Pairing mechanism in two Hubbard models that show $d_{x^2-y^2}$ pairing

Özet

Here we examine various aspects of the pairing mechanism for two models, the two-dimensional and two-leg ladder Hubbard models. Both of these models exhibit pairing correlations with $d_{x^2-y^2}$ symmetry. However, the undoped insulating states of these two systems are different with the two-dimensional lattice characterized by a ground state with long-range antiferromagnetic order and the two-leg ladder having a spin gap in its ground state. Our aim is to gain a better understanding of the underlying pairing mechanism which causes $d_{x^2-y^2}$ pairing in these two models.