Unconventional superconductivity mediated solely by isotropic electron-phonon interaction

Fabian Schrodi,Alex Aperis,Peter M Oppeneer

doi:10.1103/physrevb.104.l140506

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 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 ${s}_{\ifmmode\pm\else\textpm\fi{}}$ 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.

Highlights

Superconductors with unconventional—that is, non-swave—gap symmetries continue to attract great interest, because of their unique properties [1,2] and because they are closely linked to the as yet unexplained phenomenon of high-Tc superconductivity [3,4]
It has been demonstrated that a small-q-peaked electron-phonon interaction (EPI) can give rise to the unconventional gap of the cuprates and the Fe pnictides in the presence of enhanced Coulomb repulsion between electrons [18,19]
Our calculations reveal that the strongly momentumdependent gap symmetries in these superconductors can be obtained solely via isotropic EPI provided that vertex corrections to the electron self-energy are taken into account

Summary

Introduction

Superconductors with unconventional—that is, non-swave—gap symmetries continue to attract great interest, because of their unique properties [1,2] and because they are closely linked to the as yet unexplained phenomenon of high-Tc superconductivity [3,4]. In the case of phonons, Migdal showed that when the so-called nonadiabatic ratio α = / F is small (∼10−2), vertex corrections to the electron self-energy due to the EPI are negligible [21].

Results

Conclusion