We propose that if there are two small pocketlike Fermi surfaces, and the spin susceptibility is pronounced around a wave vector Q that bridges the two pockets, the spin-singlet superconductivity mediated by spin fluctuations may have a high transition temperature. Using the fluctuation exchange approximation, this idea is confirmed for the Hubbard on a lattice with alternating hopping integrals, for which T-c is estimated to be almost an order of magnitude larger than those for systems with a large connected Fermi surface.
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