A Variational Estimate of the Binding Energy of Charge-Transfer Excitons in the Cuprate Superconductors.

TL;DR

This paper develops a variational method to estimate the binding energy of charge-transfer excitons in insulating cuprate superconductors, highlighting the role of Coulomb repulsion and exciton symmetry.

Contribution

It introduces a variational approach based on a three-band Hubbard model to estimate exciton binding energies and critical Coulomb repulsion in cuprates.

Findings

Critical Coulomb repulsion needed for bound excitons

Excitons share symmetry with copper $d_{x^2-y^2}$ orbitals

Model parameters fitted to experimental data

Abstract

We present a variational estimate for the binding energy of a Frenkel exciton in the insulating cuprate superconductors. Starting from the three band Hubbard model we perform a canonical transformation to O($t^2$), where $t$ is the bare nearest neighbour copper-oxygen hopping integral. An effective Hamiltonian is then derived to describe the hopping of the exciton through the copper oxide plane. The critical parameter in the model is the nearest neighbour copper-oxygen coulomb repulsion, $V$. It is found that a critical value of $V$ is needed to observe bound Frenkel excitons, and that these excitons have the same symmetry as the parent copper orbital, $d_{x^2-y^2}$. We determine the critical value of $V$ using a variational approach, and attempt to fit the parameters of the model to known experimental results.