Self-consistent calculations of superconductivity in a nearly antiferromagnetic Fermi liquid

Abstract

Within a Hubbard model with on-site repulsion U and nearest-neighbor hopping t¯ in the two-dimensional copper oxide plane, we have carried out self-consistent calculations of the superconducting critical temperature ${\mathit{T}}_{\mathit{c}}$ resulting from spin and charge fluctuations. The gap is found to have ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ symmetry and ${\mathit{T}}_{\mathit{c}}$≃0.016t¯. Superconductivity exists only for a narrow range of U, very near the antiferromagnetic instability (${\mathit{U}}_{\mathit{c}}$). In this region near ${\mathit{U}}_{\mathit{c}}$, the Stoner enhancement in the incommensurate peaks of the spin susceptibility near (π,π) is of order 100–200. The absolute size of the peaks at ${\mathit{T}}_{\mathit{c}}$ is of the same order as measured, as is also the relative height of peaks to background. However, the theory predicts a suppression of these structures as T is reduced below ${\mathit{T}}_{\mathit{c}}$ which is much faster than observed.