Hole pairing and phonon dynamics in generalized 2D $t-J-$Holstein models
  The formation of hole pairs in the planar t-J model is studied in the presence of independent {\it dynamic} vibrations of the in-plane oxygen atoms. In-plane (breathing modes) and out-of-plane (buckling modes) displacements are considered. We find strong evidences in favor of a stabilization of the two hole bound pair by out-of-plane vibrations of the in-plane oxygens. On the contrary, the breathing modes weaken the binding energy of the hole pair. These results are discussed in the context of the superconducting cuprates. 
T. Sakai, D. Poilblanc and D. J. Scalapino