Coexistence of High Temperature Superconductivity and Antiferromagnetic Order in a Cuprate with Multiple Hole Fermi Pockets

Abstract: The intricate relationship between high temperature superconductivity and antiferromagnetic order in cuprates, and the fundamental origin of electron pairing remain open questions. By utilizing high-resolution laser-based spatially-resolved angle-resolved photoemission spectroscopy, we investigate the seven-layer $Bi_{2}Sr_{2}Ca_{6}Cu_{7}O_{18+δ}$ (Bi2267) and identify a cuprate system that consists of multiple hole Fermi pockets. The observed Fermi pockets exhibit pronounced momentum-, temperature- and Fermi surface-dependent energy gaps. Crucially, high temperature superconductivity with a critical temperature ($T_{\mathrm{c}}$) of $\sim$75 K emerges in a system with multiple Fermi pockets and the presence of strong antiferromagnetic order and correlations. In particular, substantial electron pairing is observed along the Fermi pocket with an energy gap up to $\sim$42 meV in lightly-doped CuO$_{2}$ planes ($p\sim$0.05). These findings challenge the conventional understanding of the roles of the nodal and antinodal electronic states in driving high-temperature superconductivity. They show that superconductivity and antiferromagnetism can coexist in a cuprate with multiple Fermi pockets, offering further insights into the pairing mechanism in cuprate superconductors.

• The paper demonstrates the coexistence of robust high-Tc superconductivity and static antiferromagnetic order within distinct CuO2 layers, challenging conventional cuprate paradigms.
• It employs high-resolution ARPES and a multilayer mean-field t-U model to resolve four distinct hole Fermi pockets with varying doping levels.
• The study reports a record-high superconducting gap of up to 42 meV in underdoped planes, illustrating a unique interplay between magnetism and superconducting pairing.

Coexistence of High Temperature Superconductivity and Antiferromagnetic Order in Bi2267 with Multiple Fermi Pockets

Introduction

This study investigates the interplay between high temperature superconductivity (HTSC) and antiferromagnetic (AFM) order in the seven-layer cuprate Bi$_2$Sr$_2$Ca$_6$Cu$_7$O$_{18+\delta}$ (Bi2267), with a particular focus on the emergence of multiple, inequivalent hole Fermi pockets. Using high-resolution, spatially-resolved ARPES, the authors resolve four distinct hole-like Fermi pockets, each associated with different CuO$_2$ planes exhibiting variable hole doping levels. This paper presents direct experimental evidence for the coexistence of robust superconductivity (with $T_c \approx 75$ K), strong antiferromagnetism, and a momentum-dependent superconducting gap reaching up to 42 meV in the most underdoped inner planes (IP$_1$, $p\sim0.05$), a regime previously believed to be detrimental to superconductivity.

Fermiology and Layer-Dependent Electronic Structure

The ARPES results unambiguously identify four Fermi pockets—denoted as $\alpha$, $_2$0, $_2$1, and $_2$2—which are attributed to the OP, IP$_2$3, IP$_2$4, and IP$_2$5 CuO$_2$6 planes, respectively. The pockets possess distinct areas and hence different effective hole doping, ranging from $_2$7 (OP) to $_2$8 (IP$_2$9). The observed Fermiology stands in clear contrast to the canonical cuprate scenario of a large, contiguous Fermi surface with doping-induced evolution from arcs to full Fermi surfaces. Instead, the topology in Bi2267 derives from the weak interlayer coupling and charge imbalance intrinsic to multilayer cuprates with odd $_6$0. The experimental finding of spatially and energetically distinct pockets allows each CuO$_6$1 plane’s electronic state to be inferred independently.

The authors fit these features using a multi-layer mean-field $_6$2-$_6$3 model parametrized for intralayer hopping ($_6$4) and AFM gap ($_6$5), with each plane hosting a different chemical potential ($_6$6) due to charge imbalance. The resulting calculated band structure and Fermi surface closely match the experimental data, confirming that chemical potential shifts across planes provide the dominant mechanism for multiple Fermi pocket formation in this regime.

Superconducting Pairing and Gap Structure

A striking result is the magnitude and distribution of superconducting gaps along the various Fermi pockets. The measured gap exhibits strong momentum anisotropy, following a d-wave functional form near the nodal direction but deviating near the pocket vertices (especially for underdoped IP$_6$7). Maximum gap values are substantial: $_6$8 meV ($_6$9, OP), $_7$0 meV ($_7$1, IP$_7$2), and $_7$3 meV ($_7$4, IP$_7$5). The extrapolated intrinsic gap for IP$_7$6 ($_7$7 meV) is the largest ever reported in cuprates, exceeding values found in Bi2223 and Bi2212. The gap along the innermost, most underdoped planes thus surpasses that in the optimally doped outer planes, confirming the decoupling of pairing strength and global phase coherence temperature.

Superconducting order sets in at $_7$8 K, as determined from the temperature evolution of the EDC coherence peaks, while pseudogap onset temperatures ($_7$9) rise with decreasing doping. The fact that strong pairing and well-defined coherence peaks are observed on Fermi pockets emerging from spatially separated CuO$_{18+\delta}$0 layers, particularly in regions coexisting with AFM order, challenges the assertion that superconductivity in cuprates is primarily determined by nodal-antinodal dichotomy or restricted to a single phase regime.

Coexistence of Superconductivity and Antiferromagnetic Order

Bi2267 provides direct evidence of robust superconductivity in the presence of static AFM order, as corroborated by the momentum-space structure of the Fermi pockets and supported by prior NMR studies in multilayer cuprates. The inner planes (IP$_{18+\delta}$1, IP$_{18+\delta}$2) are in a regime of low doping ($_{18+\delta}$3) and robust AFM order, but still host significant superconducting gaps. This observation contradicts the standard cuprate phase diagram, where long-range AFM order is considered hostile to superconductivity, only allowing spin fluctuations (not static order) to act as a possible "pairing glue." The data show that significant pairing can, in fact, coexist with static AFM order, implying either a different or an augmented mechanism for electron pairing beyond traditional spin fluctuation scenarios.

The measured gaps’ magnitude and the d-wave symmetry also suggest that strong local electron correlation and magnetic interactions, modeled here by the mean-field $_{18+\delta}$4-$_{18+\delta}$5, are essential for pairing, rather than band structure details or purely antinodal states.

Implications and Future Directions

The results necessitate a re-examination of several key assumptions in cuprate physics:

• Nature of Pairing Glue: Significant pairing in antiferromagnetically ordered, underdoped planes suggests unconventional mechanisms for HTSC; phase fluctuations and interlayer pair tunneling mechanisms may require re-evaluation in this context.
• Role of the Antinodal Region: Observed high $_{18+\delta}$6 and pairing strength with gapless antinodal regions and fully nodal Fermi pockets demonstrates that a large contiguous Fermi surface and robust antinodal spectral weight are not prerequisites for high-$_{18+\delta}$7 superconductivity in cuprates.
• Doping Phase Diagrams: The existence of multiple, simultaneous superconducting and AFM planes within the same compound, each with distinct doping, implies a richer, more layered electronic phase diagram. Future work could address how phase coherence is established globally and what determines the ultimate $_{18+\delta}$8 in such highly anisotropic, inhomogeneous systems.
• Experimental Directions: The methodology combining spatially resolved ARPES with multilayer cuprate synthesis enables detailed study of plane-specific physical properties. Systematic exploration of even higher-layer-count compounds and deliberate tuning of doping gradients is now within reach.

Conclusion

This work establishes the coexistence of high temperature superconductivity and static AFM order in a cuprate system hosting multiple inequivalent Fermi pockets. The observation of extremely large, d-wave-like pairing gaps in heavily underdoped, AFM planes calls for a revision of the standard understanding of the cuprate phase diagram, Fermiology, and the roles played by different regions of $_{18+\delta}$9-space in HTSC. These results open a path to disentangling the competing and cooperative orders in multilayer cuprates and highlight the critical importance of engineering interplane charge distribution and correlation effects in quest of higher $_2$0-materials.

(2606.08643)