  Based on a two-orbit four-band tight binding model, we investigate the
low-lying electronic states around the interstitial excess Fe ions in the
iron-based superconductors by using T-matrix approach. It is shown that the
local density of states at the interstitial Fe impurity (IFI) possesses a
strong resonance inside the gap, which seems to be insensitive to the doping
and the pairing symmetry in the Fe-Fe plane, while a single or two resonances
appear at the nearest neighboring (NN) Fe sites. The location and height of the
resonance peaks only depend on the hopping $t$ and the pairing parameter
$\Delta_I$ between the IFI and the NN Fe sites. These in-gap resonances are
originated in the Andreev's bound states due to the quasiparticle tunneling
through the IFI, leading to the change of the magnitude of the superconducting
order parameter. When both $t$ and $\Delta_I$ are small, this robust
zero-energy bound state near the IFI is consistent with recent scanning
tunneling microscopy observations.

Superconductivity