Abstract
It is important to study the many-body effects of the electrons on the flat band lattice, since the flatness of the dispersion may lead to instabilities in the presence of interactions. To clarify the effects of flat dispersion for superconductivity, we investigate a simple two-band BCS Hamiltonian, where one of the bands has a flat dispersion, in the mean field approximation. A superconducting gap Δ and a critical temperature T c strongly depend on the pairing coupling constant V. Especially, for small coupling constant, Δ and T c are proportional to V, which are quite different from the single band BCS cases. Higher T c, compared to the normal BCS system, are realized due to the existence of the flat band.
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