Qualitative understanding of the sign of t' asymmetry in the extended t-J Model and relevance for pairing properties

Numerical calculations illustrate the effect of the sign of the next nearest-neighbor hopping term t' on the 2-hole properties of the t-t'-J model. Working mainly on 2-leg ladders, in the -1.0 < t'/t < 1.0 regime, it is shown that introducing t' in the t-J model is equivalent to effectively renormalizing J, namely t' negative (positive) is equivalent to an effective t-J model with smaller (bigger) J. This effect is present even at the level of a 2x2 plaquette toy model, and was observed also in calculations on small square clusters. Analyzing the transition probabilities of a hole-pair in the plaquette toy model, it is argued that the coherent propagation of such hole-pair is enhanced by a constructive interference between both t and t' for t'>0. This interference is destructive for t'<0.