Charge-transfer gap size and oxygen hole content as two mechanisms controlling $T_c$ in the Emery model

A.-M. S. Tremblay; Eleanor M. O'Callaghan; Giovanni Sordi; Nicolas Kowalski

REVIEW 3 major objections 5 minor 73 references

Charge-transfer gap size and oxygen hole content as two mechanisms controlling $T_c$ in the Emery model

T0 review · 3 major / 5 minor · reviewed 2026-07-08 · glm-5.2

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Pith's one-line read Oxygen holes drive superconducting temperature in cuprate model

desk verdict Two-mechanism Tc optimization in the Emery model: real but preliminary, with a load-bearing caveat on the dominance claim read the letter →

arxiv 2607.06462 v1 pith:7CEH4DYC submitted 2026-07-07 cond-mat.str-el cond-mat.quant-gascond-mat.supr-con

Eleanor M. O'Callaghan , Nicolas Kowalski , A.-M. S. Tremblay , Giovanni Sordi This is my paper · ORCID

classification cond-mat.str-elcond-mat.quant-gascond-mat.supr-con PACS 74.72.-h74.20.Mn71.27.+a71.30.+h

keywords Emerymodelcupratesuperconductivitycharge-transfergapoxygenholecontentZaanen-Sawatzky-Allendiagramcellulardynamicalmean-fieldtheoryd-wave

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper studies the Emery model — the standard description of electrons in the copper-oxygen planes of cuprate superconductors — using a computational method called cellular dynamical mean-field theory. The authors systematically vary two microscopic parameters — the energy difference between copper and oxygen orbitals and the strength of electron repulsion on copper — and track how the maximum superconducting transition temperature changes. They then translate these model parameters into two physically measurable quantities: the charge-transfer gap size and the oxygen hole content, which measures how much the hole is shared between copper and oxygen orbitals. The central claim is that these two quantities are independent mechanisms controlling the maximum superconducting temperature. The superconducting temperature rises monotonically as the charge gap shrinks and as the oxygen hole content grows, with oxygen hole content being the dominant driver. The authors also find that the highest temperatures are reached not only near the metal-insulator boundary, as previously known, but also deep in the charge-transfer regime where the copper repulsion is much larger than the copper-oxygen energy difference — a regime that had not been previously identified as favorable for superconductivity.

What carries the argument

The Zaanen-Sawatzky-Allen diagram serves as the navigational map. It plots the copper onsite repulsion U_d against the bare charge-transfer energy Delta (the energy distance between the upper Hubbard band and the oxygen orbital energy). Contour lines of constant charge gap size and constant oxygen hole content are overlaid on this diagram. The key structural observation is that these two sets of contour lines are not parallel, proving that charge gap size and oxygen hole content are not proportional to each other — they are genuinely independent parameters. This independence is what allows the authors to disentangle their separate effects on the superconducting temperature.

What would settle it

If including Kosterlitz-Thouless phase fluctuations were to shift the optimal doping differently for different charge gap sizes, the ranking of oxygen hole content as the dominant variable could change.

Watch

Extended reading notes

Core claim

The charge-transfer gap size and the oxygen hole content are two independent mechanisms controlling the maximum superconducting transition temperature in the Emery model. The temperature increases monotonically as the charge gap decreases and as the oxygen hole content increases, and the oxygen hole content is the dominant variable. This is established by computing superconducting domes at eight points across the Zaanen-Sawatzky-Allen diagram — which classifies insulating states by the relative sizes of the copper repulsion and the copper-oxygen energy difference — at two fixed charge gap sizes, and then mapping the results onto the two-dimensional space of physical observables. The gradient

Load-bearing premise

The superconducting temperature is computed at a mean-field level that neglects Kosterlitz-Thouless phase fluctuations, which are essential in two dimensions. These fluctuations could reduce the maximum temperature and shift the optimal doping, potentially reordering which variable — oxygen hole content or charge gap size — dominates.

Editorial extensions

If this is right

For proposed ultracold-atom realizations of the Emery model, the paper predicts that maximizing superconducting temperature requires tuning the system deep into the charge-transfer regime (large copper repulsion relative to the copper-oxygen energy difference) while keeping the charge gap small, which corresponds to staying near the metal-insulator boundary.
The finding that oxygen hole content is the dominant variable suggests that experimental correlations between superconducting temperature and oxygen hole content in real cuprates should be robust against small variations in the charge-transfer gap, providing a theoretical basis for interpreting those measurements.
The paper provides a two-dimensional optimization framework that can be extended: varying the hopping parameters (currently fixed) would add further dimensions and could reveal whether the dominance of oxygen hole content persists across a broader parameter space.
The identification of a second favorable region deep in the charge-transfer regime, beyond the previously known optimum near the metal-insulator boundary, suggests a design principle for engineering new superconducting materials: large copper-oxygen covalency combined with a narrow charge gap.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If oxygen hole content is indeed the dominant driver, then material design strategies that increase copper-oxygen covalency — for instance through chemical pressure, strain, or apical oxygen manipulation — should be more effective at raising the superconducting temperature than strategies that only narrow the charge gap.
The paper's quantitative limitations (oxygen hole content range matching only La2-xSrxCuO4, predicted temperatures about twice experimental values, optimal doping underestimated by a factor of three) suggest that extending the calculation to include Kosterlitz-Thouless physics and variable hopping parameters could shift the quantitative predictions while preserving the qualitative trend that oxyge
The observation that the parent insulating state's properties predict superconducting trends upon doping hints at a deeper organizing principle: the mixed copper-oxygen character of the ground-state hole may be a more fundamental indicator of pairing strength than any single energy scale, which would connect to the broader question of why charge-transfer insulators host higher superconducting temp

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

read the letter

The main thing to know: this paper extends the authors' companion work [39] from one charge-gap value to two, enabling a 2D optimization of Tc^max over both charge-transfer gap size Δ_I and oxygen hole content 2p_p. The genuinely new result is the demonstration that these are two independent mechanisms — Fig. 11(a) shows that the same 2p_p can give different Tc^max at different Δ_I, and vice versa. The gradient analysis in Fig. 12(b) claiming 2p_p is the dominant variable is also new, but this is where I'd put an asterisk (more below). The paper does several things well. The CDMFT methodology is standard and competently executed. The Zaanen-Sawatzky-Allen framework is a clean organizing principle for navigating the parameter space. The authors are unusually transparent about limitations — they openly state the KT caveat, the sign problem blocking access to the most relevant parameter region, the factor-of-2 discrepancy in Tc, the factor-of-3 discrepancy in gap size, and even the wrong sign on the pd-vs-2pp slope compared to experiment. That honesty earns trust. The stress-test concern about KT physics is valid but needs calibration. The concern is that superfluid stiffness ρ_s depends on quasiparticle weight Z, which is Δ_I-dependent, so the KT correction could be preferentially larger for bigger Δ_I, potentially rotating the gradient in Fig. 12(b) toward the Δ_I axis. This is a real concern, but it attacks only the dominance ranking (part 2 of the claim), not the independence of the two mechanisms (part 1). The independence result is derived from parent-state properties and is robust to KT corrections. So the paper's strongest claim survives; its flashiest claim is on shakier ground. The sparsity of data points (8 points interpolated onto a surface) is a legitimate concern but proportionate to what the authors claim — they frame this as an entry point, not a final word. This paper is for researchers working on cuprate theory and cold-atom simulators who want an organizing framework for Tc trends. It deserves a serious referee who can assess whether the KT caveat undermines the dominance claim or merely qualifies it. My read: the independence result is solid, the dominance ranking is suggestive but not yet robust. Recommend peer review.

Referee Report

3 major / 5 minor

Summary. This paper uses cellular dynamical mean-field theory (CDMFT) to study the maximum superconducting critical temperature $T_c^{max}$ in the Emery model for hole-doped cuprates. Using the Zaanen-Sawatzky-Allen diagram as a framework, the authors fix the hopping parameters ($t_{pd}=1.5$, $t'_{pp}=1$, $t_{pp}=1$) and systematically vary the bare charge-transfer energy $U_d$ and $d-p$ energy distance. They compute $T_c^{CDMFT}$ for eight parent insulating states corresponding to two charge gap sizes ($Delta_I = 0.6, 0.9$). The central claim is that $Delta_I$ and the oxygen hole content $2p_p$ are two independent mechanisms controlling $T_c^{max}$, with $T_c^{max}$ monotonically increasing as $Delta_I$ decreases and $2p_p$ increases. The authors further claim that $2p_p$ is the dominant variable, as inferred from the gradient of the interpolated $T_c^{max}$ surface in the $(Delta_I, 2p_p)$ plane (Fig. 12).

Significance. The paper tackles an important problem: disentangling the roles of charge-transfer gap size and oxygen hole content in determining $T_c$ in cuprates. The CDMFT methodology is standard and well-implemented, and the authors are transparent about limitations (Sec. V.C). A clear strength is the direct computation of $T_c^{CDMFT}$ rather than relying solely on the superconducting order parameter $Phi$ as a proxy, allowing the authors to verify (Fig. 9b, Fig. 10b) that $Phi^{max}$ and $T_c^{max}$ can exhibit different rates of change. The identification of two distinct, non-proportional mechanisms for controlling $T_c$ is a valuable conceptual contribution. The falsifiable predictions for cold-atom simulators are timely.

major comments (3)

Sec. V.B, Fig. 12: The central claim that $2p_p$ is the 'dominant variable' rests on the gradient of the interpolated $T_c^{max}$ surface. However, the gradient direction is not invariant under rescaling of the axes. The text states that $Delta_I$ varies in [0.6, 0.9] (absolute change 0.3) while $2p_p$ varies in [0.26, 0.33] (absolute change 0.07). Because the axes have 'equal aspect ratio' but the physical quantities have different units and ranges, the gradient direction is an artifact of the chosen axis scaling. If $Delta_I$ were plotted in eV (as in the secondary axis of Fig. 10, where $t_{pp}=0.4$ eV gives a range of ~0.24 to 0.36 eV), the aspect ratio and hence the gradient direction would change. The dominance claim requires a parameter-free metric, such as comparing $partial T_c^{max}/partial Delta_I$ and $partial T_c^{max}/partial (2p_p)$ in physical units, or a regression-based
sensitivity analysis. As presented, the gradient in Fig. 12(b) is not a physically meaningful measure of relative importance.
Sec. V.C and Fig. 12: The $T_c^{max}$ surface in Fig. 12 is an interpolation over only 8 data points (5 at $Delta_I=0.6$, 3 at $Delta_I=0.9$). The gradient field and contour lines are thus derived from a very sparse grid, and the monotonicity claim is supported by limited sampling. The authors should explicitly state the interpolation method used and add uncertainty estimates or error bars to the data points in Fig. 12, so that the robustness of the gradient direction and the monotonicity claim can be assessed.

minor comments (5)

Sec. V.C: The acknowledgment that KT fluctuations 'can alter the $T_c^{max}$ trends' is appreciated, but the specific risk to the dominance claim is not addressed. The superfluid stiffness $rho_s$ depends on quasiparticle coherence and bandwidth, which are directly controlled by $Delta_I$. If the KT correction is preferentially $Delta_I$-dependent, it could rotate the effective gradient in Fig. 12(b). A brief discussion of this specific risk would strengthen the paper.
Fig. 2(a): The labels for constant $2p_p$ lines list values from 0.24 to 0.28, but the text in Sec. III.A.2 states the step is 0.1, which should presumably be 0.01.
Fig. 9(a): The $T_c^{max}$ values are converted to Kelvin using $t_{pp}=0.4$ eV, yielding values around 96-108 K. However, Sec. V.C notes that this is approximately twice the experimental $T_c$ for LSCO. This discrepancy should be noted on the figure or in its caption to avoid confusion.
Sec. III.A.2: The oxygen hole content is defined as $2p_p = 2(2-n_p)$. It would help to clarify early on whether $p_p$ refers to holes per oxygen orbital or per CuO$_2$ unit cell, as the factor of 2 for orbital degeneracy can be a source of confusion.
Appendix B, Fig. 14: The data points from Ref. [30] use different hopping amplitudes, as noted in the text. It would be helpful to indicate which specific parameters differ so the reader can assess comparability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for a careful reading and for identifying two important issues with our analysis in Sec. V.B. Both points are well-taken and will be addressed in the revised manuscript.

read point-by-point responses

Referee: Sec. V.B, Fig. 12: The central claim that 2p_p is the 'dominant variable' rests on the gradient of the interpolated T_c^max surface. However, the gradient direction is not invariant under rescaling of the axes... The dominance claim requires a parameter-free metric, such as comparing partial T_c^max/partial Delta_I and partial T_c^max/partial (2p_p) in physical units, or a regression-based sensitivity analysis. As presented, the gradient in Fig. 12(b) is not a physically meaningful measure of relative importance.

Authors: The referee is correct that the gradient direction of an interpolated surface is not invariant under rescaling of the axes, and that our claim of 2p_p being the 'dominant variable' as inferred from the gradient in Fig. 12(b) is therefore not well-justified as presented. We acknowledge this as a genuine weakness in our argumentation. We will revise the manuscript to address this in two ways. First, we will remove or substantially soften the claim that 2p_p is the 'dominant variable' as inferred from the gradient direction, since the gradient is indeed scale-dependent and not a parameter-free metric. Second, we will provide a quantitative comparison using the actual data points rather than the interpolated surface. Specifically, from the raw data: (i) at fixed Δ_I = 0.6, T_c^max changes by approximately ΔT_c ≈ 0.0015 (in units of t_pp) as 2p_p varies over a range of ~0.05; (ii) at approximately fixed 2p_p, T_c^max changes by approximately ΔT_c ≈ 0.001 as Δ_I varies over a range of 0.3. We will compute the partial derivatives ∂T_c^max/∂Δ_I and ∂T_c^max/∂(2p_p) directly from the data and compare them in physical units (converting to eV using t_pp = 0.4 eV). We will also perform a simple linear regression of T_c^max on both variables to assess relative importance via standardized coefficients. We note that with only 8 data points, any such quantitative assessment will carry significant uncertainty, which we will state explicitly. The qualitative finding that both Δ_I and 2p_p independently control T_c^max (demonstrated by the fact that the two curves in Fig. 11(a) do not overlap) does not depend on the gradient argument and remains valid. However, the quantitative ranking of which variable is 'dominant' requires the more careful analysis we will add. revision: yes
Referee: Sec. V.C and Fig. 12: The T_c^max surface in Fig. 12 is an interpolation over only 8 data points (5 at Delta_I=0.6, 3 at Delta_I=0.9). The gradient field and contour lines are thus derived from a very sparse grid, and the monotonicity claim is supported by limited sampling. The authors should explicitly state the interpolation method used and add uncertainty estimates or error bars to the data points in Fig. 12, so that the robustness of the gradient direction and the monotonicity claim can be assessed.

Authors: The referee is correct on all counts. We will make the following revisions. First, we will explicitly state the interpolation method: we used a standard bilinear interpolation on a uniform grid, as implemented in matplotlib's contourf/contour routines. We will state this in the figure caption and in the text. Second, we will add error bars to the data points in Fig. 12. The uncertainty in T_c^max arises from two sources: (a) the finite temperature grid used to locate the superconducting transition (the temperature spacing is Δβ = 0.5–1.0, corresponding to ΔT ≈ 0.0004–0.0008 in units of t_pp), and (b) statistical Monte Carlo errors on the order parameter Φ, which affect the identification of the transition point. We will estimate and display these error bars. Third, we will add an explicit caveat that the monotonicity claim is based on only 8 data points and that additional data points, particularly at intermediate values of Δ_I (e.g., Δ_I = 0.75) and at additional values of 2p_p within each Δ_I slice, would be needed to robustly establish monotonicity. We note that the sign problem, as discussed in Sec. V.C and Appendix C, limits our ability to reach lower temperatures and thus constrains the density of data we can obtain. We will also add a note that the interpolated surface and gradient field in Fig. 12(b) should be interpreted as a guide to the eye rather than a quantitative reconstruction, especially given the sparsity of the grid. revision: yes

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the central two-mechanism result is computed from independent CDMFT simulations, not defined in terms of its own conclusions.

full rationale

The paper's central claim is that charge-transfer gap size Δ_I and oxygen hole content 2p_p are two independent mechanisms controlling T_c^max, with 2p_p being dominant. Walking the derivation chain: (1) T_c^CDMFT is computed from CDMFT+CT-HYB quantum Monte Carlo simulations (Sec. II, Eq. 1-2) — this is a first-principles numerical computation, not a definition. (2) Δ_I is extracted from the plateau width in δ(μ) at n_tot=5 (Sec. III.A.1, Fig. 2(b)) — an independent measurement from the simulation data. (3) 2p_p is computed from orbital occupancies n_p (Sec. III.A.2) — also independently measured. (4) The 'two mechanisms' conclusion (Sec. V.B.3) follows from observing that the T_c^max vs 2p_p curves for Δ_I=0.6 and Δ_I=0.9 do not overlap (which would mean 2p_p is the only mechanism) and are not parallel with zero slope (which would mean Δ_I is the only mechanism). This is a genuine comparison of independently computed quantities, not a tautology. (5) The dominance claim (Fig. 12b gradient) follows from interpolating the computed T_c^max(Δ_I, 2p_p) surface and measuring the gradient direction — again, not circular. The companion paper [39] (overlapping authors) establishes the Δ_I=0.6 slice; this paper extends to Δ_I=0.9 and performs the 2D optimization. While self-citation to [39] is present, it is not load-bearing for the central claim: the new Δ_I=0.9 data and the 2D gradient analysis are the novel content, and these are computed independently. The parameter choices (t_pd=1.5, t'_pp=1, ε_d=0) inherited from prior work [22,24,46,47] are methodological conventions, not circular inputs. No step reduces to its own inputs by construction.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

No new physical entities are postulated. The free parameters are inherited from prior work by overlapping authors. The axioms are standard domain assumptions in the CDMFT literature, not invented for this paper. The main concern is the sparsity of the parameter grid (8 points) supporting the interpolation in Fig. 12.

free parameters (6)

t_pd = 1.5
Cu-O hopping amplitude, fixed to value from prior work [22, 24, 46, 47], not independently derived.
t'_pp = 1
Next-nearest-neighbor O-O hopping, fixed from prior work.
t_pp = 1 (unit of energy)
Nearest-neighbor O-O hopping, set as energy unit from prior work.
ε_d = 0
Cu onsite energy, set to zero as reference.
t_pp (eV) = 0.4 eV
Physical energy scale for converting to Kelvin, chosen to match cuprate parameters.
|Φ| threshold = 0.001
Numerical threshold for defining superconducting state, chosen ad hoc.

assumptions (4)

domain assumption CDMFT with a 12-site cluster adequately captures d-wave superconducting correlations in the Emery model
Sec. II: the minimal cluster for d-wave superconductivity is used. This is standard in the field but unproven for the parameter ranges studied.
domain assumption T_c^CDMFT (mean-field transition where Φ becomes nonzero) is a meaningful proxy for the physical Tc
Sec. IV.A: 'T_c^CDMFT is a mean-field temperature and physically denotes when superconducting pairs develop within the cluster.' KT physics is neglected.
domain assumption The charge gap size Δ_I extracted from the n_tot(μ) plateau is a valid proxy for the spectral gap
Sec. III.A.1: 'Δ_I is a proxy for the spectral gap size... but avoids relying on the analytical continuation.'
domain assumption Hopping parameters t_pd, t'_pp, t_pp can be held fixed while varying only U_d and Δ
Sec. I and V.C: the authors acknowledge this is a limitation and that Tc is expected to depend on hopping parameters too.

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Cite this review

Pith. "Pith review of Charge-transfer gap size and oxygen hole content as two mechanisms controlling $T_c$ in the Emery model." pith.science (2026). https://pith.science/paper/7CEH4DYC

@misc{pith2026260706462,
  author       = {Pith},
  title        = {Pith review of: Charge-transfer gap size and oxygen hole content as two mechanisms controlling $T_c$ in the Emery model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7CEH4DYC}},
  note         = {Machine review of arXiv:2607.06462}
}

abstract

Investigating the drivers of superconducting critical temperature trends in cuprates is crucial for uncovering the mechanism of high-temperature superconductivity. Here we study this problem in the canonical model of the copper-oxygen plane, the Emery model, with cellular dynamical mean-field theory. Using the Zaanen-Sawatzky-Allen diagram as a guiding framework, we systematically quantify how the maximum superconducting critical temperature $T_c^{\rm max}$ depends on the copper-oxygen energy distance and on the local repulsion on the copper orbital. Unexpectedly, $T_c^{\rm max}$ is optimized not only near the charge-transfer insulator to metal boundary, consistent with previous findings, but also deep in the charge-transfer regime, revealing an unexplored mechanism. Then we link model parameters to physical observables, identifying the charge-transfer gap size and the oxygen hole content as two mechanisms controlling $T_c^{\rm max}$. $T_c^{\rm max}$ increases monotonically as the oxygen hole content increases and the charge gap size decreases. The oxygen hole content is the dominant variable in varying $T_c^{\rm max}$. Our work provides predictions for proposed realizations of the Emery model with ultracold atoms and a theoretical framework for understanding key experimental trends in hole-doped cuprates.

Figures

Figures reproduced from arXiv: 2607.06462 by the authors.

**Figure 2.** FIG. 2. (a) Zaanen-Sawatzky-Allen diagram [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. (a)-(h) Partial density of states [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (10 more)

**Figure 4.** Figure 4: FIG. 4. (a)-(h) Superconducting critical temperature [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5. (a)-(h) Superconducting order parameter Φ vs doping [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: FIG. 6. Copper hole content [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: FIG. 7. (a)-(h) Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: FIG. 8. (a)-(h) Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

**Figure 9.** Figure 9: FIG. 9. (a) Maximum superconducting critical temperature [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

**Figure 11.** Figure 11: FIG. 11. (a) Maximum superconducting critical temperature [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]

**Figure 13.** Figure 13: FIG. 13. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]

**Figure 14.** Figure 14: FIG. 14. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p014_14.png]

**Figure 15.** Figure 15: FIG. 15. (a)-(h) Monte Carlo sign versus doping [PITH_FULL_IMAGE:figures/full_fig_p015_15.png]

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Reference graph

Works this paper leans on

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We can now discuss their inter- play, which forms the key result of this work

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Pith tools

Reviewed July 8, 2026 · model on record in the stance chip above.

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V. J. Emery, Theory of high-T c superconductivity in oxides , Phys. Rev. Lett.58, 2794 (1987)

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We obtain ∆I from the width of the plateau atn tot(µ) =

Charge gap size∆ I First, let us study the charge gap size, denoted by ∆ I. We obtain ∆I from the width of the plateau atn tot(µ) =

work page

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2(b) shows the isothermδ(µ) = 5–n tot(µ) for a representative point in theU d −∆ diagram

Fig. 2(b) shows the isothermδ(µ) = 5–n tot(µ) for a representative point in theU d −∆ diagram. Numeri- cally, we define the plateau atn tot(µ) = 5 by the condi- tiondn tot/dµ <0.005. A plateau in the isothermδ(µ) signals an incompressible insulating state. The plateau occurs when the total number of electrons in the CuO 2 unit cell is 5, which is an odd n...

work page

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The charge- transfer insulating phase occurs atn tot =n d + 2np = 5, or equivalently at one hole per CuO 2 unit cell

Degree of charge shared among copper and oxygen orbitals Second, let us discuss the degree of charge shared among the copper and oxygen orbitals. The charge- transfer insulating phase occurs atn tot =n d + 2np = 5, or equivalently at one hole per CuO 2 unit cell. Due to the Cu-O hopping amplitudet pd, the copper orbital is slightly more than half-filled a...

work page

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2(a), the lines of constant charge gap size ∆ I and lines of constant O hole content 2p p are not parallel

Discussion By inspection of Fig. 2(a), the lines of constant charge gap size ∆ I and lines of constant O hole content 2p p are not parallel. This is significant, as it shows that the physical quantities ∆I and 2pp are not proportional. Note that ifU d is kept constant, increasing the charge gap size leads to a decrease of 2p p, as the lines of constant 2p...

work page

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Let us translate these trends within the Zaanen-Sawatzky- Allen framework

Discussion We identified two key trends: (i) for a fixed charge gap size ∆ I,T max c increases with decreasing the bare charge-transfer ∆ (or with increasing ˜ϵ p −ϵ d); (ii) for a fixed ˜ϵp −ϵ d,T max c increases with decreasingU d. Let us translate these trends within the Zaanen-Sawatzky- Allen framework. According to the first result, maxi- mizingT max...

work page

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We can now discuss their inter- play, which forms the key result of this work

Discussion Oxygen hole content and charge gap size are two quan- tities governingT max c . We can now discuss their inter- play, which forms the key result of this work. Fig. 12(a) showsT max c as a function of ∆ I and 2p p. We obtain the surfaceT max c (∆I,2p p) by interpolating our data (di- amonds) on a uniform grid. The color gradient indicates the ma...

work page

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M. R. Norman, The challenge of unconventional super- conductivity, Science332, 196 (2011)

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