Emergence of Fully-Gapped $s_{++}$-wave and Nodal d-wave States Mediated by Orbital- and Spin-Fluctuations in Ten-Orbital Model for KFe$_2$Se$_2$

TL;DR

This paper investigates the superconducting states in KFe$_2$Se$_2$, revealing how orbital and spin fluctuations lead to different gap structures, with implications for experimental identification of the pairing symmetry.

Contribution

It demonstrates the emergence of both fully-gapped $s_{++}$-wave and nodal d-wave states mediated by orbital and spin fluctuations in a ten-orbital model without hole pockets.

Findings

Spin fluctuations induce a nodal d-wave state in large Coulomb interaction regime.

Orbital fluctuations from electron-phonon interactions produce a fully-gapped $s_{++}$-wave state.

Superconducting gap structures can be distinguished by experimental measurements.

Abstract

We study the superconducting state in newly discovered high-Tc superconductor K$_x$Fe$_2$Se$_2$ based on the ten-orbital Hubbard-Holstein model without hole-pockets. When the Coulomb interaction is large, spin-fluctuation mediated d-wave state appears due to the nesting between electron-pockets. Interestingly, the symmetry of the body-centered tetragonal structure in K$_x$Fe$_2$Se$_2$ requires the existence of nodes in the d-wave gap, although fully-gapped d-wave state is realized in the case of simple tetragonal structure. In the presence of moderate electron-phonon interaction due to Fe-ion optical modes, on the other hand, orbital fluctuations give rise to the fully-gapped $s_{++}$-wave state without sign reversal. Therefore, both superconducting states are distinguishable by careful measurements of the gap structure or the impurity effect on Tc.