Emergence of fully gappeds++-wave and nodald-wave states mediated by orbital and spin fluctuations in a ten-orbital model of KFe2Se2

Abstract

We study the superconducting state in recently discovered high-${T}_{\mathrm{c}}$ superconductor ${\mathrm{K}}_{x}$Fe${}_{2}$Se${}_{2}$ based on the ten-orbital Hubbard-Holstein model without hole pockets. When the Coulomb interaction is large, a spin-fluctuation-mediated $d$-wave state appears due to the nesting between electron pockets. Interestingly, the symmetry of the body-centered tetragonal structure in ${\mathrm{K}}_{x}$Fe${}_{2}$Se${}_{2}$ requires the existence of nodes in the $d$-wave gap, although a fully gapped $d$-wave state is realized in the case of a simple tetragonal structure. In the presence of moderate electron-phonon interaction due to Fe-ion optical modes, however, 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 ${T}_{\mathrm{c}}$.