The superconducting instabilities of the doped repulsive 2D Hubbard model are studied in the intermediate to strong coupling regime with the help of the dynamical cluster approximation. To solve the effective cluster problem we employ an extended noncrossing approximation, which allows for a transition to the broken symmetry state. At sufficiently low temperatures we find stable $d$-wave solutions with off-diagonal long-range order. The maximal $T_c\approx 150\mathrm{K}$ occurs for a doping $\delta \approx 20\%$ and the doping dependence of the transition temperatures agrees well with the generic high- $T_c$ phase diagram.

• Received 24 February 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.1524