The two-dimensional t-t'-U model as a minimal model for cuprate materials

TL;DR

This study investigates the two-dimensional t-t'-U Hubbard model using the Composite Operator Method to assess its effectiveness in describing various cuprate superconductors, comparing theoretical predictions with experimental data.

Contribution

The paper applies the Composite Operator Method to the t-t'-U model, analyzing its ability to replicate key features of cuprate materials and highlighting its limitations across different compounds.

Findings

The model describes NCCO and LSCO well with specific parameters.

It fails to accurately reproduce the van Hove singularity in YBCO.

A single model may not capture the diversity of cuprate superconductors.

Abstract

The addition to the Hubbard Hamiltonian of a t' diagonal hopping term, which is considered to be material dependent for high-Tc cuprate superconductors, is generally suggested to obtain a model capable to describe the physics of high-Tc cuprate materials. In this line of thinking, the two-dimensional t-t'-U model has been studied by means of the Composite Operator Method, which allows to determine the dynamics in a fully self-consistent way by use of symmetry requirements, as the ones coming from the Pauli principle. At first, some local quantities have been calculated to be compared with quantum Monte Carlo data. Then, the structure of the energy bands, the shape of the Fermi surface and the position of the van Hove singularity have been computed as functions of the model parameters and studied by the light of the available experimental data. The results of our study show that there exists two sets of parameters that allows the model to describe the relevant features of 1-layer compounds NCCO and LSCO. On the other hand, for the 2-layer compound YBCO is not possible to find a reasonable set of parameters which could reproduce the position of the van Hove singularity as predicted by ARPES experiments. Hence, it results questionable the existence of an unique model that could properly describe the variety of cuprate superconductors, as the t-t'-U model was thought to be.