We present a strong-coupling study of the competition and interplay between the d-density wave (DDW) and d-wave superconducting (DSC) states within the fluctuation-exchange approximation for the two-dimensional Hubbard model. We find the occurrence of a new DDW state with phase fluctuations induced by spin fluctuations above $T_C$. It is shown that in this state the density of states has a pseudogap, which is strong in the underdoped regime, but is weak in the overdoped regime. We obtain new results for the full reduction of $T_C$ in the strong DDW state, a strong enhancement of $T_C$ in the weak DDW state, and the coexistence of the ordered DDW and DSC states below $T_C$. This sheds new light on a comprehensive explanation of both the pseudogap and high-$T_C$ superconductivity in cuprates.

我们对二维Hubbard模型的波动交换近似中的d密度波（DDW）和d波超导（DSC）状态之间的竞争和相互作用进行了强耦合研究。我们发现出现了一种新的DDW状态，该状态具有由自旋波动引起的相位波动，高于${Ť}_C$。结果表明，在这种状态下，状态密度具有伪间隙，在掺杂不足的情况下很强，而在掺杂过量的情况下很弱。我们获得了新的结​​果，可以完全减少${Ť}_C$ 在强大的DDW状态下， ${Ť}_C$ 处于弱DDW状态，并且以下有序DDW和DSC状态共存 ${Ť}_C$。这为伪间隙和高间隙的全面解释提供了新的思路。${Ť}_C$ 铜酸盐的超导性。