c 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-T_c 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 interpocket attractive force, which is as important as the 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 T_c in other Fe-based superconductors.

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