Theory of Electronic Raman Scattering in Disordered $d-$wave Superconductors

A theory for the effect of impurity scattering on electronic Raman scattering in unconventional superconductors is presented. The impurity dependence of the the spectra can be used to to distinguish between conventional (anisotropic $s-$wave) or unconventional ($d$-wave) energy gaps, and excellent agreement with the data on three cuprate superconductors is shown for $d_{x^{2}-y^{2}}$ pairing. The full frequency dependence of the spectra can be reproduced by including inelastic scattering due to spin fluctuations and/or Coulomb scattering on a partially nested Fermi surface.