Superconducting states from spin-fluctuation mechanisms.

Abstract

The exchange of antiferromagnetic spin fluctuations leads to highly anisotropic pairing interactions that have attractive as well as repulsive contributions. With these pairing interactions, the self-consistency equation for the order parameter is solved in a square Brillouin zone for different quasiparticle dispersion relations and band fillings. Solutions that transform as the various basis functions of the irreducible representations of the group ${\mathit{D}}_{4}$ are found. Compared to the basis functions usually employed, these solutions show considerably more structure and, most importantly, this structure changes with band filling and with temperature. The sensitivity of the transition temperature to various model parameters is studied and the stability of the different solutions is compared. Unless the attractive interaction resulting from the spin-bag approach dominates, which appears to be unlikely, a state that transforms as cos${\mathit{k}}_{\mathit{x}}$-cos${\mathit{k}}_{\mathit{y}}$ is found to be the most stable one. The spin-bag mechanism does, however, contribute to the stability of this state. The most likely state resulting from spin-fluctuation exchange would thus have nodes in the energy gap on the Fermi line, unless at some temperature the symmetry of the order parameter changes. We have searched for such bifurcations in the solution of the nonlinear self-consistency equation but have found none in the relevant parameter regime. The effect of specific momentum dependences of the order parameter on the density of states and the size of the apparent gap is discussed.