A Model for High Temperature Superconductors using the Extended Hubbard Model

TL;DR

This paper develops a theoretical model based on an extended Hubbard Hamiltonian to accurately predict the phase diagram and critical temperature of high-temperature superconductors like YBaCuO and La(Sr,Ba)CuO, aligning well with experimental data.

Contribution

It introduces a novel variational method using an extended Hubbard potential to derive the phase diagram and critical temperature of HTCS.

Findings

Good agreement with experimental phase diagrams

Accurate prediction of critical temperatures

Method applicable to different compounds

Abstract

We derive a method to study the phase diagram for high temperature superconductors (HTCS). Our starting point is the Hubbard Hamiltonian with a weak attractive interaction to obtain the formation of bound pairs. We consider this attractive potential at different positions for different compounds accordingly to the experimental results of the coherence length. We then construct a wave function of the BCS type by a variational method using the Fourier transform of this extended Hubbard potential and then derive an energy gap equation. This approach allows us to obtain the critical temperature as function of the doping concentration which gives very good agreement with the experimental phase diagrams of YBaCuO and La(Sr,Ba)CuO compounds.