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High-Tc pairing mechanism absent of hole-pockets in heavily electron-dopedFeSe is one of the key unsolved problems in Fe-based superconductors. Here,this problem is attacked by focusing on the higher-order many-body effectsneglected in conventional Migdal-Eliashberg formalism. We uncover twosignificant many-body effects for high-Tc superconductivity: (i) Due to the"vertex correction", the dressed multiorbital Coulomb interaction acquiresprominent orbital dependence for low-energy electrons. The dressed Coulombinteraction not only induces the orbital fluctuations, but also magnifies theelectron-boson coupling constant. Therefore, moderate orbital fluctuations givestrong attractive pairing interaction. (ii) The "multi-fluctuation-exchangepairing process" causes large inter-pocket attractive force, which is asimportant as usual single-fluctuation-exchange process. Due to these twosignificant 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 otherFe-based superconductors.

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