We report the observation by angle-resolved photoemission spectroscopy of an impurity state located inside the superconducting gap of Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ and vanishing above the superconducting critical temperature, for which the spectral weight is confined in momentum space near the Fermi wave vector positions. We demonstrate, supported by theoretical simulations, that this in-gap state originates from weak non-magnetic scattering between bands with opposite sign of the superconducting gap phase. This weak scattering, likely due to off-plane Ba/K disorders, occurs mostly among neighboring Fermi surfaces, suggesting that the superconducting gap phase changes sign within holelike (and electronlike) bands. Our results impose severe restrictions on the models promoted to explain high-temperature superconductivity in these materials.
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