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Superconductivity assisted by inter-layer pair hopping in multi-layered cuprates

In order to explore why the multi-layered cuprates have such high Tc's, we have examined various inter-layer processes. Since the inter-layer one-electron hopping has little effects on the band structure, we turn to the inter-layer pair hopping. The superconductivity in a double-layer Hubbard model with and without the inter-layer pair hopping, as studied by solving the Eliashberg equation with the fluctuation exchange approximation, reveals that the inter-layer pair hopping acts to increase the pairing interaction and the self-energy simultaneously, but that the former effect supersedes the latter and enhances the superconductivity. The inter-layer pair hopping considered here is for off-site pairs, for which we discuss the effect of retaining SU(2) symmetry, along with how the the sign of the pair hopping determines the relative configuration of d-waves between the adjacent layers.