Relevance of quadratic electron-phonon coupling for the superconducting transition temperature

The two-phonon exchange contribution to the electron-phonon coupling constant is investigated using realistic models for the electron and phonon system, and taking into account the full momentum dependence of the scattering matrix elements. In the case of Pb, which is a paradigm for an anharmonic crystal, this contribution is found to be very small, indicating the irrelevance of lattice anharmonicity for Tc as long as a perturbational treatment of the anharmonic interaction is adequate