The pairing glue of high-T_c superconductivity in heavily electron-doped (e-doped) FeSe, in which hole pockets are absent, has been an important unsolved problem. Here, we focus on a heavily e-doped bulk superconductor Li_1−xFe_xOHFeSe (T_c∼40K). We construct a multiorbital model beyond the rigid band approximation and analyze the spin and orbital fluctuations by taking both vertex corrections (VCs) and self-energy into consideration. Without e-doping (x=0), the ferro-orbital order without magnetism in FeSe is reproduced by the VCs. The orbital order quickly disappears when the hole pocket vanishes at x∼0.03. With increasing x further, the spin fluctuations remain small, whereas orbital fluctuations gradually increase with x due to the VCs. The negative feedback due to the self-energy is crucial to explain experimental phase diagram. Thanks to both vertex and self-energy corrections ,the orbital-fluctuation-mediated s₊₊-wave state appears for a wide doping range, consistent with experiments.

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