Mean field analysis of a model for superconductivity in an anti-ferromagnetic background

Abstract We study a lattice fermion model for superconductivity in the presence of an anti-ferromagnetic background, described as a fixed external staggered magnetic field. We discuss the possibility that our model provides an effective description of coexistence of anti-ferromagnetic correlations and superconductivity, and its possible application to high-temperature superconductivity. We also argue that, under certain conditions, this model describes a variant of the periodic Anderson model for heavy fermions. Using a path integral formulation we construct mean field equations, which we study in some detail. We evaluate the superconducting critical temperature and show that it is strongly enhanced by anti-ferromagnetic order. We also evaluate the superconducting gap, the superconducting density of states, and the tunneling conductivity, and show that the most stable channel usually has a d x 2 − y 2 -wave gap.