The mechanism of high-temperature superconductivity (HTS) and the correlation between the antiferromagnetic long-range order (AFLRO) and superconductivity (SC) phases are the central issues of the study of HTS theory. SC and AFLRO of the hole-doped two-dimensional extended t-J model are studied by the variational Monte Carlo method. The results show that SC is greatly enhanced by the long-range hopping terms t' and t" for the optimal and overdoped cases. The phase of coexisting SC and AFM in the t-J model disappears when t' and t" are included. It is concluded that the extended t-J model provides a more accurate description for HTS than the traditional t-J model does. The momentum distribution function n(k) and the shape of Fermi surface play critical roles for establishing the phase diagram of HTS materials.
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