Persistent Fermi Pockets and Robust Electron Pairing in Lightly Doped CuO$_2$ Planes of Cuprate Superconductors

Abstract: High temperature superconductivity in cuprate superconductors is generally considered to be generated from doping the Mott insulators. The fundamental nature of the doped parent compounds as well as the microscopic origin of electron pairing remain critical issues in understanding the emergence of superconductivity. Here, using high-resolution spatially-resolved laser angle-resolved photoemission spectroscopy, we investigate the intrinsic electronic structures of the CuO$<em>2$ planes in multilayer cuprates Bi$_2$Sr$_2$Ca$</em>{n-1}$Cu$<em>n$O$</em>{2n+4+δ}$ (n=5$\sim$8). The inner CuO$_2$ planes are well shielded from the disorders and provide a rare and ideal platform to probe the intrinsic electronic phase diagram. We observe well-defined Fermi pockets with hole doping levels as low as 0.007, demonstrating an abrupt transition from the parent Mott insulator to a metallic state upon the introduction of an infinitesimal amount of doping. The innermost CuO$_2$ planes (IP$_0$) display gapless Fermi pockets, while the second innermost planes (IP$_1$) exhibit anisotropic superconducting gaps up to $\sim$33$\,$meV, indicative of robust electron pairing coexisting with strong antiferromagnetic order. Our findings provide a revised framework for understanding the doping-driven transitions and pairing mechanisms in cuprate superconductors.

• The paper demonstrates that well-defined Fermi pockets appear in the innermost CuO2 planes at ultralow hole doping, marking an abrupt insulator-to-metal transition.
• The paper employs high-resolution laser ARPES and an ARToF analyzer to map doping-dependent evolution and anisotropic spectral weight of Fermi pockets in multilayer cuprates.
• The paper finds robust d-wave superconducting pairing, with gap amplitudes up to 33 meV in IP1 layers, challenging conventional phase diagram assumptions.

Persistent Fermi Pockets and Robust Electron Pairing in Lightly Doped CuO$_2$ Planes of Cuprate Superconductors

Background and Motivation

The electronic phase diagram of cuprate superconductors traditionally posits a transition from a parent antiferromagnetic Mott insulator to a metallic and superconducting state upon sufficient hole doping. The microscopic nature of this transition—particularly whether lightly doped CuO$_2$ planes intrinsically exhibit metallic behavior or remain insulating—has been under debate due to disorder effects inherent to single- and bilayer cuprates. The emergence of small Fermi pockets in multilayer cuprates with disorder-shielded inner CuO$_2$ planes challenges conventional paradigms, motivating a reevaluation of the phase diagram and electron pairing mechanisms in the context of disorder-free environments.

Experimental Methodology

The authors utilized high-resolution spatially-resolved laser ARPES on multilayer Bi-based cuprates, $\mathrm{Bi_2Sr_2Ca_{n-1}Cu_nO_{2n+4+\delta}}$ ($n=5 \text{ to } 8$), capitalizing on the protected inner CuO$_2$ planes as platforms for intrinsic electronic structure measurements. The ARToF electron energy analyzer provided comprehensive momentum-space coverage and enhanced signal-to-noise ratios, allowing identification and characterization of multiple Fermi surface sheets corresponding to distinct CuO$_2$ plane types. Hole doping levels were inferred from the enclosed areas of the observed Fermi pockets.

Key Findings

Intrinsic Electronic Structure and Metallic Transition

The study demonstrates the emergence of well-defined Fermi pockets in the innermost CuO$_2$ planes ($\mathrm{IP_0}$) at ultralow hole doping levels ($p=0.007$), indicative of an abrupt insulator-to-metal transition upon infinitesimal doping. The ARPES data reveal coherent quasiparticle bands forming directly at the Fermi level, in stark contrast to previous reports in single and bilayer systems where disorder-induced localization obfuscates intrinsic metallicity. The chemical potential shifts downward with minimal doping, marking the formation of a Zhang-Rice singlet band at the Fermi level.

Doping and Layer-Dependent Fermi Pocket Evolution

Fermi pockets in both $_2$0 and $_2$1 layers span a wide doping range (0.007–0.088), maintaining elliptical morphology with minor variations in aspect ratio ($_2$2 between 1.6 and 2.0). The spectral weight is maximal at the left minor axis, decreasing towards the right; this anisotropy intensifies with higher doping. The ARToF system's superior detection efficacy enabled the intrinsic mapping of spectral weight distribution, avoiding the nonlinear artifacts of conventional hemispherical analyzers.

Energy Gap Structure and Robust Pairing

$_2$3 pockets are consistently gapless across the measured doping range, while $_2$4 pockets exhibit highly anisotropic superconducting gaps up to 33 meV. The gap vanishes at nodal directions ($_2$5) and peaks at the major axis vertices, exhibiting a $_2$6-wave symmetry in gap distribution. Notably, the minimum doping required for robust electron pairing in the $_2$7 planes is as low as $_2$8, with substantial gap amplitudes persisting in regimes with strong antiferromagnetic order. This is a significant departure from canonical phase diagrams, which restrict superconductivity to regions with suppressed antiferromagnetic order.

Mean-Field Modeling and Chemical Potential Evolution

The mean-field $_2$9–$_2$0 model, incorporating in-plane hopping and antiferromagnetic gap parameters, accurately reproduces the observed Fermi pocket evolution and band structure. A single parameter set with doping-tuned chemical potential suffices to capture the transition, evidencing that the essential physics resides in the interplay between electron correlation, antiferromagnetic order, and chemical potential shifts.

Implications for Cuprate Phase Diagram and Pairing Mechanism

The data compel revision of the cuprate phase diagram. The intrinsic disorder-free CuO$_2$1 plane undergoes an abrupt metallic transition with minimal hole doping, and superconducting pairing can occur even in the presence of substantive antiferromagnetic correlations. This finding undermines the conventional assumption that metallicity and pairing emerge only after antiferromagnetic suppression. It also aligns with theoretical proposals that antiferromagnetic superexchange may directly mediate electron pairing, but the disparity between gapless $_2$2 pockets and gapped $_2$3 pockets under comparable conditions suggests additional mechanisms (e.g., interlayer coupling, structural influences) are critical in governing the emergence and magnitude of pairing gaps.

Practical and Theoretical Impact

This revised framework clarifies the intrinsic behavior of lightly doped Mott insulators and suggests new routes for engineering higher critical temperatures by optimizing layer structure and disorder shielding in cuprates. The robust pairing in $_2$4 layers under strong antiferromagnetism implies that multi-layer architectures can facilitate unconventional superconductivity outside the previously identified doping regimes. The findings will inform both condensed matter theory and the development of new cuprate materials for quantum technological applications.

Conclusion

Through spatially-resolved laser ARPES, the authors establish that lightly doped, disorder-free CuO$_2$5 planes in multilayer cuprates manifest persistent, well-defined Fermi pockets and robust $_2$6-wave electron pairing at minimal doping. The data necessitate a revision of the intrinsic phase diagram of hole-doped cuprates, demonstrating that superconducting states can coexist with strong antiferromagnetic order, and metallicity emerges abruptly with infinitesimal doping. Future studies should explore the interplay between interlayer coupling, pairing symmetry, and structural factors to elucidate the full complexity of superconducting mechanisms in cuprate systems (2604.23162).