The temperature dependence below $T_{ c}$ of the lineshape of optical phonons of different symmetry as seen in Raman scattering is investigated for superconductors with anisotropic energy gaps. It is shown that the symmetry of the electron-phonon vertex produces non-trivial couplings to an anisotropic energy gap which leads to unique changes in the phonon lineshape for phonons of different symmetry. The phonon lineshape is calculated in detail for $B_{ 1g}$ and $A_{ 1g}$ phonons in a superconductor with $d_{ x^{ 2}-y^{ 2}}$ pairing symmetry. The role of satellite peaks generated by the electron-phonon coupling are also addressed. The theory accounts for the substantial phonon narrowing of the $B_{ 1g}$ phonon, while narrowing of the $A_{ 1g}$ phonon which is indistinguishable from the normal state is shown, in agreement with recent measurements on BSCCO.
Categories: cond-mat