Effect of long-range hopping onTcin a two-dimensional Hubbard-Holstein model of the cuprates

Abstract

We study the effect of long-range hoppings on ${T}_{c}$ for the two-dimensional (2D) 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, ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, generally suppress ${T}_{c}$. We argue that this trend remains valid for larger clusters. In the presence of the Holstein phonons, a finite ${t}^{\ensuremath{'}}$ 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.