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$_2$
  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. 
Tetsuro Saito, Seiichiro Onari, Hiroshi Kontani
cond-mat.supr-con cond-mat.str-el