Fluctuation Effect in Superconductivity in an Electron Model with d-Wave Attraction

On the basis of $t$-matrix approximation, we study the superconductivity in the tight-binding model with d-wave attraction. The low-lying collective modes are considered as the predominant long-range fluctuations in the system. The Green's function is obtained as an analytic solution to a cubic equation. The superconducting order parameter and the transition temperature are substantially reduced from the values of the mean-field theory. The results for the pseudogap parameter at $T_c$ are compared with experiments. The calculated phase boundary of the superconductivity can reasonably describe the experiment results for the cuprates. The results for density of states are presented.