Abstract
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 $t\text{\ensuremath{-}}J$ 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.
Highlights
Despite the large variety in material properties, there is a certain list of common features robust across various hightemperature superconductors
Our work is motivated by a remarkable similarity between the resonating valence bond (RVB) state [1] for high-temperature superconductivity and the composite fermion (CF) state [16] for the fractional quantum Hall effect (FQHE)
As a result, capturing both AF at half filling and strongly correlated superconductivity (SCSC) at moderate doping, a unified theory is obtained by computing the numberweighted overlap squared between the exact ground states of the t-J model and the projected BCS theory with the d-wave pairing symmetry
Summary
Despite the large variety in material properties, there is a certain list of common features robust across various hightemperature superconductors. A problem is that, at half filling, the RVB state reduces to a spin liquid rather than the true antiferromagnet with the long-range order, i.e., the Néel state. A breakthrough of the unified theory is that the Gutzwiller projection is directly applied onto the BCS Hamiltonian itself, not just its ground state. It is shown that the projected BCS theory provides excellent trial states for the exact ground states of the t-J model in the square lattice for a wide range of hole concentration. The projected BCS theory with the d-wave pairing symmetry continues to provide excellent trial states for the t-J model, demonstrating the merit of unifying AF and SCSC, as emphasized by the SO(5) theory [15]. The projected BCS theory can be used to investigate the relevance of the s-wave pairing symmetry as well as the geometrical frustration to high-temperature superconductivity
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