Unconventional superconductivity mediated solely by isotropic electron-phonon interaction

TL;DR

This paper demonstrates that isotropic electron-phonon interactions can mediate unconventional superconductivity with various gap symmetries, challenging the traditional view that EPI cannot produce sign-changing gaps.

Contribution

It introduces a comprehensive Eliashberg theory including vertex corrections, showing EPI can lead to unconventional pairing in different superconductor classes.

Findings

Cuprates exhibit d-wave and nematic states.

Fe-based superconductors show s± gap symmetry.

Heavy-fermion CeCoIn5 has d-wave pairing.

Abstract

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 selfconsistently 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 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 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.