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We studied pairing mechanism of the heavily electron doped FeSe (HEDIS)systems, which commonly have one incipient hole band -- a band top below theFermi level by a finite energy distance $\epsilon_b$ -- at $\Gamma$ point andordinary electron bands at $M$ points in Brillouin zone (BZ). We found that thesystem allows two degenerate superconducting solutions with the exactly same$T_c$ in clean limit: the incipient $s^{\pm}_{he}$-gap ($\Delta_h^{-} \neq 0$,$\Delta_e^{+} \neq 0$) and $s_{ee}^{++}$-gap ($\Delta_h =0$, $\Delta_e^{+} \neq0$) solutions with different pairing cutoffs, $\Lambda_{sf}$ (spin fluctuationenergy) and $\epsilon_b$, respectively. The $s_{ee}^{++}$-gap solution, inwhich the system dynamically renormalizes the original pairing cutoff$\Lambda_{sf}$ to $\Lambda_{phys}=\epsilon_b$ ($< \Lambda_{sf}$), thereforeactively eliminates the incipient hole band from forming Cooper pairs, butwithout loss of $T_c$, becomes immune to the impurity pair-breaking. As aresult, the HEDIS systems, by dynamically tuning the pairing cutoff andselecting the $s_{ee}^{++}$-pairing state, can always achieve the maximum $T_c$-- the $T_c$ of the degenerate $s^{\pm}_{he}$ solution in the ideal clean limit-- latent in the original pairing interactions, even in dirty limit.

Pairing Mechanism of the Heavily Electron Doped FeSe Systems: Dynamical Tuning of the Pairing Cutoff Energy