High Temperature Superconductivity in the 2D t-J Model at   Metal-Insulator Transition: Variational Mean Field Results
  Conventional Hartree-Fock mean field theory is used, for the first time, to investigate the full two-dimensional t-J model. To date, all other nontrivial mean field approaches modify the Hamiltonian or violate the double occupancy constraint. Unlike conventional mean field theory, these methods do not give variational results for the t-J model. The mean field phase diagram of the t-J model predicts enhanced superconductivity at the crossover between an insulating phase at low doping and a metallic phase at moderate doping. This behavior is remarkably similar to that of high temperature superconductors, for which the model is expected to provide a good description. In the mean field approximation, the t-J model is described by self-interacting spinless fermions hopping on a background lattice with spiral antiferromagnetic order. The interaction is attractive and high temperature superconductivity arises from the narrow bandwidth at the insulator to metal crossover. 
Ken Cappon