We investigate superconductivity in a two-band system with an electron- and hole-like band, where one of the bands is away from the Fermi level (or incipient). We argue that the incipient band contributes significantly to spin-fluctuation pairing in the strong coupling limit where the system is close to a magnetic instability, and can lead to a large Tc. In this case, Tc is limited by a competition between the frequency range of the coupling (set by an isolated paramagnon) and the coupling strength itself, such that a dome-like Tc dependence on the incipient band position is obtained. The coupling of electrons to phonons is found to further enhance Tc. The results are discussed in the context of experiments on monolayers and intercalates of FeSe.
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