Mean-field theories of cuprate superconductors: A systematic analysis

The lattice Anderson model believed to be relevant to high-temperature superconductors and heavy-fermion metals exhibits a variety of different behaviors, including mixed-valence, heavy-fermion, and Mott-insulating states. We determine, via an auxiliary-boson mean-field theory, the parameter regimes in which these behaviors exist. For the two-dimensional ${\mathrm{CuO}}_2$ Anderson model we calculate the susceptibility, and quasiparticle plasma frequency. By comparing these to specific-heat, susceptibility and optical data for high-${\mathit{T}}_{\mathit{c}}$ superconductors, we determine that the materials are in a regime controlled by proximity to a Mott transition and that magnetic correlations play an essential role.