Exploring multichannel superconductivity in ThFeAsN

TL;DR

This paper theoretically investigates the superconducting state of ThFeAsN, showing that spin fluctuations can explain a low $T_c$ and suggesting that vertex corrections to the electron-phonon interaction are key to understanding the higher experimental $T_c$.

Contribution

It introduces the role of first-order vertex corrections to the electron-phonon interaction in explaining the high $T_c$ and gap magnitude in ThFeAsN, beyond standard Eliashberg theory.

Findings

Spin fluctuations alone yield $T_c$ up to ~7.5 K with $s_{±}$ symmetry.

Other interaction combinations suppress $T_c$ due to phase frustration.

Vertex corrections to EPI support $s_{±}$ symmetry and enhance spin fluctuation effects.

Abstract

We investigate theoretically the superconducting state of the undoped Fe-based superconductor ThFeAsN. Using input from $ab~initio$ calculations, we solve the Fermi-surface based, multichannel Eliashberg equations for Cooper-pair formation mediated by spin and charge fluctuations, and by the electron-phonon interaction (EPI). Our results reveal that spin fluctuations alone, when coupling only hole-like with electron-like energy bands, can account for a critical temperature $T_c$ up to $\sim7.5\,\mathrm{K}$ with an $s_{\pm}$-wave superconducting gap symmetry, which is a comparatively low $T_c$ with respect to the experimental value $T_c^{\mathrm{exp}}=30\,\mathrm{K}$. Other combinations of interaction kernels (spin, charge, electron-phonon) lead to a suppression of $T_c$ due to phase frustration of the superconducting gap. We qualitatively argue that the missing ingredient to explain the gap magnitude and $T_c$ in this material is the first-order correction to the EPI vertex. In the noninteracting state this correction adopts a form supporting the $s_{\pm}$ gap symmetry, in contrast to EPI within Migdal's approximation, i.e., EPI without vertex correction, and therefore it enhances tendencies arising from spin fluctuations.