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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
Submission summary
| Authors (as registered SciPost users): | David Sénéchal |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2503.07810v1 (pdf) |
| Data repository: | https://osf.io/e2maz/ |
| Date submitted: | 2025-03-17 15:12 |
| Submitted by: | Sénéchal, David |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| 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 ($n_p$) and copper occupation ($n_d$). 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 $\epsilon_p$ between oxygen and copper orbitals. Since the occupations ($n_p$ and $n_d$) have been estimated from NMR for a few materials (LCO, YBCO and NCCO), this allows us to estimate the value of $U-\epsilon_p$ for these materials, within this model. We compute the density of states for these and the effect of $(U,\epsilon_p)$ on the $n_d$-$n_p$ curve, superconductivity, and antiferromagnetism.
Current status:
Reports on this Submission
Report
The paper analyzed various properties of the Emery model or
a three-band model for the cuprates. Based on a comparison of CDMFT calculations
of the Cu and O occupations, and NMR experiments, the authors obtain
the parameters of the model. They analyze the dependence of the superconducting amplitude
on such parameters showing the correlation between superconductivity and superexchange
encoded in the Emery model. On the other hand they are unable to reproduce the observed
superconductivity in NCCO from the parameters they have extracted from the NMR experiments.
This suggests that either CDMFT is unable to capture longer range spatial correlations
or that the Emery model neglects important ingredients relevant to NCCO materials
or both.
In general I believe that the paper is interesting providing support on the Emery model as a
plausible model for the cuprates. It can serve as a platform to improve methods and/or
add more terms to the three-band model considered. Hence, I believe the paper deserves publication
in Scipost. I enclose some questions/comments that may help to sharpen the message
for their consideration.
Comments:
- — — - —-
-The results of Fig. 2 namely, that doped holes mostly go into the O orbitals
is somehow expected from the relative position of the O and Cu energy levels since
e_p>ed? Isn’t this also the idea behind the formation of the Zhang-Rice singlet?
-Wouldn’t the parameter regime U=8-9 shown in Fig. 3 (top) be more consistent with
the phase diagram of the cuprates since the electron doped system will show a lower Tc
than the hole doped side?
-The CDMFT calculation consists on embedding 4 Cu orbitals + 8 O orbitals
in a bath. The bath consists on 8 orbitals connected to the Cu d orbitals.
Do the results depend on the size of the bath? For instance, by enlarging (if possible)
the bath to three bath orbitals per Cu orbital?
-Interestingly the authors point out: “Note that the data shown in red, with constant nominal gap,
corresponds to a single value of J, but a sizeable variation of Ψmax, demonstrating that J is not the
only factor at play.” Do the authors have any idea of which other factors may be playing a role
in the superconductivity found within their present model?
-The optimal set of parameters for superconductivity seems to be e_p=2, U=8 and x=-0.2
within the present study. Is the general conclusion that for this hole doping range one
needs to maximize the superexchange J in order to achieve the strongest
superconducting pairing amplitude?
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)