d-wave superconductivity and its coexistence with antiferromagnetism in the t–J–U model : statistically consistent Gutzwiller approach

We discuss the coexistence of antiferromagnetism and d-wave superconductivity within the so-called statistically consistent Gutzwiller approximation (SGA) applied to the t–J–U model. In this approach, the averages calculated in a self-consistent manner coincide with those determined variationally. Such consistency is not guaranteed within the standard renormalized mean-field theory. With the help of SGA, we show that for the typical value $J/\left | t \right |=\frac{1}{3}$, coexistence of antiferromagnetism (AF) and superconductivity (SC) appears only for $U/\left | t \right |> 10.6$ and in a very narrow range of doping $\left ( \delta _{\sim }^{<} 0.006 \right )$ in the vicinity of the Mott insulating state, in contrast to some previous reports. In the coexistent AF+SC phase, a staggered spin-triplet component of the superconducting gap appears also naturally; its value is very small