  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.
