s- and d-wave symmetries of the solutions of the Eliashberg equations

We examine the different possible symmetries of the superconducting gap obtained by solving the Eliashberg equations. We consider an electron-phonon interaction in a strong coupling scenario. The Coulomb pseudopotential plays the crucial role of providing the repulsion needed to favour the d-wave symmetry. But the key parameter that allows very anisotropic solutions even with very strong coupling is the small angular range of the interaction due to predominantly electron-phonon forward scattering that is found in the high-T_c superconductors. We find both s- and d-wave solutions whose stability depends mainly on the angular range of the interaction.