η-pairing superconductivity in the spin-polarized strong-coupling negative-U Hubbard model

Abstract

We have calculated the effect of a single unpaired electron on superconductivity in the strong-coupling negative-U Hubbard model employing a diagram technique with generalized Matsubara frequencies. Using a generalization of the Hamiltonian to n orbitals per site and applying a geometry-controlled approximation in the limit of high coordination numbers z, we perform a loop expansion of the model. This allows us to incorporate fluctuation corrections to the mean-field solution, which emerges as result in lowest order of the loop expansion. We show that in the limit ‖U‖→∞ the mean-field solution exhibits a phase transition to a state that is characterized by a ‘‘staggered’’ local superconducting order parameter with its sign alternating from site to site. This superconducting state (referred to as the ‘‘η-pairing’’ state by a number of authors) for the attractive case is related to the Nagaoka ground state of the repulsive Hubbard model by a partial particle-hole transformation. We have found that the model in the slightly spin-polarized case (i.e., when a single unpaired electron is present) for highly coordinated lattices and in lowest loop order is equivalent to a pair-hopping model with temperature-dependent repulsive coupling. In this paper we report the mean-field results for the transition temperature, the order parameter, the chemical potential, the upper critical magnetic field Hc2 and excitation spectra both above and below Tc and demonstrate that the system exhibits a complete Meissner effect.

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