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

We studied 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 $\mathrm{\Gamma }$ 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 (${\mathrm{\Delta }}_h^{-}\mathrm{\ne }0$, ${\mathrm{\Delta }}_e^{+}\mathrm{\ne }0$) and $s_{ee}^{++}$-gap (${\mathrm{\Delta }}_h=0$, $\Delta_e^{+} \neq 0$)solutionswithdifferentpairingcutoffs,$\Lambda_{sf}$ (spin fluctuation energy) and ${ϵ}_b$, respectively. The $s_{ee}^{++}$-gap solution, in which the system dynamically renormalizes the original pairing cutoff ${\mathrm{\Lambda }}_{sf}$ to ${\mathrm{\Lambda }}_{phys}={ϵ}_b$ ($<{\mathrm{\Lambda }}_{sf}$), 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 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 dirty limit.