Theoretical study of spin-fluctuation-mediated superconductivity in two-dimensional Hubbard models with an incipient flat band

One promising way to enhance superconductivity is to have coexisting wide and incipient narrow bands, where the Fermi level intersecting the wide band lies just above the narrow band, by which finite-energy spin fluctuations act as glue to mediate pair scattering. As an extreme case of the narrow band dispersion, we investigate spin-fluctuation-mediated superconductivity in two-dimensional Hubbard models with an incipient flat band. For all of the systems investigated in this study, the Kagome, Lieb, and bilayer square lattices with a flat band, we find that spin-singlet pairing superconductivity is enhanced when the flat band is nearly fully filled, due to the interband pair scattering even when the flat band becomes dispersive by correlation effects. Among these models, enhancement of superconductivity is weak in the Lieb lattice, possibly because the density of states of the wide band goes to zero at the Dirac point where the flat and wide bands intersect. Also, when the electron density is smaller so that the flat band approaches half-filling, ferromagnetic spin fluctuations and spin-triplet pairing arises, which does not develop strongly compared to the case of the spin-singlet pairing for the incipient band situation.