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REVIEW 5 major objections 5 minor 9 references

Introduction to High-Temperature Superconductivity for Solid State Chemists

T0 review · 5 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read Cuprate superconductivity's parabolic Tc dome is an artifact of random chemical disorder; the intrinsic Tc of a clean CuO2 plane rises with hole doping until apical oxygen cuts it down.

desk verdict Hiroi's review is an honest, speculative synthesis of cuprate chemistry, but its central Tco–po correlation is built on p calibrations that don't yet share a common metric. read the letter →

arxiv 2602.12608 v2 pith:GUS4RQTI submitted 2026-02-13 cond-mat.supr-con

Zenji Hiroi This is my paper · ORCID
classification cond-mat.supr-con PACS 74.72.-h74.20.Mn
keywords cupratesuperconductorshigh-temperaturesuperconductivityoxygen-hole/copper-spinsingletBCS-BECcrossoverd-wavepairingapicaloxygendisorderandholetrappingTcoptimization
topics High-Temperature Superconductivity
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 review argues that cuprate high-temperature superconductivity, once stripped of materials complications, has a plain mechanism: a doped hole binds to a copper spin to form a mobile composite singlet, pairs of these singlets attract because they share the magnetic energy cost of breaking antiferromagnetic bonds, and the pairs condense in the BCS-to-BEC crossover. On this picture the intrinsic superconducting critical temperature rises in proportion to the number of mobile holes, and the familiar bell-shaped Tc dome centered at 16 percent doping is not intrinsic: it is produced by random chemical substitutions and excess oxygen in the block layers that trap holes at low doping and break pairs elsewhere. Material differences in Tc are controlled by two structural factors — the distance to the apical oxygen, which destabilizes the singlet once doping exceeds an optimum, and block-layer disorder — which together explain why three-layer compounds with a protected inner CuO2 plane reach the highest Tc, and why higher optimal doping accompanies higher Tc. A sympathetic reader would care because the paper converts a fragmented, seemingly theory-resistant field into a concrete materials-chemistry strategy: maximize the clean, apical-oxygen-free CuO2 plane and maximize the doping it can accept.

What carries the argument

The central object is the composite singlet formed when a doped oxygen hole binds antiparallel to a copper d-electron spin in the antiferromagnetic CuO2 plane. It is mobile, carries one hole, and carries the spin degree of freedom needed for magnetic pairing. The argument's engine is magnetic-energy bookkeeping: two separated singlets destroy eight antiferromagnetic bonds (cost 8J), while a nearest-neighbor pair destroys only seven and pays reduced kinetic energy — producing a net attraction when J dominates the effective hopping. The BCS–BEC crossover is the thermodynamic chassis: in the underdoped regime small preformed pairs form at high temperature and condense at the BEC temperature TB

What would settle it

Measure the full Tc–doping dome of a single-layer cuprate doped by a clean, disorder-free method (for example electrostatic field-effect doping or intercalation that leaves the block layer chemically untouched) and check whether the underdoped side rises linearly with p, the dome is asymmetric, and the optimum moves to p ≈ 0.2–0.26. If the dome remains the symmetric parabola centered at p = 0.16 that chemical doping shows, the randomness/apical-oxygen explanation of the dome would be falsified; alternatively, if inserting apical atoms at a fixed short Cu–O distance fails to suppress Tc, the ap

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Extended reading notes

Core claim

The paper's central claim is that the cuprate Tc–p dome is a composite of two extrinsic suppression mechanisms imposed on a simple intrinsic law. In a clean CuO2 plane, Tc should follow the Bose–Einstein condensation temperature of preformed pairs, rising linearly with the mobile hole concentration p; the pairing glue is the antiferromagnetic background, and the Cooper pair is a d-wave singlet formed either between hole-doped composite singlets (underdoped, BEC side) or between band-like d holes (overdoped, BCS side). The parabolic dome and the supposedly universal optimal doping p = 0.16 are artifacts of randomness: random block-layer charges trap holes at low doping and cause pair breaking

Load-bearing premise

Everything rests on identifying the mobile hole as a tightly bound oxygen-hole/copper-spin singlet whose stability is governed by the apical-oxygen distance, and on attributing the material-to-material scatter in Tc to block-layer disorder — an interpretive mapping the paper does not derive from a microscopic Hamiltonian.

Editorial extensions

If this is right

  • Material optimization for higher Tc becomes a chemistry problem: maximize the hole concentration a clean CuO2 plane can carry before apical-oxygen or disorder suppression sets in, rather than trying to reproduce the universal p = 0.16 dome.
  • Three-layer cuprates outperform one- and two-layer ones because the inner CuO2 plane has no apical oxygen and is shielded from block-layer dopants, so its Tc keeps following the rising BEC line to higher p.
  • Data analysis that converts measured Tc into hole concentration using a universal parabola can be systematically wrong; dome shapes vary asymmetrically and the optimum can lie well above p = 0.2.
  • The underdoped side of the dome should be understood as mobile-hole-limited: the effective doping is lower than nominal, so properties correlate with superconducting carrier density rather than chemical doping.
  • Cuprates sit in the BCS–BEC crossover, so high-Tc strategies should look for other systems with strong short-range attraction and low pair density, where Tc is set by pair density and by how much of the glue energy survives as a prefactor.

Reading between the lines

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

  • If the apical-oxygen picture is the whole story, then a single-layer cuprate whose apical sites are replaced by farther or monovalent anions — or doped without introducing block-layer disorder, for instance electrostatically — should reach Tc comparable to the best three-layer compounds rather than the 25–40 K typical of chemically doped single layers.
  • A testable extension: the same logic predicts that in ultra-clean films the underdoped branch of Tc–p should be linear in p, not parabolic, and the dome should be visibly asymmetric; data on relatively clean Hg and multilayer compounds already lean in that direction.
  • The heuristic that maximum Tc is about 10 percent of the glue energy (here the magnetic exchange J ≈ 1500 K) suggests two independent levers for other superconductor families: raise the relevant excitation energy and reduce the exponential suppression factor, which the paper identifies with randomness and structural relaxation.
  • If confirmed, this picture would redirect the room-temperature superconductor search away from exotic new pairing mechanisms and toward cleaner materials chemistry: isoelectronic, disorder-free doping of strongly coupled two-dimensional planes.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. The manuscript is a wide-ranging, pedagogically oriented review aimed at solid-state chemists. After introducing BCS theory, the BCS–BEC crossover, and superconducting gap symmetry, it devotes its core to cuprate superconductors. The central thesis is that, once extrinsic material complications are removed, the cuprate story is simple: the intrinsic transition temperature is controlled by the two-dimensional BEC temperature TB ∝ p, while the observed material dependence of Tc (including the maximum Tco and the optimal doping po) is governed by two factors—apical-oxygen destabilization of Zhang–Rice singlets and randomness/charge trapping in the block layers. The paper argues that Presland's parabolic Tc–p relation is not universal, that Tco and po are positively correlated, and that the parabolic Tc-p dome is largely an artifact of randomness. It concludes with a survey of other superconductivity mechanisms and strategies for raising Tc toward room temperature.

Significance. If the central empirical and mechanistic claims hold, this paper would offer a useful organizing principle for cuprate materials chemistry: raise Tco by increasing po, which means reducing apical-oxygen influence and block-layer randomness. The manuscript has real strengths: the Cn-Bm structural classification is clear, the compilation of Tc–p data and of p-determination methods (CT, neutron diffraction, NMR, ARPES) is valuable, the figures are dense but informative, and the author is admirably explicit about which steps are speculative, even labeling Eq. (5) 'a wild guess.' The paper also makes falsifiable predictions, such as a clean CuO2 plane with Tc ∝ p and a left-shifted dome in cleaner systems. However, the central quantitative claims are not yet secured: the Tco–po correlation relies on heterogeneous p calibrations, the randomness term is not independently quantified, and the apical-oxygen mechanism is an interpretive assignment rather than a derived result. Its value at present is therefore more pedagogical and hypothesis-generating than archival.

major comments (5)
  1. [§4.3.1, Eq. (5)] The analysis of material dependence is framed by Tc = J exp(-1/λ), with the reduction factor 0.09 read off the known maximum Tc = 135 K. The text itself calls Eq. (5) 'a wild guess.' This is not a derived bound: the strong-coupling generalization of Eq. (3) is not justified for the ZRS pairing, and the 'maximum exponential term ≈ 0.1' is an empirical observation, not a prediction. This step is load-bearing because it motivates the later question 'why is Tc low in most cuprates?' and the assignment of suppression to apical oxygen and randomness. Please either provide a derivation or clearly mark this as an illustrative assumption, and separate that illustrative frame from the empirical trends in Section 4.4.
  2. [§4.4.4-4.4.5, Fig. 26] The claim 'Tco and po are positively correlated' is the empirical bridge on which the later mechanism is built. The plot in Fig. 26 mixes p values determined on different scales: CT and neutron-diffraction measurements give the average hole content over all CuO2 planes, whereas NMR and ARPES give plane-resolved p for some compounds. For multilayers, the paper itself argues in §4.6.2 that the inner plane may set Tco, so an average-p value is systematically displaced relative to a plane-resolved value. In addition, the bivariate plot does not control for n, the number of CuO2 planes; since both Tco and po rise with n within each family, the apparent correlation may be a proxy for n. To support the central inference, please re-analyze Fig. 26 with fixed n or fixed p-calibration method, or otherwise show that the correlation survives such controls.
  3. [§4.4.5, Eq. (8)] The p-calibration used for NMR data is not independent of the relation the paper seeks to test. The text notes that some NMR work uses 'p = 0.492Ksab(RT) - 0.023' based on Presland's relation, while the author instead chooses Eq. (8), 'p = 0.502Ksab(RT) + 0.0462,' described as previously established. But the constants in Eq. (8) must also originate from some set of independent p determinations. If a subset of the points in Figs. 25 and 26 is calibrated using an assumption equivalent to a parabolic dome centered at p = 0.16, then the conclusion that Presland's relation is not universal is at least partially circular for those points. Please state the independent data used to calibrate Eq. (8) and demonstrate that the Tco–po trend in Fig. 26 does not rely on points whose p values presuppose the dome shape.
  4. [§4.5.2.4] The statement that the parabolic Tc–p dome is 'just an artifact' is stronger than what the presented evidence supports. The hole-trapping model gives no quantitative expression for p*, the mobile hole concentration, and the text acknowledges that the TB* curve is 'just a demonstration.' Randomness is invoked post hoc to absorb every outlier (La214, Cl214, Bi2201), but no independent metric of randomness is provided or computed for each material. This makes the attribution difficult to falsify and conflates two distinct effects: hole trapping in the UD regime and pair breaking near optimum doping. Please either (i) formulate a concrete disorder parameter (e.g., screened impurity potential or positional variance) and tabulate it for the compounds in Fig. 26, or (ii) soften the conclusion to 'randomness can substantially deform the dome' rather than declaring the parabolic dome an artifact.
  5. [§4.5.1.1-4.5.1.3] The apical-oxygen mechanism is supported by the Ohta-Tohyama-Maekawa electrostatic correlation and by the doping dependence of d(Cu–Oa) in Fig. 28, but these are correlations. No microscopic Hamiltonian or first-principles calculation is provided to show that the d(Cu–Oa) contraction causes the ZRS-to-d-hole transition; alternative mechanisms that also vary with n—such as interlayer coupling, charge order, or inhomogeneous carrier distributions across planes—are not quantitatively excluded. The conclusion that C3 beats C1 because of apical-oxygen count is thus an interpretive assignment. A concrete test would be to compare materials with similar d(Cu–Oa) but different block-layer disorder, or to compute the Oa potential from a first-principles electronic structure for the same families plotted in Fig. 26.
minor comments (5)
  1. [§2.4.1] The name is usually spelled 'Ginzburg–Landau,' not 'Ginsburg–Landau.'
  2. [§4.4.5] Typo: 'APRES experiment' should be 'ARPES experiment.'
  3. [Eq. (6)] The right-hand side 'l – 82.6(p – 0.16)2' appears to use a lowercase 'l' where '1' is intended.
  4. [§1.3] The manuscript states that it has 'a lack of specificity in the conclusion and the absence of notable novel proposals.' This sentence conflicts with the later strong claims about the Tco–po correlation and the parabolic dome artifact; please clarify whether the paper is intended as a pedagogical review or as a research contribution, and adjust the framing accordingly.
  5. [§4.5.2.2, Fig. 29] The 20 × 20 lattice with randomly placed substitution atoms is described as if it were a calculation, but it is only an illustration. Please state explicitly in the caption or text that the distribution is schematic and does not include screening or percolation thresholds.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the central Tco–po correlation rests on independent p determinations, and heuristic arguments are explicitly labeled as such.

full rationale

The paper's central empirical inference—that Tco and po are positively correlated—is assembled from chemical titration, neutron-diffraction refinement, NMR Knight-shift, and ARPES determinations of p (Sec. 4.4.5), not from the Uemura-derived p values. Uemura's plot is used as a consistency check ('The observed trend is consistent with the Uemura plot prediction...'), and the paper explicitly avoids the Presland-calibrated NMR relation, rejecting Mukuda's modified relation in favor of Eq. 8. The Eq. 5 reduction factor (0.09) is an explicit post-hoc calibration to the known maximum Tc ('With J set to 1500 K, the current maximum Tc of 135 K corresponds to an exponential term of 0.09'), presented as an empirical regularity rather than as a prediction, and it does not carry the material-dependence derivation. The TB* construction in Sec. 4.5.2.4 is a heuristic illustration, explicitly labeled 'just a demonstration,' with mobile-hole p* as an unmeasured latent variable; this is unfalsifiable as stated but is not a mathematical reduction of an output to an input. The apical-oxygen and randomness mechanisms cite independent prior work (Ohta–Tohyama–Maekawa; Attfield; Eisaki) rather than a self-citation chain. The skeptic's concerns—mixed p scales from plane-averaged vs plane-resolved p, lack of control for n, and the difficulty of quantifying randomness—are substantive scientific validity risks, but they are not instances of equation-level circularity or fitted parameters being renamed as predictions. Thus no circular step meets the required evidentiary standard.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claims rest on interpretive assumptions rather than a closed derivation: the AFM/ZRS glue, the transfer of BCS-BEC ideas to solids, the Uemura m* assumption, the empirical p calibrations, and the disorder picture. Free parameters enter through Eq. 5's lambda (read off from known Tc) and through Eq. 8's p-calibration. No new physical entities are invented.

free parameters (3)
  • lambda in Tc = J exp(-1/lambda) = not specified; J=1500 K and Tc=135 K imply exp term 0.09, lambda ≈ 0.415
    Eq. 5 is presented as a simplified replacement for BCS Tc, but lambda is not derived; the 0.09 reduction factor is read off from the target Tc, making the relation a parameterization rather than a prediction.
  • p-calibration coefficients in Eq. 8 = p = 0.502 Ksab(RT) + 0.0462
    The NMR-based hole concentration estimate is empirically calibrated. The Tco-po correlation and the conclusion that po > 0.16 for high-Tc compounds depend on this and similar calibrations.
  • po for C2 and C3 inferred from Uemura plot = po = 0.24 (C2) and 0.26 (C3) if C1 po = 0.16
    In §4.4.2, multilayer po values are inferred by scaling muSR relaxation rates using crystal-structure volume ratios and assuming even hole distribution; these values feed the Tco-po relation in Fig. 26.
assumptions (5)
  • domain assumption Cuprate pairing is mediated by antiferromagnetic spin fluctuations, and the relevant quasiparticle is the Zhang-Rice singlet.
    Used throughout §§4.2-4.3 to construct the pairing image and Eq. 5. The paper itself notes the cuprate mechanism is still debated, so this is an unproved working assumption.
  • domain assumption The muSR relaxation rate is proportional to ns/m*, and m* is nearly material-independent across cuprates.
    Sec 4.4.2 uses this to convert Uemura's plot into a carrier-density/po trend. The material independence of m* is asserted, not demonstrated.
  • domain assumption BCS-BEC crossover applies to cuprates with doping as the control parameter, including TB ∝ p for 2D bosons.
    Sec 4.3.2 transfers the cold-atom BCS-BEC picture to a solid with variable carrier density; this is an analogy, not a derivation from a cuprate Hamiltonian.
  • domain assumption Apical-oxygen electrostatic potential controls Zhang-Rice-singlet stability.
    Sec 4.5.1 uses the Ohta-Tohyama-Maekawa potential argument to explain the C1<C2<C3 Tco ordering. The original work is a calculation/empirical correlation, not an established law.
  • domain assumption Block-layer randomness causes Anderson localization/hole trapping at low doping and pair breaking near optimum doping.
    Sec 4.5.2 models randomness with cartoons and percolation sketches; no quantitative disorder calculation is provided, yet the claim that La214's parabolic dome is extrinsic depends on this picture.

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Cite this review

Pith. "Pith review of Introduction to High-Temperature Superconductivity for Solid State Chemists." pith.science (2026). https://pith.science/paper/GUS4RQTI

@misc{pith2026260212608,
  author       = {Pith},
  title        = {Pith review of: Introduction to High-Temperature Superconductivity for Solid State Chemists},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GUS4RQTI}},
  note         = {Machine review of arXiv:2602.12608}
}
read the original abstract

Superconductivity is one of the most amazing properties that metallic conductors exhibit. Electrical resistance is completely eliminated below the critical temperature (Tc), which is the most important parameter in superconductivity. Since the discovery of copper oxide superconductors 39 years ago, many solid state chemists have made significant contributions to the field by discovering new compounds and producing high-quality samples for physical measurements. However, superconductivity research remains challenging for most solid state chemists because it requires knowledge of complicated solid state physics. This manuscript aims to provide a simple, intuitive introduction to superconductivity using only fundamental physics concepts that solid state chemists are familiar with. The author investigates a wide range of materials and classifies them according to the superconductivity mechanisms that may drive them. Specifically focusing on a series of copper oxide superconductors with the highest Tc at ambient conditions, the remarkable material dependence of Tc and the underlying, unconventional superconductivity mechanism that leads to the high Tc are thoroughly examined. Although our understanding of cuprate superconductivity is still fragmented, the author believes that once the branches and leaves are removed, the story will be fairly simple, similar to the phonon-based superconductivity mechanism revealed by the BCS theory. Furthermore, potential strategies for raising the Tc of cuprates and other superconductors are discussed. The author hopes that this article will pique interest in superconductors in young solid state chemists and encourage them to pursue the discovery of still unknown and unexplored room-temperature superconductors in the future.

Figures

Figures reproduced from arXiv: 2602.12608 by the authors.

Figure 3
Figure 3. depicts a simple Fermi surface made up of s-electrons, yielding a sphere in momentum space. The anisotropic shape of the orbitals, directional chemical bonding, and number of occupied electrons all contribute to the Fermi surface's overall complexity. "Frontier electrons" exist near the Fermi level and govern the electrical conductivity of materials [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 2
Figure 2. Electrons propagating through a crystal. In real space (a), an electron (red ball) in the highest atomic orbital moves across the crystal, forming a wave (magenta wavy arrow) with wavelength λ and wavevector k. The kinetic energy increases with the magnitude k, resulting in the dispersion curve with an energy spread of W, as depicted in momentum space (b). Electrons in a crystal can have electronic states ranging fr… view at source ↗
Figure 5
Figure 5. Cartoons depicting how the electrical resistance R occurs in a solid (a) and how zero resistance is attained (b). In the normal conducting state at high temperatures above Tc, a single electron is easily scattered by a crystal defect (blue cross), resulting in a finite resistance. At low temperatures below Tc, a pair of electrons (Cooper pair) is produced in the superconducting state and is not scattered by a defect… view at source ↗
Figures from the paper (26 more)
Figure 6
Figure 6. Figure 6: depicts a schematic comparison of the electrical resistivity between a superconductor (such as Pb) and a normal conductor (Au). At higher temperatures, excited phonons scatter more electrons, leading to higher electrical resistivity than ρ0. Pb has a higher electrical …
Figure 7
Figure 7. Figure 7: Schematic representation of Cooper pairing via electron–phonon interactions in BCS superconductivity. (a) Consider two electrons, k↑ and –k↓, with opposite momenta and spins in the initial state. They conduct in a crystal made up of atoms that are presumed to be positi…
Figure 8
Figure 8. Figure 8: Basic concept of the BCS theory. For the sake of simplicity, we consider a two-dimensional electron system with a circular Fermi surface rather than a sphere and an energy￾independent DOS profile ( [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: β-pyrochlore osmium oxide supercondutor AOs2O6 [42]. (a) The electronic heat capacity Ce divided by T reveals superconducting transitions at Tc = 3.3, 6.3, and 9.6 K for A = Cs, Rb, and K, respectively. In comparison, Cd2Re2O7, an α￾pyrochlore oxide superconductor, has…
Figure 10
Figure 10. Figure 10: Evolution of electron pairings from the BCS to the BEC regime, with increasing pairing interaction, based on research on the cold fermionic atom gas system [44, 45, 48]. Two red balls on a shaded circle represent an electron pair, with their orientations mimicking wav…
Figure 11
Figure 11. Figure 11: Superconducting gaps in momentum space (above) and Cooper pair wavefunctions in real space (below) for (a) s-wave and (b) dx2 –y2 -wave superconductivity, respectively. The superconducting gap opens isotropically in the s-wave and reverses sign across the node at <110…
Figure 13
Figure 13. Figure 13: Typical phase diagram for copper oxide superconductivity, with La2–xSrxCuO4 on the right and Nd2– xCexCuO4 on the left. The Sr and Ce substitutions introduce holes and electrons into the parent insulating phases with Cu2+, respectively, resulting in superconductivity …
Figure 15
Figure 15. Figure 15: Fundamental structure of the conduction layer in copper oxide superconductors. In the n = 1 compound (C1), the copper atom is octahedrally coordinated by six oxide atoms: four Op atoms in the CuO2 plane and two apical Oa atoms in the block layer. In the n = 2 compound…
Figure 16
Figure 16. Figure 16: Structure types composed of a Cn conduction layer containing n CuO2 planes and a Bm block layer containing m cation sheets. All copper oxide superconductors are classified as Cn-Bm. Multilayer Hg and Ba series compounds with n larger than 5 will be listed below the ta…
Figure 17
Figure 17. Figure 17: Six distinct types of block layers. (a) The minimum block layer is made up of a single Sr sheet (m = 1) sandwiched O Ba/Sr Hg/Tl/Cu/Pb Oδ (d) B3-NC (f) B4-NC Sr O (a) B1 Cu CuO2 plane O Ba Cu Oδ (e) B3-PV O Nd (c) B2-CF CuO2 plane La O (b) B2-NC Block layer a c Oδ Oδ …
Figure 18
Figure 18. Figure 18: Basic energy diagram of the CuO2 plane in copper oxide superconductors. When a Cu2+ ion with a 3d9 electron configuration is placed in an elongated oxygen octahedron composed of four in-plane Op atoms and two distant apical Oa atoms, the unpaired electron occupies the…
Figure 19
Figure 19. Figure 19: Schematic representations of the CuO2 plane with Cu spins in the dx2 –y2 orbital that are coupled together by the antiferromagnetic interaction J and arranged in antiferromagnetic order, as well as what happens when holes are introduced. (a) A doped hole on the O 2p o…
Figure 20
Figure 20. Figure 20: depicts the electronic phase diagram of La2– xSrxCuO4 [140], a typical cuprate superconductor, with the characteristic temperatures for emerging phases or states plotted against hole concentration p, which is assumed to be equal to Sr content x. The parent phase, La2C…
Figure 21
Figure 21. Figure 21: (a) T–p phase diagram and Cooper pairing for copper oxide superconductivity based on the BCS–BEC crossover in cold atom gas systems, as shown in [PITH_FULL_IMAGE:figures/full_fig_p025_21.png]
Figure 22
Figure 22. Figure 22: Tco versus n plots for various compound series ( [PITH_FULL_IMAGE:figures/full_fig_p026_22.png]
Figure 23
Figure 23. Figure 23: Uemura's plot of the relationship between Tc and μSR relaxation rates, extrapolated to zero temperatures. The latter scales to ns/m* , where ns and m* are superconducting carrier density per unit volume and effective carrier mass, respectively [163]. The arrows repres…
Figure 24
Figure 24. Figure 24: Tc variations with decreasing p in the Tl2 series of compounds [170]. For each compound, Δp represents the hole concentration in comparison to the as-grown sample prepared at 880–890 ºC in an oxygen atmosphere. To determine p changes, oxygen loss was measured in weigh…
Figure 25
Figure 25. Figure 25: a compares Tl2201 and La214, assuming that Δp = 0 corresponds to p = 0.41 for Tl2201, based on NMR experiments: (Tc/K, p) = (72, 0.27), (42, 0.30), (0, 0.41) [171]. The Tc dome of the Tl2201 appears to be larger than that of the La214, with higher p and Tc values. Fig…
Figure 26
Figure 26. Figure 26: depicts the relationship between Tco and po for a variety of compounds. The aforementioned experimental uncertainty affects the determination of po; for Bi2212, it ranges from 0.17 to 0.27. Regardless of scatter, Tco and po in the Bi and Hg series tend to rise as n in…
Figure 27
Figure 27. Figure 27: Schematic representation of the Tc–p relationship for the C1, C2, and C3 compounds in the absence of randomness effects, demonstrating the apical oxygen effect. The TB line, proportional to p, represents the BEC temperature in two dimensions. The Tp curve, which gener…
Figure 28
Figure 28. Figure 28: Doping dependence of the Cu–O distances, d(Cu–Op) (left axis) and d(Cu–Oa) (right axis), as determined by powder neutron diffraction experiments for (a) La214 [195, 200], (b) Tl2201 [128], and (c) Hg1201 [194]. In Tl2201 and Hg1201, the occupancy at the excess oxygen …
Figure 29
Figure 29. Figure 29: Cartoons illustrating how random chemical substitution in the block layers causes uneven distributions of substitution atoms, resulting in inhomogeneous electronic states in the CuO2 plane. The La214 stacking unit, (La, Sr)O– CuO2–(La, Sr)O, randomly arranges Sr atoms…
Figure 30
Figure 30. Figure 30: Schematic phase diagram demonstrating how randomness alters its appearance. Nominal p does not equal p* which represents the actual mobile hole concentration; p* is less p TB 0 0 T Inhomogeneous Tc Hole trapping TB TN * AFI SC Tp AFM Pair breaking [PITH_FULL_IMAGE:fi…
Figure 32
Figure 32. Figure 32: Calculated hole concentration, normalized to pB, for each CuO2 plane of various Hg compounds. The horizontal axis represents the distance d along the c axis from the block layer center at the HgOδ sheet in the B3-NC block layer (Fig. 17d) for C1 (blue line) [194], C2 …
Figure 37
Figure 37. Figure 37: summarizes the relationship between Tc and p based on the NMR and ARPES experiments. NMR experiments show that the Tc domes of Hg C1, C2, and C3 have similar shapes and gradually expand into the high-doped regime, with Tco observed at po = 0.16, 0.21, and 0.25 [166, 2…
Figure 42
Figure 42. Figure 42: General phase diagram for superconductivity derived from a relevant long-range order (LRO). LROs in ferromagnetic metal (FM), antiferromagnetic metal (AFM), charge-density wave (CDW) insulators, and others can be suppressed by increasing a control parameter, such as c…

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Reviewed August 2, 2026 · model on record in the stance chip above.