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arxiv: 2606.05653 · v1 · pith:WSZOHHYPnew · submitted 2026-06-04 · ❄️ cond-mat.supr-con · cond-mat.mtrl-sci· cond-mat.str-el

BCS-BEC crossover driven by small Fermi pockets of a high-Tc cuprate superconductor

Junhyeok Jeong , Yamato Enomoto , Yoshimitsu Kohama , Tomotaka Nakayama , Kotaro Ando , Kifu Kurokawa , Soonsang Huh , Zhuo Yang
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Toshihiro Nomura Matthew D. Watson Timur K. Kim Cephise Cacho Chun Lin Makoto Hashimoto Donghui Lu Shiro Sakai Takami Tohyama Kazuyasu Tokiwa Takeshi Kondo
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Pith reviewed 2026-06-27 23:39 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.mtrl-scicond-mat.str-el
keywords BCS-BEC crossoverFermi pocketcuprate superconductorquantum oscillationsARPESd-wave pairingmultilayer cuprateantiferromagnetic order
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The pith

Small Fermi pockets in a cuprate carry a superconducting gap large enough to mark the BCS-BEC crossover.

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

The paper establishes that quantum oscillations and angle-resolved photoemission spectroscopy detect small Fermi pockets coexisting with a large superconducting gap in the clean inner CuO2 layers of the four-layer cuprate. This combination produces a gap-to-Fermi-energy ratio near 0.6 and a critical-to-Fermi-temperature ratio near 1.3, values that reach the upper theoretical bound for two-dimensional superconductivity and identify the BCS-BEC crossover. The crossover appears as carrier density increases within a doping window narrower than one percent, even in the presence of antiferromagnetic order. The observation supplies a microscopic basis for d-wave pairing in doped antiferromagnetic Mott insulators.

Core claim

In the clean inner CuO2 layers of Ba2Ca3Cu4O8(F,O)2, a small Fermi pocket coexists with a large superconducting gap, yielding Delta_pocket/e_F approximately 0.6 and Tc/TF approximately 1.3. These ratios reach the theoretical upper bound for two-dimensional superconductivity and constitute a hallmark of the BCS-BEC crossover. The crossover emerges abruptly as carrier density increases across a doping range of less than one percent, despite antiferromagnetic order.

What carries the argument

The small Fermi pocket in the inner layers, whose size sets the Fermi energy that is compared to the measured superconducting gap to produce the crossover ratios.

Load-bearing premise

The quantum oscillation and photoemission signals originate exclusively from the small Fermi pockets in the inner layers without significant contribution from outer layers or reconstruction effects.

What would settle it

A direct measurement on a sample engineered to isolate only the inner-layer pockets that yields a gap-to-Fermi-energy ratio well below 0.5 would falsify the crossover identification.

Figures

Figures reproduced from arXiv: 2606.05653 by Cephise Cacho, Chun Lin, Donghui Lu, Junhyeok Jeong, Kazuyasu Tokiwa, Kifu Kurokawa, Kotaro Ando, Makoto Hashimoto, Matthew D. Watson, Shiro Sakai, Soonsang Huh, Takami Tohyama, Takeshi Kondo, Timur K. Kim, Tomotaka Nakayama, Toshihiro Nomura, Yamato Enomoto, Yoshimitsu Kohama, Zhuo Yang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p020_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p024_5.png] view at source ↗
read the original abstract

Fermi arcs observed in underdoped cuprates have sparked debate over whether they represent segments of a large Fermi surface or small Fermi pockets. This ambiguity has long hindered their classification as either the conventional Bardeen-Cooper-Schrieffer (BCS) regime or the strongly coupled Bose-Einstein condensation (BEC) crossover limit. Here, using angle-resolved photoemission spectroscopy and quantum oscillations, we demonstrate the coexistence of a small Fermi pocket and a large superconducting gap in the clean inner CuO2 layers of the four-layer cuprate Ba2Ca3Cu4O8(F,O)2. This coexistence constitutes a hallmark of the BCS-BEC crossover and has remained elusive for decades. Despite the presence of antiferromagnetic (AF) order, the superconducting gap in the small pocket is remarkably large, yielding a gap-to-Fermi-energy ratio (Delta_pocket/e_F ~ 0.6) and a critical-to-Fermi-temperature ratio (Tc/TF ~ 1.3) that reach the theoretical upper bound for two-dimensional superconductivity. Unexpectedly, this BCS-BEC crossover emerges not as the carrier density decreases but as it increases, abruptly within a narrow doping range of less than 1%. These results provide a long-sought microscopic foundation for the d-wave pairing mechanism in doped AF-Mott insulators.

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

2 major / 1 minor

Summary. The manuscript reports combined ARPES and quantum-oscillation measurements on the four-layer cuprate Ba2Ca3Cu4O8(F,O)2. It claims that small Fermi pockets coexist with a large superconducting gap in the clean inner CuO2 layers, yielding Delta_pocket/e_F ~0.6 and Tc/TF ~1.3 that reach the theoretical upper bound for 2D superconductivity. This is presented as direct evidence of a BCS-BEC crossover that appears abruptly with increasing doping within a <1% window, providing a microscopic basis for d-wave pairing in doped AF-Mott insulators.

Significance. If the layer-specific assignment of the QO frequency and ARPES gap is robust, the result would constitute a rare experimental realization of the BCS-BEC crossover regime in cuprates, with ratios at the 2D theoretical limit. The unexpected doping dependence (crossover appearing upon increasing carrier density) would supply a new constraint on theories of pairing in the presence of AF order.

major comments (2)
  1. [Results section on QO and ARPES data assignment] The central claim that both the small-pocket QO frequency and the large ARPES gap originate exclusively from the clean inner CuO2 layers is load-bearing for the reported ratios and the BCS-BEC interpretation. In a four-layer system the outer layers possess different carrier densities and are more susceptible to surface reconstruction or AF order; the manuscript provides no layer-projected band-structure modeling, doping-series isolation, or explicit comparison that rules out outer-layer weight in the observed signals.
  2. [Abstract and main-text discussion of ratios] The quoted values Delta_pocket/e_F ~0.6 and Tc/TF ~1.3 are stated without reported uncertainties, raw oscillation frequencies, or the precise procedure used to extract e_F and Delta from the two techniques. This prevents verification that the ratios actually attain the theoretical 2D upper bound.
minor comments (1)
  1. [Abstract] The abstract states the key ratios and the coexistence but does not quote the specific doping levels at which the crossover is observed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major point below, providing the strongest honest defense based on the manuscript content while indicating where revisions are warranted.

read point-by-point responses

  1. Referee: [Results section on QO and ARPES data assignment] The central claim that both the small-pocket QO frequency and the large ARPES gap originate exclusively from the clean inner CuO2 layers is load-bearing for the reported ratios and the BCS-BEC interpretation. In a four-layer system the outer layers possess different carrier densities and are more susceptible to surface reconstruction or AF order; the manuscript provides no layer-projected band-structure modeling, doping-series isolation, or explicit comparison that rules out outer-layer weight in the observed signals.

    Authors: The assignment relies on the well-established distinction in multilayer cuprates that inner CuO2 layers are protected from surface effects and AF order, exhibiting the small-pocket signals at the observed doping levels, while outer layers are overdoped or reconstructed. The manuscript's doping series (abrupt crossover in <1% window) and consistency with prior transport data on the same compound provide indirect isolation. We acknowledge the absence of new layer-projected calculations; we will add an explicit paragraph with comparisons to expected outer-layer frequencies/gaps and supporting citations. This is a partial revision to strengthen the justification without altering the central claim. revision: partial

  2. Referee: [Abstract and main-text discussion of ratios] The quoted values Delta_pocket/e_F ~0.6 and Tc/TF ~1.3 are stated without reported uncertainties, raw oscillation frequencies, or the precise procedure used to extract e_F and Delta from the two techniques. This prevents verification that the ratios actually attain the theoretical 2D upper bound.

    Authors: We agree that explicit uncertainties, raw frequencies, and extraction procedures are necessary for independent verification. The revised manuscript will include the raw QO frequencies, the Onsager-relation conversion to pocket area and e_F, the ARPES gap fitting details, and propagated uncertainties on both ratios, confirming they reach the 2D theoretical limits within error bars. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental ratios computed directly from measured ARPES and QO data

full rationale

The paper presents an experimental study using ARPES and quantum oscillations to report the coexistence of a small Fermi pocket and large gap in inner CuO2 layers of a four-layer cuprate. The key ratios (Delta_pocket/e_F ~0.6, Tc/TF~1.3) are obtained by direct division of independently measured quantities (pocket area from QO frequency for e_F, gap magnitude from ARPES spectra). No derivation chain, ansatz, fitted parameter renamed as prediction, or self-citation load-bearing step is present in the provided text; the central claim is an observation of measured values reaching a known theoretical bound rather than a result forced by the paper's own equations or prior self-citations. The work is self-contained against external benchmarks of the reported spectra and frequencies.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on the interpretation of ARPES and quantum-oscillation data as evidence for small pockets and on the validity of the extracted energy scales; no free parameters are introduced in the abstract, and no new entities are postulated.

axioms (2)
  • domain assumption ARPES and quantum oscillations can reliably distinguish small closed Fermi pockets from arcs in the presence of antiferromagnetic order.
    Invoked when the abstract equates the observed signals with small pockets.
  • domain assumption The inner CuO2 layers are sufficiently clean and decoupled that their electronic properties can be isolated from outer layers.
    Required for the claim that the pocket and gap belong to the inner layers.

pith-pipeline@v0.9.1-grok · 5866 in / 1388 out tokens · 20634 ms · 2026-06-27T23:39:12.915237+00:00 · methodology

discussion (0)

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Reference graph

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