  The enigma of unconventional superconductivity in doped cuprates presents a
formidable challenge in the realm of condensed matter physics. Recent findings
of strong near-neighbor attractions in one-dimensional cuprate chains suggest a
new avenue for investigating cuprate superconductors. Consequently, we
revisited the superconductivity in the extended Hubbard model at the mean-field
level. Anticipating a prevalence of antiferromagnetic order due to strong local
Coulomb repulsion, our calculations reveal the coexistence of superconducting
and antiferromagnetic orders across a wide range of doping at sufficiently low
temperatures. The mean-field results capture some key features of cuprate
superconductors, including $d$-wave pairing symmetry, a dome-shaped dependence
of $T_c$ on doping, and higher superconducting transition temperatures.
Additionally, we observed a nearly proportional relationship between $T_c$ and
the strength of the nearest-neighbor attraction, reminiscent of experimental
findings at the FeSe/SrTiO3 interface. The mean-field results suggest that the
extended Hubbard model could be the appropriate framework for investigating
cuprate superconductivity and offer insights for more precise calculations
within this model in future.
