Unconventional superconductivity mediated solely by isotropic electron-phonon interaction

Unconventional superconductivity is commonly linked to electronic pairing mechanisms, since it is believed that the conventional electron-phonon interaction (EPI) cannot cause sign-changing superconducting gap symmetries. Here, we show that this common understanding needs to be revised when one considers a more elaborate theory of electron-phonon superconductivity beyond standard approximations. We self-consistently solve the full-bandwidth, anisotropic Eliashberg equations including vertex corrections beyond Migdal's approximation assuming the usual isotropic EPI for cuprate, Fe-based, and heavy-fermion superconductors with nested Fermi surfaces. In the case of the high-T-c cuprates we find a d-wave order parameter, as well as a nematic state upon increased doping. For Fe-based superconductors, we obtain s(perpendicular to) gap symmetry, while for heavy-fermion CeCoIn5 we find unconventional d-wave pairing. These results provide a proof of concept that EPI cannot be excluded as a mediator of unconventional and of high-T-c superconductivity.