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Electron pairing in the presence of incipient bands in iron-based superconductors

Recent experiments on certain Fe-based superconductors have hinted at a role for paired electrons in "incipient" bands that are close to, but do not cross the Fermi level. Related theoretical works disagree on whether or not strong-coupling superconductivity is required to explain such effects, and whether a critical interaction strength exists. In this work, we consider various versions of the model problem of pairing of electrons in the presence of an incipient band, within a simple multiband weak-coupling BCS approximation. We categorize the problem into two cases: case(I) where superconductivity arises from the "incipient band pairing" alone, and case(II) where it is induced on an incipient band by pairing due to Fermi-surface based interactions. Negative conclusions regarding the importance of incipient bands have been drawn so far largely based on case(I), but we show explicitly that models under case(II) are qualitatively different, and can explain the non-exponential suppression of Tc, as well as robust large gaps on an incipient band. In the latter situation, large gaps on the incipient band do not require a critical interaction strength. We also model the interplay between phonon and spin fluctuation driven superconductivity and describe the bootstrap of electron-phonon superconductivity by spin fluctuations coupling the incipient and the regular bands. Finally, we discuss the effect of the dimensionality of the incipient band on our results. We argue that pairing on incipient bands may be significant and important in several Fe-based materials, including LiFeAs, FeSe intercalates and FeSe monolayers on strontium titanate, and indeed may contribute to high critical temperatures in some cases.