# Effect of interlayer processes on the superconducting state within t-J-U model: Full Gutzwiller wave-function solution and relation to experiment

## TL;DR

This paper investigates how interlayer effects influence the superconducting state in bilayer high-Tc cuprates using the full Gutzwiller wave-function approach within the t-J-U model, comparing results with experimental data and simpler models.

## Contribution

It provides a detailed analysis of interlayer processes on superconductivity using the full Gutzwiller wave-function in the t-J-U model, extending previous single-layer studies.

## Key findings

- Interlayer effects significantly modify the superconducting pairing symmetry.
- Results align with experimental data for Bi-2212.
- Comparison with bilayer Hubbard model highlights the importance of interlayer interactions.

## Abstract

The Gutzwiller wave function solution of the $t$-$J$-$U$ model is considered for the bilayer high-T$_C$ superconductor by using the so-called diagrammatic expansion method. The focus is on the influence of the interlayer effects on the superconducting state. The chosen pairing symmetry is a mixture of $d_{x^2-y^2}$ symmetry within the layers and the so-called $s^{\pm}$ symmetry for the interlayer contribution. The analyzed interlayer terms reflect the interlayer electron hopping, the interlayer exchange coupling, and the interlayer pair hopping. The obtained results are compared with selected experimental data corresponding to the copper-based compound Bi-2212 with two Cu-O planes in the unit cell. For the sake of comparison, selected results for the case of the bilayer Hubbard model are also provided. This paper complements our recent results obtained for the single-plane high temperature cuprates [cf. J. Spa{\l}ek, M. Zegrodnik, and J. Kaczmarczyk, Phys. Rev. B {\bf 95}, 024506 (2017)]