"W=0" pairing in Cu-O clusters and in the plane

The Cu-O plane and the clusters that possess the same C4v symmetry around a Cu ion have 2-hole eigenstates of the kinetic energy with vanishing on-site repulsion (W=0 pairs). Cluster calculations by exact diagonalisation show that these are the quasiparticles that lead to a paired ground state, and have superconducting flux-quantisation properties. Here, we extend the theory to the full plane, and show that the W=0 quasiparticles are again the natural explanation of superconducting flux-quantisation. Moreover, by a new approach which is exact in principle, we calculate the effective interaction Weff between two holes added to the ground state of the repulsive three-band Hubbard model. To explain how a noninteracting electron gas becomes a superconductor when switching the local Coulomb interaction, we obtain a closed-form analytic expression including the effects of all virtual transitions to 4-body intermediate states (exchange of an electron-hole pair). Our scheme is ready to include other interactions which are not considered in the Hubbard model but may be important. In the plane, the W=0 pairs have 1 B 2 and 1 A 2 symmetry. The effective interaction in these channels is attractive and leads to a Cooper-like instability of the Fermi liquid, while it is repulsive for triplet pairs. From Weff, we derive an integral equation for the pair eigenfunction; the binding energy |∆| of the pairs is in the range of tens of meV. However, our symmetry-based method is far more general than the model.