Theory for the effects of impurities on the Raman spectra of superconductors

A gauge-invariant theory for the effects of impurities on the electronic Raman scattering by pairs of quasiparticles in superconductors is persented. Special attention is given to the role of symmetry. The Raman spectrum for a superconductor is calculated using the exact-eigenstate formalism to account for impurity scattering in each symmetry channel $L$. We find that the Raman spectrum is strongly affected by impurity scattering in channels $L\ne 0$, and symmetry-dependent line shapes can be obtained for anisotropic impurity scattering. For strong impurity scattering the peak of the Raman spectra does not coincide with the energy gap. Also, the bound states and phonon spectral function in the $L\ne 0$ channel are investigated. Implications for the Raman spectra of the cuprates are discussed.