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.
Highlights
The discovery of superconductivity below Tcexp ∼ 30 K in ThFeAsN [1] has added another member to the growing family of Fe-based superconductors exhibiting large critical temperatures [2,3]
Density functional theory (DFT) studies revealed that the electronic structure of ThFeAsN can be considered as quasi-two-dimensional (2D), while the Fermi surface (FS) is prototypical for the Fe-based compounds [10,11,12]
−1.16 meV < 0 occurs around k = M. This is the prototypical s±-wave state that is shown here, which is the only stable symmetry for the superconducting gap in ThFeAsN, which is true for any choice of parameters we explored in this work
Summary
The discovery of superconductivity below Tcexp ∼ 30 K in ThFeAsN [1] has added another member to the growing family of Fe-based superconductors exhibiting large critical temperatures [2,3] Most compounds in this class of materials show magnetic order in the ground state and allow for a Cooper pair condensate only upon sufficient doping or pressure [4,5]. We argue that the superconducting state can potentially be explained by including spin fluctuations and vertex corrected EPI in a self-consistent Eliashberg formalism. We argue why vertex corrections to the EPI are likely to contribute cooperatively with the spin-fluctuations interaction to the gap magnitude and Tc, Sec. IV B.
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