A unified description of superconducting pairing symmetry in electron-doped Fe-based-122 compounds

The pairing symmetry is examined in highly electron-doped Ba(Fe$_{1-x}$Co$_x$As)$_2$ and A$_y$Fe$_2$Se$_2$ (with A=K, Cs) compounds, with similar crystallographic and electronic band structures. Starting from a phenomenological two-orbital model, we consider nearest-neighbor and next-nearest-neighbor intraorbital pairing interactions on the Fe square lattice. In this model, we find a unified description of the evolution from $s_\pm$-wave pairing ($2.0 < n \lesssim 2.4$) to $d$-wave pairing ($2.4 \lesssim n \lesssim 2.5$) as a function of electron filling. In the crossover region a novel time-reversal symmetry breaking state with $s_\pm+id$ pairing symmetry emerges. This minimal model offers an overall picture of the evolution of superconductivity with electron doping for both $s_\pm$-wave [Ba(Fe$_{1-x}$Co$_x$As)$_2$] and $d$-wave [A$_y$Fe$_2$Se$_2$] pairing, as long as the dopants only play the role of a charge reservoir. However, the situation is more complicated for Ba(Fe$_{1-x}$Co$_x$As)$_2$. A real-space study further shows that when the impurity scattering effects of Co dopants are taken into account, the superconductivity is completely suppressed for $n > 2.4$. This preempts any observation of $d$-wave pairing in this compound, in contrast to A$_y$Fe$_2$Se$_2$.