We study the $t\text{−}J\text{−}V$ model of a doped Mott insulator in connection to high-$T_c$ superconductors. The nearest neighbor Coulomb interaction $\left(V\right)$ is treated quantum mechanically on equal footing as the antiferromagnetic exchange interaction $\left(J\right)$. Motivated by the $SU\left(2\right)$ symmetry at half-filling, we construct a large-$N$ theory which allows a systematic study of the interplay between staggered flux order and superconductivity upon doping. We solve the model in the large-$N$ limit and obtain the ground state properties and the phase diagram as a function of doping. We discuss the competition and the coexistence of the staggered flux and the $d$-wave superconductivity in the underdoped regime and the disappearance of superconductivity in the overdoped regime.

• Received 28 April 2004

DOI:https://doi.org/10.1103/PhysRevB.70.020501