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Effect of the Coulomb repulsion and oxygen level on charge distribution and superconductivity in the Emery model for cuprates superconductors

by Louis-Bernard St-Cyr, David Sénéchal

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Submission summary

Authors (as registered SciPost users): David Sénéchal
Submission information
Preprint Link: scipost_202504_00053v1  (pdf)
Data repository: https://osf.io/e2maz/
Date accepted: May 19, 2025
Date submitted: April 30, 2025, 10:43 p.m.
Submitted by: Sénéchal, David
Submitted to: SciPost Physics Core
Ontological classification
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational

Abstract

The Emery model (aka the three-band Hubbard model) offers a simplified description of the copper-oxide planes that form the building blocks of high-temperature superconductors. By contrast with the even simpler one-band Hubbard model, it differentiates between copper and oxygen orbitals and thus between oxygen occupation (np) and copper occupation (nd). Here we demonstrate, using cluster dynamical mean field theory, how the two occupations are related to the on-site Coulomb repulsion U on the copper orbital and to the energy difference ϵp between oxygen and copper orbitals. Since the occupations (np and nd) have been estimated from NMR for a few materials (LCO, YBCO and NCCO), this allows us to estimate the value of Uϵp for these materials, within this model. We compute the density of states for these and the effect of (U,ϵp) on the nd-np curve, superconductivity, and antiferromagnetism.

Author comments upon resubmission

We thank the Editor in charge and referees for their efficient work. In the revised version we address the main points raised by the referee.

List of changes

There was typo in Figs 2 and 3 : The curves indicated as corresponding to U=9.0 were in fact pertaining to U=8.5 (there is no data for U=9). The corresponding occurrences in the text have been fixed.

At the end of Sect. 2B, we added the following remark:
"Ideally, one would prefer an infinite number of bath orbitals, but as we are using an ED impurity solver the computational complexity increases exponentially with the number of bath orbitals. It was shown in [21] that the hybridization of the impurity problem is very well approximated with a discrete bath of only 8 orbitals."

At the end of Sect. 3A, we added the following remark:
"Let us point out that increasing \epsp at constant U has the same effect as decreasing U at constant \epsp, like in Fig.2a: This causes the CTG to shrink and a smaller discontinuity of the doping curves across half-filling. The metallic or insulating character of the solutions thus depends on the relative value U and \epsp, not on each of them separately."

Regarding the results for BSCCO at U=8.0 and 8.5, we added : "These two curves are thus not in the CTI regime, making them less relevant to the study of actual cuprates. "

Towards the end of Sect. 3B, we added the following remark:
"When the CTG is very small, as for the data shown in red, the linear relationship between the super-exchange J and Ψmax is lost. In this small CTG regime, it is the size of the spectral gap that has the biggest impact on Ψmax: A smaller spectral gap leads to a larger value of Ψmax. Furthermore, when the CTG completely closes, the relationship between J and Ψmax changes even more dramatically: An increase in J could very well lead to a decrease in Ψmax, as is the case for the curves U=8, \epsp=2 and U=8.5, \epsp=2 in Fig. 3."

Various other typos and linguistic details have been fixed, with no consequence on the scientific content of the paper.

Published as SciPost Phys. Core 8, 043 (2025)

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