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 $s_{\pm }$ gap symmetry, while for heavy-fermion ${\mathrm{CeCoIn}}_5$ 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.

• Received 23 June 2021
• Revised 7 September 2021
• Accepted 18 October 2021

DOI:https://doi.org/10.1103/PhysRevB.104.L140506

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

Published by the American Physical Society