Electronic Raman scattering in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$sand other superconducting cuprates

Superconductivity-induced structures in the electronic Raman spectra of high-${\mathrm{T}}_{\mathrm{c}}$ superconductors are computed using the results of ab initio local-density approximation linear muffin-tin-orbital three-dimensional band-structure calculations via numerical integrations of the mass fluctuations, either in the whole three-dimensional Brillouin zone or limiting the integrations to the Fermi surface. The results of both calculations are rather similar, the Brillouin-zone integration yielding additional weak structures related to the extended van Hove singularities. Similar calculations have been performed for the normal state of these high-${\mathrm{T}}_{\mathrm{c}}$ cuprates. Polarization configurations have been investigated and the results have been compared to experimental spectra. The assumption of a simple ${\mathrm{d}}_{{\mathrm{x}}^2\mathrm{-}{\mathrm{y}}^2}$-like gap function allows us to explain a number of experimental features but is hard to reconcile with the relative positions of the ${\mathrm{A}}_{1\mathrm{g}}$ and ${\mathrm{B}}_{1\mathrm{g}}$ peaks.