Projected BCS theory for the unification of antiferromagnetism and strongly correlated superconductivity

A close connection between antiferromagnetism and superconductivity is at the core of high-temperature superconductivity. Here, we put forward the projected BCS theory for the unification of antiferromagnetism and strongly correlated superconductivity. Specifically, it is shown that, with the d-wave pairing symmetry, the projected BCS theory can provide excellent trial states at general doping for the exact ground states of the t-J model in the square lattice, generating a unified theory of high-temperature superconductivity as a continuous function of hole concentration. A key to the success of the projected BCS theory is an accurate treatment of the strong correlation between Cooper pairs, which not only causes the breakdown of superconductivity itself at half filling but also defines the precise nature of strongly correlated superconductivity at moderate doping. Also, via the proper incorporation of particle number fluctuations, the projected BCS theory allows direct computation of the superconducting order parameter, shedding important light on the pseudogap phenomenon.