Effect of long-range hopping on Tc in a two-dimensional Hubbard-Holstein model of the cuprates

We study the effect of long-range hoppings on T-c for the two-dimensional (213) Hubbard model with and without Holstein phonons using parameters evaluated from band-structure calculations for cuprates. Employing the dynamical cluster approximation (DCA) with a quantum Monte Carlo (QMC) cluster solver for a 4-site cluster, we observe that without phonons, the long-range hoppings, t' and t '', generally suppress T-c We argue that this trend remains valid for larger clusters. In the presence of the Holstein phonons, a finite t' enhances T-c in the under-doped region for the hole-doped system, consistent with local-density approximation (LDA) calculations and experiment. This is interpreted through the suppression of antiferromagnetic (AF) correlations and the interplay between polaronic effects and the antiferromagnetism.