| Summary: | We studied the pairing mechanism of the heavily electron doped FeSe (HEDIS) systems, which commonly have one incipient hole band—a band top below the Fermi level by a finite energy distance ε _b —at Γ point and ordinary electron bands at M points in Brillouin zone (BZ). We found that the system allows two degenerate superconducting solutions with the exactly same T _c in clean limit: the incipient ${s}_{{he}}^{\pm }$ -gap ( ${{\rm{\Delta }}}_{h}^{-}\ne 0$ , ${{\rm{\Delta }}}_{e}^{+}\ne 0$ ) and ${s}_{{ee}}^{++}$ -gap (Δ _h = 0, ${{\rm{\Delta }}}_{e}^{+}\ne 0$ ) solutions with different pairing cutoffs, Λ _sf (spin fluctuation energy) and ε _b , respectively. The ${s}_{{ee}}^{++}$ -gap solution, in which the system dynamically renormalizes the original pairing cutoff Λ _sf to Λ _phys = ε _b (<Λ _sf ), therefore actively eliminates the incipient hole band from forming Cooper pairs, but without loss of T _c , becomes immune to the impurity pair-breaking. As a result, the HEDIS systems, by dynamically tuning the pairing cutoff and therefore selecting the ${s}_{{ee}}^{++}$ -pairing state, can always achieve the maximum T _c —the T _c of the degenerate ${s}_{{he}}^{\pm }$ solution in the ideal clean limit—latent in the original pairing interactions, even in the dirty limit.
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