Exploring high-temperature superconductivity in the extended Hubbard model with antiferromagnetic tendencies

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 observe a nearly proportional relationship between $T_c$ and the strength of the nearest-neighbor attraction, reminiscent of experimental findings at the ${\mathrm{FeSe}/\mathrm{SrTiO}}_3$ 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 the future.