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Several Fe chalcogenide superconductors without hole pockets at the Fermilevel display high temperature superconductivity, in apparent contradiction tonaive spin fluctuation pairing arguments. Recently, scanning tunnelingmicroscopy measurements have measured the influence of impurities on some ofthese materials, and claimed that non-magnetic impurities do not create in-gapstates, leading to the conclusion that the gap must be $s_{++}$, i.e.conventional $s$ wave with no gap sign change. Here we critique this argument,and give various ways sign-changing gaps can be consistent with the absence ofsuch bound states. In particular, we calculate the bound states for an $s_\pm$system with a hole pocket below the Fermi level, and show that the nonmagneticimpurity bound state energy generically tracks the gap edge $E_{min}$ in thesystem, thereby rendering it unobservable. A failure to observe a bound statein the case of a nonmagnetic impurity can therefore not be used as an argumentto exclude sign-changing pairing states.

Effect of nonmagnetic impurities on $s_\pm$ superconductivity in the presence of incipient bands