Pairing of holes in stacked layers

We study the effective interaction between fermionic holons mediated by bosonic spinons in stacked layers described by the t-J model with a hopping coupling between the layers. This interaction is provided by the holon-spinon interaction beyond mean-field theory. The effective four-holon interaction drives (1) pure in-plane holon pairing; (2) holon pairing in one plane, provided that there is pairing in the other; and (3) interlayer holon pairing. The latter pairing does not lead to physical interlayer hole pairing. We discuss the influence of the Coulomb repulsion between the holons on the pairing picture that we have obtained.