Superconductivity without hole-pocket in electron-doped FeSe: Analysis beyond the Migdal-Eliashberg formalism

High-Tc pairing mechanism absent of hole-pockets in heavily electron-doped FeSe is one of the key unsolved problems in Fe-based superconductors. Here, this problem is attacked by focusing on the higher-order many-body effects neglected in conventional Migdal-Eliashberg formalism. We uncover two significant many-body effects for high-Tc superconductivity: (i) Due to the "vertex correction", the dressed multiorbital Coulomb interaction acquires prominent orbital dependence for low-energy electrons. The dressed Coulomb interaction not only induces the orbital fluctuations, but also magnifies the electron-boson coupling constant. Therefore, moderate orbital fluctuations give strong attractive pairing interaction. (ii) The "multi-fluctuation-exchange pairing process" causes large inter-pocket attractive force, which is as important as usual single-fluctuation-exchange process. Due to these two significant effects dropped in the Migdal-Eliashberg formalism, the anisotropic $s_{++}$-wave state in heavily electron-doped FeSe is satisfactorily explained. The proposed "inter-electron-pocket pairing mechanism" will enlarge Tc in other Fe-based superconductors.