Superconductivity-induced effects on phononic and electronic Raman scattering in twin-freeYBa2Cu3O7−xsingle crystals

Raman scattering spectra have been investigated in twin-free ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}x}$ single crystals with various oxygen content. Superconductivity-induced effects are found for all ${A}_{g}$ phonons in the overdoped crystals, but they rapidly weaken with reducing oxygen content. The 340 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonon line is analyzed in detail by means of the Green function, as well as the standard Fano formula. The results provide much evidence for the nodal structure of a superconducting gap. The polarization dependence, which is significant in the highly doped crystals, illustrates the x-y anisotropy of the electronic response $\ensuremath{\chi}(\ensuremath{\omega})=\ensuremath{-}R(\ensuremath{\omega})+i\ensuremath{\rho}(\ensuremath{\omega})$ and implies a difference of the superconducting gap amplitudes ${\ensuremath{\Delta}}_{x}\ensuremath{\ne}{\ensuremath{\Delta}}_{y}$ in the ${\mathbf{k}}_{x}$ and ${\mathbf{k}}_{y}$ directions in the two-dimensional Brillouin zone for orthorhombic ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}x}.$ The gap energy difference $({\ensuremath{\Delta}}_{y}\ensuremath{-}{\ensuremath{\Delta}}_{x})$ decreases as the doping level is deduced.