Cooper Pairing Mediated by Onsite Exchange: A Possible Mechanism For High-Temperature Superconductivity

Abstract

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 multi-orbital interaction $U_\text{eff}=U-J$ is predominantly repulsive, an attractive component driven by the Hund's coupling parameter $J$ is sufficient to bind fractional charges. This attractive multi-orbital contribution and a repulsive term of the single-band Hubbard model yield the superconducting pairing gap $Δ_0$ and an estimate of 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 mainly dependent on the Hubbard $U$ and Hund $J$ parameters that reproduces the empirical superconducting dome is derived. Furthermore, the model addresses the characteristic electron and hole doping asymmetry observed in cuprates by accounting for Hund's coupling parameters. Finally, while the model describes strange metal behavior, it currently provides only a qualitative explanation for the pseudogap phase and the underdoped isotope effect.