  Recent experiments on Zn-doped 122-type iron pnictides,
Ba(Fe$_{1-x-y}$Co$_y$Zn$_x$)$_2$As$_2$, are challenging our understanding of
electron doping the 122s and the interplay between doping and impurity
scattering. To resolve this enigma, we investigate the disorder effects of
nonmagnetic Zn impurities in the strong (unitary) scattering limit on various
properties of the system in the $s_{\pm}$-wave superconducting pairing state.
The lattice Bogoliubov-de Gennes equation (BdG) is solved self-consistently
based on a minimal two-orbital model with an extended range of impurity
concentrations. We find that Zn impurity is best modeled as a defect, where
charge is mainly localized, but scattering is extended over a few lattice
sites. With increasing Zn concentration the density of states shows a gradual
filling of the gap, revealing the impurity-induced pair breaking effect.
Moreover, both the disorder configuration-averaged superconducting order
parameter and the superfluid density are dramatically suppressed towards the
dirty limit, indicating the violation of the Anderson theorem for conventional
s-wave superconductors and the breakdown of the Abrikosov-Gorkov theory for
impurity-averaged Green's functions. Furthermore, we find that the
superconducting phase is fully suppressed close to the critical impurity
concentration of roughly $n_\text{imp}\approx 10%$, in agreement with recent
experiments.
