# Universal properties of high-temperature superconductors from real-space pairing III: The role of correlated hopping and intersite Coulomb interaction within the t-J-U model

## TL;DR

This study investigates how correlated hopping and intersite Coulomb interactions influence the d-wave superconducting state in high-temperature superconductors using the t-J-U model and the DE-GWF method, revealing effects on pairing and electronic properties.

## Contribution

It introduces a detailed analysis of correlated hopping and Coulomb interactions within the t-J-U model, going beyond mean-field theory to better understand high-temperature superconductivity.

## Key findings

- Correlated hopping enhances pairing on the electron-doped side.
- The non-BCS regime narrows with increased correlated hopping.
- Doping dependence of Fermi velocity and double occupancy aligns with experimental data.

## Abstract

We study the effect of the correlated hopping term and the intersite Coulomb interaction term on principal features of the $d$-$wave$ superconducting (SC) state, in both the electron and hole doped regimes within the t-J-U model. In our analysis we use the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF) which allows us to go beyond the renormalized mean field theory (RMFT). We show that the correlated hopping term enhances the pairing at the electron-doped side of the phase diagram. Moreover, the so-called non-BCS regime (which manifests itself by the negative kinetic energy gain at the transition to the SC phase) is narrowed down with the increasing magnitude of the correlated hopping $\sim K$. Also, the doping dependences of the nodal Fermi velocity and Fermi momentum, as well as the average number of double occupancies, are analyzed with reference to the experimental data for selected values of the parameter $K$. For the sake of completeness, the influence of the intersite Coulomb repulsion on the obtained results is provided. Additionally, selected results concerning the Hubbard-model case are also presented. A complete model with all two-site interactions is briefly discussed in the Appendix for reference.