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arXiv:2606.05653 · Nature Communications

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

Junhyeok Jeong, Yamato Enomoto, Yoshimitsu Kohama, Tomotaka Nakayama, K. Andô, Kifu Kurokawa, Soonsang Huh, Zhuo Yang, Toshihiro Nomura, Matthew D. Watson, Timur K. Kim, Céphise Cacho, Chun Lin, Makoto Hashimoto, Dong-Hui Lu, 志朗酒井, Takami Tohyama, K. Tokiwa, Takeshi Kondo

Published Jun 2, 2026• 0 citations

Abstract

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 CuO 2 layers of the four-layer cuprate Ba 2 Ca 3 Cu 4 O 8 (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 (Δ pocket / ε F ~ 0.6) and a critical-to-Fermi temperature ratio ( T c / T F ~ 0.13) 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.

DOI: 10.1038/s41467-026-73081-5

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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 CuO 2 layers of the four-layer cuprate Ba 2 Ca 3 Cu 4 O 8 (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 (Δ pocket / ε F ~ 0.6) and a critical-to-Fermi temperature ratio ( T c / T F ~ 0.13) 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.

Abstract We examine key aspects of the theory of the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover, focusing on the temperature dependence of the chemical potential, μ. We identify an accurate method of determining the change of μ in the cuprate high temperature superconductors from angle-resolved-photoemission data (along the ‘nodal’ direction), and show that μ varies by less than a few percent of the Fermi energy over a range of temperatures from far below to several times above the superconducting transition temperature, Tc. This shows, unambiguously, that not only are these materials always on the BCS side of the crossover (which is a phase transition in the d-wave case), but are nowhere near the point of the crossover (where the chemical potential approaches the band bottom).

Tuning across the BCS-BEC crossover in the multiband superconductor Fe

_{1+y}

Se

_x

Te

_{1-x}

: An angle-resolved photoemission study

The crossover from Bardeen-Cooper-Schrieffer (BCS) superconductivity to Bose-Einstein condensation (BEC) is difficult to realize in quantum materials because, unlike in ultracold atoms, one cannot tune the pairing interaction. We realize the BCS-BEC crossover in a nearly compensated semimetal Fe

_x

Se

_x

Te

_{1-x}

by tuning the Fermi energy,

ε_F

, via chemical doping, which permits us to systematically change

Δ/ ε_F

from 0.16 to 0.5 were

Δ

is the superconducting (SC) gap. We use angle-resolved photoemission spectroscopy to measure the Fermi energy, the SC gap and characteristic changes in the SC state electronic dispersion as the system evolves from a BCS to a BEC regime. Our results raise important questions about the crossover in multiband superconductors which go beyond those addressed in the context of cold atoms.

Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) occur at opposite limits of a continuum of pairing interaction strength between fermions. A crossover between these limits is readily observed in a cold atomic Fermi gas. Whether it occurs in other systems such as the high temperature superconducting cuprates has remained an open question. We uncover here unambiguous evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio 2Δ/k_{B}T_{c}≈6.5 (where Δ is the pairing gap and T_{c} is the transition temperature) at which paired fermion condensates become optimally robust. At this gap ratio, corresponding to the unitary point in a cold atomic Fermi gas, the measured condensate fraction N_{0} and the height of the jump δγ(T_{c}) in the coefficient γ of the fermionic specific heat at T_{c} are strongly peaked. In the cuprates, δγ(T_{c}) is peaked at this gap ratio when Δ corresponds to the antinodal spectroscopic gap, thus reinforcing its interpretation as the pairing gap. We find the peak in δγ(T_{c}) also to coincide with a normal state maximum in γ, which is indicative of a pairing fluctuation pseudogap above T_{c}.

Bardeen-Cooper-Schrieffer (BCS) superfluidity and Bose-Einstein condensation (BEC) are the two extreme limits of the ground state of the paired fermion systems. We report crossover behavior from the BCS limit to the BEC limit realized by varying carrier density in a two-dimensional superconductor, electron-doped zirconium nitride chloride. The phase diagram, established by simultaneous measurements of resistivity and tunneling spectra under ionic gating, demonstrates a pseudogap phase in the low-doping regime. The ratio of the superconducting transition temperature and Fermi temperature in the low-carrier density limit is consistent with the theoretical upper bound expected in the BCS-BEC crossover regime. These results indicate that the gate-doped semiconductor provides an ideal platform for the two-dimensional BCS-BEC crossover without added complexities present in other solid-state systems.

One of the primary reasons that superconductivity in underdoped cuprates is enigmatic is that it emerges from an incoherent Fermi-arc state, so the applicability of the Bardeen-Cooper-Schrieffer (BCS) theory is questionable. Here we approach this problem by investigating unconventional

d

-wave superconductivity in a recently proposed solvable model for strongly correlated Fermi arcs. We show analytically that the exact incorporation of Fermi arcs fundamentally modifies the BCS equations, which enables us to isolate a many-body effect that suppresses the superconducting transition temperature

T_c

beyond the simple reduction expected from a shrinking Fermi surface. The theory unambiguously produces: (i) a

T_c

tracing out a dome as a function of hole doping, (ii) a new low-energy mode upon entering superconductivity, (iii) a suppressed superfluid stiffness in the underdoped regime, and (iv) a gap-to-

T_c

ratio far exceeding the BCS limit, all consistent with experimental observations in cuprate superconductors. These findings provide an analytic benchmark for understanding how superconductivity emerges from a correlated Fermi-arc state in high-

T_c

superconductors.

In paired Fermi systems, strong many-body effects exhibit in the crossover regime between the Bardeen–Cooper–Schrieffer (BCS) and the Bose–Einstein condensation (BEC) limits. The concept of the BCS–BEC crossover, which is studied intensively in the research field of cold atoms, has been extended to condensed matters. Here by analyzing the typical superconductors within the BCS–BEC phase diagram, we find that FeSe-based superconductors are prone to shift their positions in the BCS–BEC crossover regime by charge doping or substrate substitution, since their Fermi energies and the superconducting gap sizes are comparable. Especially at the interface of single-layer FeSe on SrTiO 3 substrate, the superconductivity is relocated closer to the crossover unitary than other doped FeSe-based materials, indicating that the pairing interaction is effectively modulated. We further show that hole-doping can drive the interfacial system into the phase with possible pre-paired electrons, demonstrating its flexible tunability within the BCS–BEC crossover regime.