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

TL;DR

This study investigates how long-range hopping influences the superconducting transition temperature (Tc) in a 2D Hubbard-Holstein model relevant to cuprates, revealing that long-range hopping suppresses Tc generally, but can enhance it under certain conditions with phonons.

Contribution

It provides the first detailed analysis of long-range hopping effects on Tc in the Hubbard-Holstein model using DCA and QMC, incorporating parameters from band-structure calculations.

Findings

Long-range hoppings suppress Tc without phonons.

Finite t' enhances Tc with Holstein phonons in under-doped regimes.

The trend persists for larger clusters.

Abstract

We study the effect of long-range hoppings on Tc 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' and t'', generally suppress Tc. We argue that this trend remains valid for larger clusters. In the presence of the Holstein phonons, a finite t' enhances Tc 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.