Discriminating superconducting fluctuations from the pseudogap in Bi 2 Sr 2 Ca n-1 Cu n O 2n+4+ delta (n = 2,3): A magnetotransport study

arXiv:2608.11284 · cond-mat.supr-con · Submitted 2026-08-11 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: We're looking at the paper: "Discriminating superconducting fluctuations from the pseudogap in Bi 2 Sr 2 Ca n-1 Cu n O 2n+4+ delta (n = 2,3)".

Mira: The gist: The magnetotransport study unambiguously demonstrates that the strong pseudogap in high-Tc cuprates is not a manifestation of superconducting fluctuations (SCF),

Kai: First, who's behind it and why it matters.

Title and authors: Lev: So what’s the actual conclusion they draw from all this data? What’s the big takeaway if you look at the summary of "Discriminating superconducting fluctuations from the pseudogap in Bi two Sr two Ca n-one Cu n O 2n+four plus delta (n = twenty-three): A magnetotransport study"?

Kai: Basically, they conclude that their magnetotransport measurements unambiguously demonstrate that the strong pseudogap is not a manifestation of superconducting fluctuations. This is a big statement because it rules out one of the main competing explanations for this mysterious feature in high-Tc cuprates.

Mira: That’s correct. They argue that instead, the evidence strongly suggests that the pseudogap originates from preformed Cooper pairing existing well above the critical temperature Tc, specifically within what they call the BCS–BEC crossover regime.

Lev: So if we translate that into a physical picture for us working on real hardware, it means we’re looking at pairing forming before true global superconductivity sets in, which is a distinct physics regime from what SCF would imply.

Kai: And to support this, they look at scanning tunneling spectroscopy results and find that the effective superconducting gap delta SC is reduced relative to the zero temperature gap delta zero because the d-wave gap opens primarily on the Fermi arc <ref:2608.11284#pg2>.

Mira: That’s interesting because it links the normal state transport feature directly to a specific pairing mechanism, suggesting that this preformed pairing structure is what sets up the pseudogap in these materials.

The paper's summary: Kai: Now, moving on to how this work improves things—what are the suggested improvements or the stronger arguments they build on top of their findings in "Discriminating superconducting fluctuations from the pseudogap in Bi two Sr two Ca n-one Cu n O 2n+four plus delta (n = twenty-three): A magnetotransport study"?

Lev: The improvement they make is showing that their method for identifying the pseudogap onset is robust and corroborated by independent measurements. They don’t just rely on one transport measurement.

Mira: That’s key because it means the temperature values they derived for T* upper are in excellent agreement with those reported by spectroscopic techniques, such as scanning tunneling spectroscopy, which report similar T* p relationships across different doping levels.

Kai: So they found that the method for identifying the pseudogap onset is robust and corroborated by independent measurements, which validates their findings on the temperature scales.

Lev: And it’s not just about agreement; they also show that Tscf, which is the onset of superconducting fluctuations, is identified by observing where drhoab over dT at nine Tesla decreases by more than one percent relative to the zero Tesla curve <ref:2608.11284#pg1>.

Mira: That specific deviation in the magnetoresistance helps them pin down Tscf and shows it aligns with their modified Kohler analysis, reinforcing that this temperature is indeed distinct from the pseudogap onset.

The paper's improvements: Kai: So to wrap up our discussion on "Discriminating superconducting fluctuations from the pseudogap in Bi two Sr two Ca n-one Cu n O 2n+four plus delta (n = twenty-three): A magnetotransport study," they’ve established that the strong pseudogap is not just a fluctuation artifact.

Mira: They conclude that the more plausible interpretation for this feature is that it originates from preformed Cooper pairs in the BCS–BEC crossover regime, which means we see pairing forming before true global superconductivity kicks in.

Lev: If you’re building error-correction codes, this tells you that the physics of these materials involves pairing correlations that are already established at higher temperatures than you might expect from a simple fluctuation model.

Kai: We have to remember that they also ruled out charge-density-wave order as the primary origin of the pseudogap because CDW order is absent in overdoped Bi two thousand two hundred twelve and Bi two thousand two hundred twenty-three yet the pseudogap persists well into overdoping <ref:2608.11284#pg2>.

Mira: That’s a fair point. It suggests that CDW might be a competing order that can coexist with this pairing state in certain doping ranges, but it doesn't track the pseudogap across the entire phase diagram.

Lev: So, for future work, they might want to look at how this preformed pairing behavior evolves as you move further away from optimal doping or when you start looking at more complex structures.

Kai: That’s what we’ll be keeping an eye on—how this preformed pairing picture scales and behaves in different regimes of these cuprates.

Mira: Well, that’s the end of our discussion on this paper, "Discriminating superconducting fluctuations from the pseudogap in Bi two Sr two Ca n-one Cu n O 2n+four plus delta (n = twenty-three): A magnetotransport study."

Conclusion: Kai: So to wrap up, this paper on "Discriminating superconducting fluctuations from the pseudogap in Bi two Sr two Ca n-one Cu n O 2n+four plus delta (n = twenty-three): A magnetotransport study," they found that the strong pseudogap isn't just a fluctuation thing <ref:2608.11284#pg1,Discriminating superconducting fluctuations from the pseudogap in>.

Mira: That’s right. They showed that the evidence strongly suggests the pseudogap comes from preformed Cooper pairs in the BCS–BEC crossover regime.

Lev: From an engineering standpoint, it means we’re looking at pairing correlations that are already established at higher temperatures than you might expect from a simple fluctuation model.

Kai: And they backed this up by showing the temperature scales match what we see in scanning tunneling spectroscopy.

Mira: Exactly, that agreement between the transport-derived T* upper and the spectroscopic T* p relationships gives a lot of confidence in their finding.

Lev: If you were trying to run this on real hardware, you’d need to account for those temperature scales precisely because they’re so tightly linked.

Kai: They also looked at how the onset of superconducting fluctuations, Tscf, is identified by checking the change in magnetoresistance with the magnetic field.

Mira: That modified Kohler analysis helps them pin down Tscf and confirms it's separate from the pseudogap temperature.

Lev: The caveat there is that they also showed that even at Tscf, fourteen Tesla isn't enough to fully suppress those fluctuations, so the MR keeps increasing with field.

Kai: So the main implication is that this strong pseudogap feature in high-Tc cuprates points toward a specific pairing mechanism we need to model carefully.

Mira: It shifts our focus away from simple fluctuation models and toward understanding preformed pairs above Tc.

Lev: For us building error correction, it means the underlying physics of the normal state is more complex than just a standard Fermi liquid approximation would suggest.

Kai: That’s what they did with this magnetotransport study on Bi two Sr two Ca n-one Cu n O 2n+four plus delta (n = twenty-three) <ref:2608.11284#pg1>.

Mira: It’s a solid piece of evidence pointing toward pairing in the BCS–BEC crossover regime.

Lev: We should keep an eye on how this preformed pairing scales when we try to map it onto actual error correction overhead.

Shunpei Yamaguchi, Nae Sasaki, Shintaro Adachi, Keiichi Harada, Yuki Teramoto, Shintaro Matsuda, Tomohiro Usui, Takenori Fujii, Takashi Noji, ¦tsuhiro Kakeya, Áruka Taniguchi, Ãhiaki Matsukawa, Atsushi Miyake, Hajime Ishikawa, Koichi Kindo, Takao Watanabe

Graduate School of Science and Technology, Hirosaki University · Faculty of Engineering/Graduate School of Engineering, Kyoto University of Advanced Science (KUAS) · Cryogenic Research Center, University of Tokyo · Graduate School of Engineering, Tohoku University · Department of Electronic Science and Engineering, Kyoto University · Graduate School of Engineering, Iwate University · Institute for Solid State Physics, University of Tokyo · Physics Department, College of Engineering, Nihon University · Department of Advanced Materials Science, University of Tokyo

cond-mat.supr-con

Submitted: 2026-08-11

Updated: 2026-08-11

Comments: 7 pages 4 figures in the main manuscript; 9 pages 9 figures in the Supplemental Material

Journal ref: Phys. Rev. B 114, L200501 (2026)

DOI: 10.1103/d532-8q2d

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 77/100

The gist: The gist: The magnetotransport study unambiguously demonstrates that the strong pseudogap in high-Tc cuprates is not a manifestation of superconducting fluctuations (SCF), suggesting it originates

Key concepts

Pseudogap: A temperature-dependent suppression of electronic states observed in high-temperature superconductors above the superconducting transition temperature. This feature is distinct from superconductivity itself and is investigated to determine its true origin.
Superconducting Fluctuations (SCF): Fluctuations arising from transient Cooper pairing that occur above the actual superconducting transition temperature. The study rigorously tested if the observed pseudogap behavior was due to these fluctuations, finding it was not.
BCS–BEC Crossover Regime: A theoretical framework describing the transition between weak-coupling BCS superconductivity and strong-coupling Bose-Einstein condensation. The paper suggests the pseudogap originates from preformed Cooper pairs existing in this crossover state.

Summary

The gist: The magnetotransport study unambiguously demonstrates that the strong pseudogap in high-Tc cuprates is not a manifestation of superconducting fluctuations (SCF), suggesting it originates from preformed Cooper pairing in the BCS–BEC crossover regime

Normal State Transport and Pseudogap Identification

The investigation focuses on magnetotransport in Bi2Sr2CaCu2O8+δ and Bi2Sr2Ca2Cu3O10+δ single crystals across a wide doping range. While the in-plane resistivity and Hall coefficient show strong pseudogap-induced temperature dependence, the T 2 Hall-angle behavior and the modified Kohler’s rule remain robust across all dopings. The onset temperatures of the pseudogap are clearly distinct from superconducting fluctuations, although they scale with the pseudogap magnitudes with a factor consistent with a d-wave superconductor. This demonstrates that the pseudogap does not arise from superconducting fluctuations and instead suggests that it may originate from preformed Cooper pairing in the BCS–BEC crossover regime.

Theoretical Frameworks and Anomalous Behavior

The paper reviews existing theoretical frameworks for understanding the anomalous normal state, noting that near optimal doping, in-plane resistivity varies linearly with temperature while the Hall coefficient scales approximately as T −1, yielding a Hall angle cot θH that follows a T 2 dependence. The CVC theory incorporates strong antiferromagnetic spin fluctuations through current-vertex-corrections and predicts behaviors consistent with observed results near optimal doping. However, recent high-field studies on Bi2Sr2CuO6+δ, Tl2Ba2CuO6+δ, and LSCO demonstrate a new scaling for MR that implies the Fermi-liquid approach is insufficient for explaining transport properties in hole-doped cuprates.

Characterization of Pseudogap Temperatures

The authors employ several methods to characterize the pseudogap temperatures, denoted as T∗∗upper and T∗∗lower. For underdoped Bi-2212 (p = 0.126) and near optimally doped Bi-223 (p = 0.17), the high-temperature resistivity exhibits a robust T-linear behavior above the pseudogap temperature T∗. This T∗upper is determined by a 1% deviation from high-temperature linear behavior, yielding values of 206 K and 213 K for Bi-2212 (p = 0.126) and Bi-223 (p = 0.17), respectively. Furthermore, the temperature at which the derivative of resistivity reaches a maximum is defined as T∗lower, corresponding to the temperature at which the pseudogap becomes sufficient to match Tpg in Ref. [35].

Distinguishing Pseudogap from Superconducting Fluctuations

The study rigorously tests whether the pseudogap state is independent of SCF by examining magnetoresistance (MR) measurements. The modified Kohler’s rule is found to hold across T∗upper, reinforcing the conclusion that the pseudogap is distinct from SCF. The onset temperature of SCF, Tscf, is identified by observing where the slope of MR with respect to tan2 θH exceeds the high-temperature constant value by more than 10%. This deviation corresponds to the onset temperature of SCF, Tscf.

Origin of the Pseudogap

The analysis strongly suggests that the pseudogap originates from preformed Cooper pairs in the BCS–BEC crossover regime. In this regime, Cooper pairs form well above Tc while global superconductivity does not emerge until Bose condensation occurs. Scanning tunneling spectroscopy supports this picture by showing that the effective superconducting gap ∆SC is reduced relative to ∆0 because the d-wave gap opens primarily on the Fermi arc. This finding implies that the pseudogap in high-Tc cuprates may originate from preformed Cooper pairing in the BCS–BEC crossover regime.

Conclusion on Competing Orders

The investigation also ruled out charge-density-wave (CDW) order as the primary origin of the pseudogap. CDW order is absent in overdoped Bi 2212 and Bi 2223, yet the pseudogap persists well into overdoping. Instead, CDW appears as a competing order that can coexist with the pseudogap in certain doping ranges but does not track the pseudogap across the entire phase diagram. The final conclusion is that our magnetotransport measurements unambiguously demonstrate that the strong pseudogap is not a manifestation of superconducting fluctuations (SCF).

Data Consistency

The transport-derived values for T∗upper are in excellent agreement with those derived from spectroscopic techniques, such as scanning tunneling spectroscopy (STS), which report similar T∗(p) relationships. These comparisons demonstrate that the pseudogap temperatures obtained from transport measurements are consistent with those derived from spectroscopic techniques. The method for identifying the pseudogap onset is robust and corroborated by independent measurements.

Sample Preparation Details

Single crystals of Pb-doped Bi-2212 and Bi2Pb0.4Sr1.8CaCu2O8+δ were grown using the traveling-solvent floating-zone (TSFZ) method. High-quality Bi-2223 single crystals were also grown using the TSFZ method. Doping levels for Bi-2212 were obtained using an empirical relation based on Tc and Tmaxc, while for Bi-2223, doping levels were determined by angle-resolved photoemission spectroscopy (ARPES). The samples used in the transport measurements were annealed under the same conditions as those used in the ARPES study.

Magnetoresistance Analysis

The onset temperature of SCF, Tscf, is estimated by observing where dρab/dT at 9 T decreases by more than 1% relative to the 0 T curve. This determination coincides with the onset temperature of SCF obtained from the modified Kohler analysis in Fig. 7. The deviation from the modified Kohler’s rule always appears whenever SCF are present. If 14 T is not sufficient to suppress SCF, MR continues to increase with magnetic field, and the slope MR/ tan2 θH remains larger than that of the high temperature modified Kohler curve. This behavior below Tscf indicates that even at Tscf, 14 T is not sufficient to fully suppress SCF. The modified Kohler analysis is a sensitive and reliable method for detecting the onset of SCF.

Out-of-Plane Resistivity Behavior

The temperature dependence of the out-of-plane resistivity ρc(T) provides an independent and well-established method for identifying the pseudogap onset. Because the opening of the pseudogap causes ρc to increase rapidly, the temperature at which ρc reaches a minimum is taken as T∗∗ρcupper, following Ref. [1]. The comparison between T∗upper obtained from in-plane transport and T∗∗ρcupper obtained from ρc(T) coincides across all doping levels, confirming that the pseudogap onset extracted from the minimum in dρab/dT is supported by an independent transport observable.

Final Interpretation

The resulting pseudogap temperatures are plotted as a function of p in Fig. 1(d), and notably, the pseudogap region in Bi-2223 is broader than that in Bi-2212, consistent with the respective pseudogap magnitudes observed by ARPES. The resulting conclusion is that the pseudogap cannot be attributed to simple SCF. A more plausible interpretation is that it originates from preformed Cooper pairs in the BCS–BEC crossover regime. This work demonstrates that our method for identifying the pseudogap onset is robust and corroborated by independent measurements. The authors acknowledge the useful discussions with H. Kontani, R. Ikeda, T. Tohyama, and A. Fujimori. This work was supported by JSPS KAKENHI Grant Numbers 25400349, 20K03849, and 23K03317. The data that support the findings of this article are not publicly available. The authors' e-mail address is watanabe.takao@nihon-u.ac.jp.

Summary of Key Findings

The paper concludes that the strong pseudogap in high-Tc cuprates may originate from preformed Cooper pairing in the BCS–BEC crossover regime. This is supported by the fact that T∗upper represents a characteristic pairing temperature.

Improvements for AI systems

Confidence in normal-state characterization of high-Tc cuprates: The improved AI system can reliably distinguish between pseudogap origins by calculating whether transport behavior is consistent with expeimental results not only on hole-doped La2−xSrxCuO4 (LSCO) and YBa2Cu3O7−δ (YBCO) [12, 18], each at near optimal doping, but also on electron-doped La2−xCexCuO4 (LCCO) [21].
Predictive modeling of pseudogap temperature scales: The system can predict the scaling of the pseudogap onset temperatures by calculating the factor consistent with a d-wave superconductor when comparing them to the pseudogap magnitudes, as suggested by the conclusion that results demonstrate that the pseudogap does not arise from superconducting fluctuations.
Mechanism discrimination in underdoped regimes: The AI can determine if an observed anomalous normal state behavior is due to superconducting fluctuations or preformed pairing by assessing whether it unambiguously demonstrate[s] that the strong pseudogap is not a manifestation of superconducting fluctuations (SCF), leading to the conclusion that the pseudogap in high-Tc cuprates may originate from preformed Cooper pairing in the BCS–BEC crossover regime.
Identification of competing orders: The system can evaluate whether observed deviations from standard Fermi liquid theory are due to competing orders by checking if they rule out CDW-related mechanisms as the origin of the observed deviation, noting that CDW order is absent in overdoped Bi 2212 and Bi 2223, yet the SCF related deviation is clearly observed in this regime.
Robustness verification via independent observables: The improved system can validate its findings by confirming that pseudogap onset temperatures are supported by independent measurements, as demonstrated when Tscf obtained from the modified Kohler analysis coincides across all doping levels with those derived from other methods like STS.

Abstract

Understanding the normal state is essential for uncovering the mechanism of high- T c superconductivity. We investigate magnetotransport in Bi 2 Sr 2 CaCu 2 O 8+δ and Bi 2 Sr 2 Ca 2 Cu 3 O 10+δ single crystals over a wide doping range. While the in-plane resistivity and Hall coefficient show strong pseudogap-induced temperature dependence, the T squared Hall-angle behavior and the modified Kohler's rule remain robust across all dopings. The onset temperatures of the pseudogap are clearly distinct from superconducting fluctuations, although they scale with the pseudogap magnitudes with a factor consistent with a d-wave superconductor. These results demonstrate that the pseudogap does not arise from superconducting fluctuations and instead suggest that it may originate from preformed Cooper pairing in the BCS-BEC crossover regime.

Sources

Evidence for spin-fluctuation-mediated superconductivity in electron-doped cuprates