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

Using high-resolution laser-based ARPES, researchers discovered that the seven-layer cuprate Bi2267 exhibits high-temperature superconductivity ($T_c \approx 75$ K) coexisting with strong antiferromagnetic order and multiple hole Fermi pockets, challenging conventional views on the roles of nodal and antinodal states in electron pairing.

The Gist

Imagine a high-tech city where electricity flows without any resistance at all. This is superconductivity, a magical state that usually only happens at extremely cold temperatures. Scientists have been trying to figure out how to make this happen at "high" temperatures (like the temperature of liquid nitrogen) for decades, but the secret recipe has remained hidden.

This paper is like a detective story where the researchers finally found a new suspect: a specific crystal called Bi2267. Here is what they discovered, explained simply:

1. The Mystery of the "Traffic Jams"

In most superconducting materials, the electrons (the tiny particles carrying electricity) move in one big, smooth highway called a "Fermi surface." Think of it like a giant roundabout where everyone is driving in a circle.

However, in this new crystal (Bi2267), the researchers found something weird. Instead of one big roundabout, the electrons are stuck in four separate, small parking lots (called "Fermi pockets").

• The Analogy: Imagine a city where, instead of one giant highway, traffic is forced into four tiny, isolated cul-de-sacs. Usually, you'd think this would make traffic (electricity) slow down or stop. But in this case, the cars are zooming through these tiny pockets at incredible speeds.

2. The "Ghost" in the Machine

There is a long-standing debate in physics: Do you need the "main roads" (the outer edges of the electron highway) to get superconductivity, or is it enough to just have the "side streets" (the center)?

• The Old Belief: Scientists thought you needed the big, outer roads to get the high-speed superconductivity.
• The New Discovery: This paper shows that you don't need the big roads. Even though the electrons are trapped in those tiny "pockets" (side streets), they are still superconducting at a very high temperature (about -198°C or 75 Kelvin). It's like proving you can drive a race car at top speed even if you are only allowed to drive in a small parking lot.

3. The Unlikely Roommates

Here is the most surprising part. In the world of superconductors, there is a "feud" between two forces:

1. Superconductivity: Electrons dancing together in pairs.
2. Antiferromagnetism: Electrons standing still and pointing in opposite directions (like a frozen, rigid army).

Usually, these two forces hate each other. If the "frozen army" shows up, the "dancing pairs" disappear.

• The Discovery: In this crystal, the researchers found that the "frozen army" (strong magnetic order) and the "dancing pairs" (superconductivity) are living in the same room and getting along perfectly.
• The Analogy: It's like finding a party where the music is so loud and energetic that the guests are dancing wildly, but at the same time, the guests are also standing perfectly still in a rigid formation. It shouldn't be possible, but it is happening.

4. The "Heavy" Doping

The crystal has seven layers of material. The researchers found that the layers in the middle are very "under-doped" (meaning they have very few extra electrons).

• The Result: In these middle layers, the electrons are forming pairs with a massive energy gap (up to 42 meV).
• The Analogy: Think of the energy gap as the "glue" holding the electron pairs together. The glue found in this crystal is the strongest glue ever measured in any superconductor. It's so sticky that even though the electrons are in a very rigid, magnetic environment, they are still tightly bound together.

Why Does This Matter?

This discovery changes the rulebook.

• It proves that you don't need a big, continuous highway for superconductivity; small, isolated pockets work just fine.
• It proves that superconductivity doesn't have to fight against magnetism; they can coexist.
• It suggests that the "glue" holding electrons together might be something different than what scientists previously thought (it's not just about magnetic fluctuations, but something deeper happening inside the magnetic order itself).

In short: The researchers found a crystal where electrons are trapped in tiny pockets, living alongside a rigid magnetic army, yet they are still dancing together in a superconducting waltz with the strongest glue ever seen. This gives scientists a new map to understand how to make better superconductors in the future.

Technical Summary

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

Problem Statement
The fundamental mechanism underlying high-temperature superconductivity (HTS) in cuprates remains unresolved, particularly regarding the nature of the "pairing glue" and the interplay between superconductivity and antiferromagnetic (AFM) order. Conventional electronic phase diagrams suggest that long-range AFM order is rapidly suppressed by slight hole doping, giving way to superconductivity at higher doping levels. Furthermore, the prevailing view posits that antinodal electronic states are essential for driving HTS, while nodal states alone are insufficient. The relationship between strong AFM correlations and the emergence of superconductivity, especially in systems exhibiting multiple Fermi surfaces, requires further investigation to clarify the microscopic origin of electron pairing.

Methodology
The study utilizes high-resolution, laser-based spatially-resolved angle-resolved photoemission spectroscopy (ARPES) to investigate the electronic structure of the seven-layer cuprate Bi$_2$Sr$_2$Ca$_6$Cu$_7$O$_{18+\delta}$ (Bi2267).

• Sample Preparation: Single crystals of Bi2Sr$_2$Ca$_2$Cu$_3$O$_{10+\delta}$ (Bi2223) were grown via the traveling solvent floating zone method and post-annealed. Scanning transmission electron microscopy (STEM) confirmed the presence of intergrowth phases ($n=1-9$).
• Spatial Resolution: The researchers employed a laser spot size of $\sim$20 $\mu$m to identify and isolate specific multilayer regions on the sample surface. They successfully located and measured two distinct regions containing the seven-layer Bi2267 phase.
• Experimental Conditions: Measurements were conducted at temperatures ranging from 20 K to 115 K using a 6.994 eV vacuum-ultraviolet (VUV) laser and a DA30L hemispherical analyzer, achieving energy and angular resolutions of 1 meV and 0.3$^\circ$, respectively.
• Theoretical Modeling: The observed band structures and Fermi surfaces were analyzed using a mean-field $t-U$ model, incorporating intralayer hopping parameters ($t, t', t''$), chemical potential ($\mu$), mean-field gaps ($\Delta_{MF}$), superconducting gaps ($\Delta_{SC}$), and interlayer hopping terms.

Key Contributions and Results

1. Identification of Multiple Hole Fermi Pockets:
   The study reveals a unique Fermi surface topology in Bi2267 consisting of four distinct hole-like Fermi pockets ($\alpha, \beta, \gamma, \delta$) centered at the $(\pi/2, \pi/2)$ nodal region. These pockets are attributed to the four inequivalent types of CuO$_2$ planes (outer plane OP, and inner planes IP2, IP1, IP0) within the seven-layer structure.

   • The doping levels ($p$) for these pockets were estimated as: $\alpha$ (OP) $\approx$ 0.124–0.146, $\beta$ (IP2) $\approx$ 0.076–0.084, $\gamma$ (IP1) $\approx$ 0.044–0.055, and $\delta$ (IP0) $\approx$ 0.024.
   • Unlike the large Fermi surfaces observed in Bi2201 and Bi2212, these pockets exhibit a monotonic decrease in nodal Fermi momentum ($k_F$) with increasing doping, consistent with the $t-U$ model description of strong electron correlation rather than band folding.

2. Coexistence of HTS and Antiferromagnetic Order:
   The system exhibits high-temperature superconductivity with a critical temperature ($T_c$) of $\sim$75 K. Crucially, this superconductivity coexists with strong antiferromagnetic order and correlations.

   • The $\gamma$ and $\delta$ pockets correspond to heavily underdoped planes ($p \sim 0.05$), a regime where long-range AFM order is expected to persist.
   • The observation of Fermi pockets rather than a large Fermi surface in these underdoped planes suggests that strong electron correlation and AFM order are present across all seven CuO$_2$ layers.

3. Anisotropic Energy Gaps and Pairing Strength:
   Significant energy gaps were observed along the Fermi pockets, exhibiting strong momentum, temperature, and Fermi surface dependence.

   • Gap Magnitude: The maximum energy gaps ($\Delta_{max}$) at the major vertices are $\sim$19 meV ($\alpha$), $\sim$32.5 meV ($\beta$), and $\sim$42 meV ($\gamma$). The extrapolated intrinsic gaps ($\Delta_0$) are even larger, reaching $\sim$76 meV for the $\gamma$ pocket, the largest value reported in any cuprate to date.
   • Temperature Dependence: The $\alpha$ pocket shows a superconducting transition at $T_c \approx 75$ K, with a pseudogap onset ($T^*$) at $\sim$95 K. The $\beta$ and $\gamma$ pockets exhibit pseudogaps at even higher temperatures, consistent with their lower doping levels.
   • Intrinsic Nature: The large gaps in the inner planes (IP1, IP2) are not merely induced by the outer planes but are intrinsic to the specific doping levels and magnetic interactions of those planes.

4. Challenging Conventional Paradigms:

   • Nodal vs. Antinodal: The study demonstrates that high-temperature superconductivity ($T_c \sim 75$ K) can be sustained by electronic states confined to the nodal region (Fermi pockets) alone, challenging the conventional view that antinodal states are strictly necessary for HTS.
   • AFM Coexistence: The findings show that strong electron pairing (up to 42 meV) can occur in CuO$_2$ planes with slight doping ($p \sim 0.05$) where robust long-range AFM order persists, suggesting a pairing mechanism distinct from simple spin fluctuations in the paramagnetic regime.

Significance
The paper claims that these findings provide vital insights into the microscopic origin of high-temperature superconductivity. By identifying a cuprate system with multiple hole Fermi pockets that sustains HTS while coexisting with strong AFM order, the work challenges the conventional understanding of the roles of nodal and antinodal states. It suggests that strong pairing strength and phase coherence can be achieved within the nodal region alone, even in the presence of robust antiferromagnetism. This observation motivates further theoretical investigation into whether HTS can be realized solely through nodal electronic states and clarifies the pairing mechanism in the antiferromagnetic state of cuprates. The results also refine the understanding of the electronic phase diagram in multilayer cuprates, highlighting the complex interplay between layer-dependent doping, interlayer coupling, and magnetic order.