New superconductivity induced by d-density wave in high-temperature superconductors

We present a self-consistent theory of the interplay between the d-density wave (DDW) and superconductivity on the basis of the fluctuation-exchange (FLEX) approximation for the two-dimensional (2D) Hubbard model with the nearest-neighbor hopping t and on-site Coulomb repulsion U. In order to stabilize the DDW state with respect to phase separation at lower dopings a small nearest-neighbor Coulomb repulsion V is included within the Hartree–Fock approximation. The competition between the DDW and superconductivity can generically result in the appearance of a new superconducting state, which has the π-pairing order parameter. We solve the gap equations for competing DDW, BCS, and π-pairing order parameters with d-wave symmetry, together with calculating the FLEX interaction self-consistently, and calculating the corresponding three transition temperatures T⁎, Tc, and Tc⁎ as a function of hole doping. The calculated phase diagram has a quantum critical point (QCP) separating a pure BCS superconducting state at large dopings δ>δ0 from a coexisting DDW and π-pairing state at lower dopings δ<δ0. Remarkable is the much higher value of the Tc⁎ for the π-pairing superconductivity as compared with the pure BCS superconductivity.