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 two-hole properties of the t-t^′-J model. Working mainly on two-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 2×2 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.