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arxiv: 2606.28906 · v1 · pith:ZPPBDVNZnew · submitted 2026-06-27 · ❄️ cond-mat.supr-con

Theory of High-Tc Superconductivity in Cuprates

E. C. Marino This is my paper

Pith reviewed 2026-06-30 08:31 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords high-Tc superconductivitycupratesSpin-Fermion-Hubbard Modelt-J modelZhang-Rice singletsCuO2 planeshole doping
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The pith

The Spin-Fermion-Hubbard Model successfully describes high-Tc superconductivity in hole-doped cuprates.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper argues that the Spin-Fermion-Hubbard Model captures the essential physics in the CuO2 planes better than the t-J model. In this framework, localized spins on copper sites interact with doped holes moving on oxygen sites through Kondo-like magnetic coupling plus Hubbard repulsion. The author reviews the reasons this modeling choice has produced a consistent account of the superconducting state. A sympathetic reader would care because the correct reduction of the three-band Hubbard model determines whether the pairing mechanism can be understood from first principles in these materials.

Core claim

The author maintains that the Spin-Fermion-Hubbard Model, in which the Cu++ electrons form a square lattice of localized spins while the doped holes move along the oxygen sub-lattices and undergo a Kondo-like magnetic interaction with the localized spins besides the Hubbard-like electric repulsion, has led to a successful theory for High-Tc superconductivity in hole-doped cuprates, in contrast to the alternative that forms Zhang-Rice singlets and yields the t-J model.

What carries the argument

The Spin-Fermion-Hubbard Model, which keeps doped holes on the oxygen sublattice interacting with localized copper spins via Kondo-like coupling and on-site repulsion.

If this is right

  • The Kondo-like interaction between oxygen holes and copper spins supplies the pairing glue for superconductivity.
  • Explicit retention of oxygen degrees of freedom resolves features of the cuprate phase diagram that the t-J model misses.
  • The three-band Hubbard model reduces to an effective description that remains tractable yet faithful to the CuO2 plane physics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same modeling logic could be tested in electron-doped cuprates where the carrier sign changes the interaction character.
  • Analogous Kondo-lattice reductions might apply to other doped Mott insulators beyond the cuprates.
  • Numerical simulations that keep oxygen sites explicit could directly compare the two model families on equal footing.

Load-bearing premise

The Spin-Fermion-Hubbard Model rather than the t-J model correctly captures the essential physics of doped holes interacting with localized spins in the CuO2 planes.

What would settle it

Spectroscopic or transport data showing that Zhang-Rice singlet formation dominates the low-energy dynamics of doped holes would falsify the central modeling choice.

Figures

Figures reproduced from arXiv: 2606.28906 by E. C. Marino.

Figure 1
Figure 1. Figure 1: FIG. 1: The [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The lattice configuration for the hole doping of the non-dime [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Arrangement of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The Lines [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The Lines [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: The Lines [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: The [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Resistivity of LSCO at zero magnetic field: [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Resistivity of LSCO at a magnetic field: [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Resistivity of LSCO at a magnetic field: [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Effects of an applied external pressure of up to 15 [PITH_FULL_IMAGE:figures/full_fig_p024_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Ground-state of the unperturbed Hamiltonian in Rayleigh- [PITH_FULL_IMAGE:figures/full_fig_p026_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Intermediate states that contribute to the effective He [PITH_FULL_IMAGE:figures/full_fig_p026_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Intermediate states that contribute to the effective Ha [PITH_FULL_IMAGE:figures/full_fig_p027_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Intermediate states that contribute to the effective Ha [PITH_FULL_IMAGE:figures/full_fig_p028_16.png] view at source ↗
read the original abstract

The essential physical processes underlying the phenomenon of High-Tc superconductivity in cuprates occur in the $CuO_2$ planes, found in these materials. The dynamics of the active electrons belonging to such planes is well described by the Three Bands Hubbard Model (3BHM). The complexity of such model, however, led the researchers to look for simpler and yet relevant alternatives. In the attempts to circumvent the complexity of this model,two main simplified versions of the (3BHM) were considered. In the first alternative, one eliminates the doped holes and their respective sub-lattices by tying them to the $Cu^{++}$ electrons, thereby forming the so called Zhang-Rice singlets. The remaining dynamics consists in doping a Mott-Hubbard insulator and is described by the t-J Model. The second alternative maintains that the $Cu^{++}$ electrons form a square lattice of localized spins, while the doped holes move along the oxygen sub-lattices and undergo a Kondo like magnetic interaction with the localized spins, besides the Hubbard-like electric repulsion. This scenario is described by the Spin-Fermion-Hubbard Model. Most of the researchers in the field chose to follow the first road, while, I chose the second one. In this article I review in detail the reasons why that choice has led to a successful theory for High-Tc superconductivity in hole doped cuprates.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript reviews the dynamics of electrons in the CuO2 planes of cuprates, contrasting two simplifications of the three-band Hubbard model: the t-J model (via Zhang-Rice singlets) and the Spin-Fermion-Hubbard Model (localized Cu spins with doped holes on oxygen sublattices interacting via Kondo-like coupling plus Hubbard repulsion). The author asserts that the latter choice has produced a successful theory of high-Tc superconductivity in hole-doped cuprates and reviews the reasons for preferring it.

Significance. A well-substantiated microscopic theory capable of reproducing key cuprate phenomenology (d-wave pairing, doping dependence of Tc, spectral functions) would be highly significant. The manuscript functions as a perspective advocating one model over another, but its assertion of success is not accompanied by new derivations or quantitative results, limiting its contribution to a discussion of model selection rather than a demonstration of predictive power.

major comments (1)
  1. [Abstract] Abstract: the central claim that the Spin-Fermion-Hubbard Model 'has led to a successful theory' is stated without reference to any concrete outputs (e.g., solution of a gap equation, predicted Tc versus doping curve, or computed spectral functions) or direct experimental comparisons. This renders the claim non-load-bearing as presented.
minor comments (2)
  1. [Abstract] Abstract: missing space after comma in 'model,two main simplified versions'.
  2. [Abstract] Abstract: notation 'Cu^{++}' is nonstandard; consistency with Cu^{2+} would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment on the abstract. We address it below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the Spin-Fermion-Hubbard Model 'has led to a successful theory' is stated without reference to any concrete outputs (e.g., solution of a gap equation, predicted Tc versus doping curve, or computed spectral functions) or direct experimental comparisons. This renders the claim non-load-bearing as presented.

    Authors: We agree that the abstract would be strengthened by explicit reference to concrete results obtained with the Spin-Fermion-Hubbard Model. The manuscript is a perspective that reviews the body of work showing that the model yields d-wave pairing via solution of the gap equation, reproduces the dome-shaped Tc versus doping curve, and matches key features of ARPES spectral functions. In the revised version we will add a sentence in the abstract that briefly cites these specific achievements together with the relevant references, thereby making the claim more directly supported while preserving the review character of the paper. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The supplied text consists of an abstract that qualitatively contrasts the t-J model and the Spin-Fermion-Hubbard Model, states the author's preference for the latter, and asserts that this choice 'has led to a successful theory.' No equations, derivations, fitted parameters, predictions, or explicit self-citations appear. Without any load-bearing derivation chain or observable that reduces to an input by construction, none of the enumerated circularity patterns can be exhibited. The central claim remains an interpretive summary rather than a demonstrated result that could be checked for self-definition or fitted-input renaming.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no free parameters, axioms, or invented entities can be extracted from the text.

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Works this paper leans on

89 extracted references · 2 canonical work pages · 1 internal anchor

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    INTRODUCTION The discovery of high-Tc superconductivity in cuprates [1] was a lan dmark in physics. Yet, in the 40 years that have elapsed since then, the theories that have been proposed to desc ribe the new phenomenon, were partially successful in describing the vast amount of experimental results that have be en generated so far. There is a general agr...

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    Theory of High-Tc Superconductivity in Cuprates

    This relates the presence or not of a dimerization in the underlying lattice to the nature of the the lowest energy states. For the Zhang-Rice singlets to be the lowest energy state s produced by doping we need a non-dimerized lattice. Conversely, the occurrence of dimerization leads directly to a supe rconducting R VB-like state formed by a coherent arXi...

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    THEOR Y 2.1) Microscopic degrees of freedom The formulation of a theory, meant to describe any given physical s ystem, necessarily starts from a judicious choice of the microscopic variables that will represent such a system at a m icroscopic level. In the case of the High-Tc cuprates, we assume these are analogous to the Spin-Fermion [15, 30] degrees of ...

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    PHASE DIAGRAM Using the thermodynamic potentials found in the previous section, w e may determine the full T × x phase diagram of the hole-doped cuprates [21]. We show below a sample of this proce dure for the Tc(x) and T ∗(x) lines of this phase diagram and refer the reader to [21] for the complete result, exhib iting TNeel (x), TSpinGlass(x), TChargeOrd...

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    THE RESISTIVITY OF HIGH-TC CUPRATES We describe here how we can derive from our theory a general expr ession for the resistivity of the high-Tc cuprates, as well as the effects of an applied magnetic field on it [17, 18]. From the very outset, let us remark that, assuming the resistivity is produced by hole-exciton scattering, using a Drude formula approach...

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    CONCLUSION Two roads emerge from the simplifications that were obtained from t he 3BHM, respectively associated to the t-J Model, and to the Spin-Fermion-Hubbard Model (SFHM). The forme r provides the framework for Anderson’s R VB- Theory. In the framework of this theory, an effective ground-st ate |GS⟩, the R VB-state, was conjectured and it was shown to c...

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