Abstract
The phonon self-energy due to the interaction with electrons is studied for superconductors with s- and d-wave pairing. Addition of impurities not only changes the electronic states, but it also generates a channel of the electron-phonon interaction due to electron scattering from vibrating impurities. Impurity-induced electron-phonon coupling results in significant modifications of the phonon self-energy. For a d-wave superconductor the phonon attenuation coefficient (the imaginary part of the phonon self-energy) has been calculated in the Born approximation and in the unitary limit for electron-impurity scattering. In the case of weak electron-impurity potential, the attenuation decreases if temperature reduces below ${T}_{c},$ while an increase of the attenuation in the superconducting state has been found in the unitary limit. The theory shows a good agreement with measured disorder-dependent coupling of the ${B}_{1g}$ phonon mode to superconducting electrons in high-${T}_{c}$ samples: the Born approximation well describes temperature dependence of the attenuation in YBaCuO single crystals, the unitary limit corresponds to polycrystals and twinned crystals.
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