Superconducting instability of staggered-flux phase in the t-J model

We use a renormalized mean-field theory to study competitions between the flux phase and the resonating-valence-bond d-wave states in the t-J model. The staggered (antiferromagnetic) flux phase is unstable against infinitesimal electron-pairing amplitude at all non-half fillings. This instability finally leads to a pure d-wave resonating-valence-bond state. The hole-hole repulsive Coulomb interaction tends to stabilize the flux phase.