The phase diagram of the t-J-V model is discussed using a 1/N expansion in terms of X operators. It is shown that a flux phase of d-wave symmetry is stabilized by the Coulomb interaction V at intermediate dopings and competes with d-wave superconductivity. Since the flux wave instability is stronger than the superconducting one optimal doping is essentially determined by the onset of the flux phase. Below optimal doping the flux phase coexists with superconductivity at low and exists as a pseudo gap phase at higher temperatures. It is also found that the flux phase boundary is much less sensitive to impurity scattering than the boundary for superconductivity in agreement with experiments in Zn doped La-214 and (Y,Ca)-123.
We study the bilayer generalization of the $t\text{\ensuremath{-}}J$ model with both hopping and exchange coupling between the two layers. Within the enlarged mean-field parameter space, we find dimerized,
s+id, flux ladder and planar flux phases. Of particular interest is the planar flux phase that persists farther away from half-filling, and coexists with, and even stabilizes, ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-superconductivity. The orbital currents in the phase generate staggered moments that are rotated away from the
c-axis.