η-pairing superconductivity in the spin-polarized strong-coupling negative-UHubbard 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 \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\rightarrow}\ensuremath{\infty} 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 ``\ensuremath{\eta}-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 ${\mathit{H}}_{\mathit{c}2}$ and excitation spectra both above and below ${\mathit{T}}_{\mathit{c}}$ and demonstrate that the system exhibits a complete Meissner effect.