Cooper pairing with the onsite exchange interaction: A possible mechanism of high-temperature superconductivity

Among the various mechanisms proposed for unconventional superconductivity, this paper focuses on the Coulomb interaction responsible for $d$-wave and $s\pm$-wave pairing symmetries in cuprates and iron pnictides. Although the effective interaction $U_\text{eff}=U-J$ is predominantly repulsive, an attractive component arising from the Hund's coupling parameter $J$ is sufficient to bind fractional charges. Evaluating this binding energy within a single-band Hubbard model yields a superconducting pairing gap $\Delta_0$ and estimates the transition temperature $T_c$. Given the complex electronic structure and vast compositional space of these materials, the model focuses exclusively on the doped superconducting plane hosting these fractional charges. Through this approach, an analytical expression dependent on the Hubbard $U$ and Hund $J$ parameters that accurately reproduces the superconducting dome is derived. Furthermore, the model successfully addresses the characteristic electron and hole doping asymmetry observed in cuprates by accounting for Hund's coupling parameters. Finally, while the theory accurately describes strange metal behavior, it currently provides only a qualitative explanation for the pseudogap phase and the underdoped isotope effect.