibit the same behavior regardless of the mechanism for superconductivity. In addition, the marginal-Fermi-liquid model shows no unusual behavior at zero temperature in the phonon self-energy, with the exception of a possible narrowing of the phonon width below 2DELTA0 the clean limit. As an aside, we also present renormalized BCS formulas that agree well with the full numerical strong-coupling calculations and could be easily implemented for use in model fits.