Superconductivity-induced dynamic and static changes inq≠0phonons of high-Tcoxides

Superconductivity-induced self-energies of q≠0 phonons and changes in static local lattice properties are calculated for ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ using strong-coupling theory, the harmonic approximation for phonons in the normal state, and a recently introduced screened ionic model for the electron-phonon coupling. The main results are (i) dynamic changes in the frequency and the damping of phonons decrease with increasing momentum, however, they still should be observable for momentum transfers up to ‖q‖∼2${\mathit{k}}_{\mathit{F}}$ and phonon frequencies near the gap and (ii) in spite of the low Fermi energy and a rather large average coupling constant λ of about 3, relative changes due to superconductivity in static quantities such as the Debye-Waller factor and the kinetic energy of an atom are very small and of the order of ${10}^{\mathrm{-}3}$. Recently reported large changes in channeling rates and in the width of a Cu nuclear-absorption resonance near and below ${\mathit{T}}_{\mathit{c}}$ thus remain unexplained within the present approach.