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

TL;DR

This study reveals that heavily electron doped FeSe systems can dynamically tune their pairing cutoff energy, favoring an impurity-immune superconducting state with maximum critical temperature, by eliminating the incipient hole band from pairing.

Contribution

It demonstrates the existence of two degenerate pairing solutions with different cutoff energies and shows how the system dynamically selects an impurity-resistant state to maximize $T_c$.

Findings

The system supports two degenerate superconducting solutions with different pairing cutoffs.

The $s_{ee}^{++}$ solution dynamically renormalizes the pairing cutoff to eliminate the incipient hole band.

The $s_{ee}^{++}$ state is immune to impurity pair-breaking and achieves maximum $T_c$.

Abstract

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 $\epsilon_b$ -- at $\Gamma$ 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 $s^{\pm}_{he}$-gap ($\Delta_h^{-} \neq 0$, $\Delta_e^{+} \neq 0$) and $s_{ee}^{++}$-gap ($\Delta_h =0$, $\Delta_e^{+} \neq 0$) solutions with different pairing cutoffs, $\Lambda_{sf}$ (spin fluctuation energy) and $\epsilon_b$, respectively. The $s_{ee}^{++}$-gap solution, in which the system dynamically renormalizes the original pairing cutoff $\Lambda_{sf}$ to $\Lambda_{phys}=\epsilon_b$ ($< \Lambda_{sf}$), 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 $s^{\pm}_{he}$ solution in the ideal clean limit -- latent in the original pairing interactions, even in dirty limit.