Probing the Meissner effect in single crystals of $\mathbf{Bi_2Sr_2Ca_2Cu_3O_{10+\delta}}$ via wide-field quantum microscopy under high pressure

Using wide-field quantum microscopy, this study reveals that the superconducting transition temperature of optimally doped Bi-2223 single crystals remains robust up to 23 GPa in KBr but vanishes above 11 GPa in cBN, demonstrating the material's extreme sensitivity to the hydrostaticity of the pressure-transmitting medium.

The Gist

Imagine you have a tiny, magical crystal that can conduct electricity with zero resistance, but only when it's very cold. This is a superconductor. Scientists love these crystals because they could revolutionize everything from power grids to MRI machines.

One famous type of superconductor is called Bi-2223. For years, scientists have been trying to squeeze this crystal with immense pressure to see if it gets better at superconducting (conducting at higher temperatures).

Here's the problem: When they squeezed it, the results were a mess. Sometimes, the crystal got super-conductive at higher temperatures. Other times, it just stopped working entirely and turned into an insulator (like a rubber band).

Why the confusion? It turns out how you squeeze the crystal matters just as much as how hard you squeeze it.

The "Squeeze" Analogy: The Jello vs. The Brick

Think of the pressure-transmitting medium (the stuff you put around the crystal to squeeze it) as the environment the crystal is living in.

1. The Fluid Medium (The Jello): Imagine putting the crystal in a bucket of thick, liquid Jello. When you press down, the Jello squishes evenly from all sides. The crystal feels a perfect, uniform squeeze. This is called hydrostatic pressure.
2. The Solid Medium (The Brick): Now imagine putting the crystal between two rough, solid bricks. When you press down, the bricks don't flow. They press unevenly, creating sharp, jagged stress points. The crystal gets pinched and twisted in weird ways. This is non-hydrostatic pressure.

The Experiment: A New Pair of Eyes

In the past, scientists measured these crystals by running wires through the pressure machine. But wires are clumsy; they break easily under high pressure, and they can't tell you what's happening in a tiny, specific spot on the crystal.

The researchers in this paper used a super-powered microscope based on Nitrogen-Vacancy (NV) centers in diamonds.

• The Metaphor: Imagine the diamond is a security camera with night vision. Inside the camera, there are tiny "sensors" (the NV centers) that can feel the magnetic field of the crystal.
• The Magic Trick: When a superconductor works, it pushes magnetic fields away (this is called the Meissner effect). It's like a forcefield. The camera sensors can see this forcefield disappearing or appearing. If the forcefield is there, the crystal is superconducting. If it's gone, the crystal has quit.

What They Found

The team put the Bi-2223 crystal in a high-pressure machine (a Diamond Anvil Cell) and squeezed it up to 23,000 times the atmospheric pressure. They did this twice: once with KBr (a soft salt that acts like a fluid) and once with cBN (a hard, solid material).

The Results:

• With KBr (The "Jello" Squeeze): The crystal kept its superconducting powers all the way up to 23 GPa! Even at 70 Kelvin (very cold, but not absolute zero), it was still pushing away magnetic fields. The "forcefield" was strong and healthy.
• With cBN (The "Brick" Squeeze): The crystal gave up much earlier. Above 11 GPa, the forcefield vanished. The crystal stopped superconducting and acted like an insulator. It wasn't just "less" superconducting; it was broken.

The Big Takeaway

This experiment solved a long-standing mystery. It proved that the crystal wasn't "failing" because of the pressure itself. It was failing because of uneven pressure.

When you squeeze a delicate quantum material with a solid, uneven medium (like cBN), you are essentially crushing it with a sledgehammer. The crystal's internal structure gets distorted, and its superconducting magic dies. But when you squeeze it evenly (like with KBr), it can handle the pressure and might even get stronger.

Why This Matters

This study is like finding the right recipe for a soufflé. If you use the wrong pan (solid medium), the soufflé collapses. If you use the right pan (fluid-like medium), it rises perfectly.

By using this new "quantum camera" (NV microscopy), scientists can now watch these tiny crystals in real-time without breaking them. This opens the door to finding new superconductors that work at room temperature, which would be a game-changer for our world. It tells us that to find the next big breakthrough in energy, we need to be gentle and precise with our pressure, not just strong.

Technical Summary

1. Problem Statement

High-pressure techniques are essential for modulating material structures and discovering emergent physical properties, such as superconductivity. However, characterizing superconductors under extreme pressures (tens of GPa) presents significant challenges:

• Conflicting Literature: Previous studies on optimally doped Bi-based cuprates (specifically Bi-2223) have reported contradictory behaviors regarding the pressure dependence of the superconducting transition temperature ($T_c$). Some studies using fluid media report a resurgence of $T_c$ at high pressures, while those using solid media observe an insulating-like transition and the disappearance of the zero-resistance state.
• Lack of Direct Comparison: There has been no direct comparative study evaluating superconducting properties across different pressure-transmitting media (solids vs. fluids) in the high-pressure regime.
• Experimental Limitations:
  • Transport Measurements: Require electrical contacts and wiring, which are difficult to implement with fluid media in diamond anvil cells (DACs).
  • Conventional Magnetometry: Signal amplitude scales with sample volume, limiting pressure ranges and making it difficult to detect signals from micrometer-sized samples.
  • Hydrostaticity: Achieving isotropic (hydrostatic) compression is crucial for stabilizing superconducting phases, but solid media often introduce non-hydrostatic stress, potentially distorting results.

2. Methodology

The authors employed wide-field quantum microscopy based on Nitrogen-Vacancy (NV) centers in diamond to probe magnetic responses under high pressure. This approach offers contact-free, spatially resolved detection of the Meissner effect.

• Sample: Optimally doped $\text{Bi}_2\text{Sr}_2\text{Ca}_2\text{Cu}_3\text{O}_{10+\delta}$ (Bi-2223) single crystals, annealed to achieve $T_c \sim 110$ K.
• Pressure Media: Two solid media with different mechanical properties were used to test hydrostaticity:
  1. Potassium Bromide (KBr): Known for better hydrostaticity.
  2. Cubic Boron Nitride (cBN): Known for higher stiffness and potentially lower hydrostaticity.
• Experimental Setup:
  • Diamond Anvil Cell (DAC): A CuBe DAC with a 300 $\mu$m culet diamond anvil.
  • NV Center Integration: Type Ib diamond anvils were implanted with $^{12}\text{C}^+$ ions and annealed to create a thin layer of NV centers at the sample interface.
  • Measurement Technique: Optically Detected Magnetic Resonance (ODMR). A green laser excites the NV centers, and microwaves are applied to manipulate their spin states.
  • Detection Principle: In the presence of a magnetic field, NV spin sublevels undergo Zeeman splitting. When the superconductor enters the superconducting state (below $T_c$), it expels magnetic flux (Meissner effect). This reduces the local magnetic field sensed by the NV centers directly above the sample, resulting in a measurable reduction in the ODMR splitting frequency compared to the background.
• Procedure: Pressure was applied at room temperature. The sample was cooled below 20 K, Zero-Field Cooled (ZFC), and ODMR spectra were acquired during warming to map the diamagnetic response.

3. Key Contributions

• First Direct Comparison: This study provides the first direct spatial comparison of Bi-2223 superconductivity under high pressure using different solid pressure-transmitting media (KBr vs. cBN) within the same experimental framework.
• Application of NV Magnetometry: It demonstrates the efficacy of NV-center-based wide-field microscopy for detecting the Meissner effect in micrometer-sized samples at ultra-high pressures (up to 23 GPa), overcoming the volume limitations of SQUID magnetometry and the contact requirements of transport measurements.
• Decoupling Hydrostaticity: By using spatially resolved imaging, the study isolates the effects of hydrostatic pressure from non-hydrostatic stress and local strain, which are difficult to separate in bulk measurements.

4. Key Results

The study revealed a stark contrast in the pressure dependence of superconductivity depending on the medium used:

• In KBr (Better Hydrostaticity):

  • A clear diamagnetic signal (indicative of the Meissner effect) was observed near 70 K.
  • Superconductivity persisted up to 23 GPa.
  • The onset temperature of the diamagnetic signal shifted to lower temperatures as pressure increased, suggesting a gradual decrease in $T_c$, but the superconducting state remained robust.

• In cBN (Poorer Hydrostaticity):

  • At 0 GPa, a diamagnetic signal was observed across the sample.
  • At 6 GPa, a signal was still detectable beneath the sample.
  • At 11 GPa (above 70 K), the diamagnetic signal was suppressed/disappeared.
  • At 19 GPa, no clear diamagnetic signal was detected down to 30 K.
  • Irreversibility: Upon releasing pressure from 19 GPa, a weak diamagnetic signal re-emerged below 60 K, but it did not fully recover to the initial state. This suggests that the suppression in cBN is not solely due to reversible lattice compression but involves extrinsic effects like lattice distortion or grain refinement caused by non-hydrostatic stress.

• Temperature Dependence:

  • In KBr, the transition temperature ($T_c$) decreased with pressure but remained observable.
  • In cBN, non-hydrostatic pressure significantly suppressed superconductivity, leading to an insulating-like behavior consistent with previous electrical transport studies using cBN.

5. Significance

• Critical Role of Hydrostaticity: The results definitively demonstrate that the "insulating-like" transition observed in Bi-based cuprates at high pressures is largely an artifact of non-hydrostatic stress (specifically in cBN), rather than an intrinsic property of the material under isotropic compression.
• Validation of Fluid Media: The persistence of superconductivity in KBr (which offers better hydrostaticity than cBN) supports the hypothesis that fluid media might allow for the observation of a secondary superconducting dome or higher $T_c$ at ultra-high pressures, a phenomenon previously reported but difficult to verify directly.
• Future Directions: This technique paves the way for systematic studies across a broader range of quantum materials (e.g., nickelates, van der Waals compounds) under controlled hydrostatic environments. It enables the construction of accurate pressure-temperature phase diagrams without the interference of non-hydrostatic stress, potentially leading to the discovery of novel high-pressure superconducting phases.

In conclusion, the paper establishes that the pressure environment is a decisive factor in the superconducting behavior of cuprates and highlights wide-field quantum microscopy as a superior tool for resolving these discrepancies in high-pressure physics.