Emergent quantum phenomena via phase-coherence engineering in infinite-layer nickelate superconductors

By fabricating nano-holes in infinite-layer nickelate superconductors to engineer Josephson junction arrays, this study demonstrates that enhanced phase fluctuations drive a two-stage transition to an anomalous metallic state and reveal hidden intertwined orders, including charge-2e coherence and a reversal of superconducting anisotropy.

The Gist

The Big Idea: Dancing in a Crowd vs. Dancing Alone

Imagine a superconductor as a massive ballroom where electrons are the dancers. In a normal metal, everyone is dancing chaotically, bumping into each other, and creating resistance (friction). In a superconductor, the dancers pair up (forming "Cooper pairs") and move in perfect unison, gliding across the floor with zero friction.

For this perfect dance to happen, two things are needed:

1. The Pairs: The dancers must find partners.
2. The Rhythm: All the pairs must move to the exact same beat (this is called phase coherence).

In most 3D materials, once the pairs form, they automatically lock into the same rhythm. But in thin, 2D materials (like the nickelate films in this study), the rhythm is fragile. If the dancers get too distracted or the floor gets too crowded, they lose the beat, and the superconductivity breaks down.

What Did the Scientists Do? (The "Hole Punch" Experiment)

The researchers wanted to see what happens when they intentionally mess with the rhythm. They took a thin film of a superconducting material called Nickelate (specifically Nd-based) and used a high-tech "hole punch" to create a grid of tiny holes in it.

Think of this like taking a large dance floor and cutting it into thousands of tiny islands, connected only by narrow bridges.

• The Islands: Where the dancers can still pair up and dance locally.
• The Bridges: The narrow connections where the dancers have to try to sync up with the next island.

By making these holes, they created a Josephson Junction Array. This setup forces the electrons to struggle to keep their rhythm across the whole floor, amplifying "quantum fluctuations" (the jitteriness of the quantum world).

The Surprising Discoveries

When they turned up the heat (or rather, cooled it down) and applied magnetic fields, three amazing things happened:

1. The Two-Step Dance (The "Local" vs. "Global" Beat)

Usually, a superconductor turns on all at once. But in their patterned film, the superconductivity happened in two stages:

• Stage 1: The dancers on each tiny island found partners and started dancing locally. They were happy on their own little island.
• Stage 2: Only at a much lower temperature did the dancers finally manage to sync their rhythms across the bridges to the other islands.
• Analogy: Imagine a stadium where every section of seats is cheering for its own team (local superconductivity). It takes a long time before the whole stadium starts chanting the same song together (global superconductivity).

2. The "Anomalous Metal" (The Ghost Dance)

As they cooled the film down to near absolute zero, instead of becoming a perfect superconductor (zero resistance) or an insulator (no movement), the material became an "Anomalous Metal."

• It had a small, constant resistance that wouldn't go away, even at the coldest temperatures.
• Analogy: It's like a dance floor where the music never stops, but the dancers are stuck in a "frozen" shuffle. They aren't fully stopped (insulator), but they aren't gliding perfectly (superconductor) either. This state is driven by quantum "tunneling," where the dancers magically jump over the gaps between islands.

3. The Magic Trick: Flipping the Rules (Anisotropy Reversal)

This was the most shocking part. In almost all flat superconductors, it is much harder to destroy the superconductivity with a magnetic field pointing up (perpendicular to the film) than with a field pointing sideways (parallel). It's like a flat sheet of paper is easier to tear if you pull it from the top than from the side.

However, in their patterned Nd-nickelate film, the rules flipped.

• The material became more fragile to magnetic fields coming from the side than from the top.
• Analogy: Imagine a flat pancake that suddenly becomes harder to crush from the top than from the side.
• Why? The scientists believe the "holes" they punched removed the usual 2D rules, revealing a hidden 3D secret inside the material. The Nickel atoms have a special magnetic "personality" (from their inner electrons) that interacts strangely with the magnetic field, acting like a hidden internal magnet that fights the external field in a specific direction.

Why Does This Matter?

This research is like finding a new way to tune a radio. By using nano-patterns (the holes), the scientists proved they can:

1. Control the "jitteriness" of quantum states.
2. Uncover hidden properties of materials that are usually invisible (like that weird 3D magnetic behavior in Nickelates).
3. Understand High-Temperature Superconductors: Since Nickelates are cousins to Cuprates (the famous high-temp superconductors), understanding how they react to these "phase fluctuations" helps us figure out how to make better superconductors for things like MRI machines, maglev trains, and quantum computers.

The Takeaway

The scientists didn't just find a new material; they found a new tool. By punching holes in superconductors, they can force the material to reveal its deepest secrets, showing us that even in a flat world, there are deep, hidden 3D mysteries waiting to be discovered.

Technical Summary

1. Problem Statement

The study addresses the fundamental role of phase fluctuations in unconventional high-temperature superconductors, specifically the infinite-layer nickelates ($R_{1-x}Sr_xNiO_2$, where $R$ = La, Nd).

• Context: In conventional 3D superconductors, phase stiffness is strong, and Cooper pairing and phase coherence occur simultaneously. In low-dimensional or low-carrier-density systems, phase stiffness is weak, making the superconducting transition dominated by phase fluctuations. This can lead to exotic ground states like the anomalous metallic state (a finite-resistance state at zero temperature) and the Berezinskii-Kosterlitz-Thouless (BKT) transition.
• Specific Gap: While cuprates are well-studied, the dimensionality and phase fluctuation mechanisms in nickelates remain debated. Specifically, the interplay between 2D geometric confinement and intrinsic 3D electronic/magnetic characteristics in Nd-based nickelates is unclear. Unlike La-based nickelates (which are predominantly 2D), Nd-based films show complex dimensionality, but the underlying mechanisms (e.g., the role of Nd 4f moments) are not fully understood.
• Objective: To systematically enhance and control phase fluctuations to uncover hidden orders, determine the dimensionality of superconductivity, and investigate the emergence of anomalous metallic states and anisotropy reversals.

2. Methodology

The researchers employed a "top-down" nano-patterning engineering approach to create Josephson Junction Arrays (JJAs) in thin films.

• Material Synthesis: 15-nm-thick infinite-layer $Nd_{0.8}Sr_{0.2}NiO_2$ and $La_{0.8}Sr_{0.2}NiO_2$ films were grown via pulsed laser deposition (PLD) followed by topochemical reduction.
• Nano-Patterning: Using a transferred anodized aluminum oxide (AAO) membrane mask, the films were etched using Reactive Ion Etching (RIE) to create periodic arrays of nano-holes (~70 nm diameter, ~125 nm spacing).
  • This creates a network of superconducting islands (the un-etched regions) connected by Josephson links.
  • Variable Control: Different etching times (5s, 10s, 15s) were used to progressively weaken the inter-island coupling, thereby enhancing phase fluctuations in a controllable manner.
• Transport Measurements: Comprehensive electrical transport measurements were conducted in dilution refrigerators (down to 50 mK) and under high magnetic fields (up to 16 T).
  • Key Metrics: Sheet resistance ($R_S$) vs. Temperature ($T$) and Magnetic Field ($B$).
  • Anisotropy: Measurements were taken with magnetic fields applied both perpendicular ($B_\perp$) and parallel ($B_\parallel$) to the film plane, as well as at various polar angles ($\theta$).
  • Quantum Oscillations: Analysis of magnetoconductance to detect charge-2e quantum oscillations ($h/2e$) to probe phase coherence.

3. Key Contributions & Results

A. Two-Stage Superconducting Transition and Anomalous Metal

• Two-Stage Transition: In the nano-patterned films, the superconducting transition splits into two distinct stages:
  1. $T_1$ (Local Superconductivity): Formation of Cooper pairs and intra-island phase coherence.
  2. $T_2$ (Inter-island Coherence): Establishment of global phase coherence via Josephson coupling between islands.
• Anomalous Metallic State: As phase fluctuations are enhanced (via etching), the system fails to reach zero resistance at low temperatures. Instead, it enters a saturating resistance plateau below ~1.4 K.
  • Evidence: The resistance saturation correlates with the phase coherence length ($L_\Phi$) saturation ($R \propto 1/L_\Phi^2$).
  • Nature: The persistence of charge-2e ($h/2e$) quantum oscillations down to 65 mK and the vanishing Hall coefficient confirm that this state is composed of bosonic Cooper pairs, not fermionic quasiparticles. This validates the existence of a bosonic anomalous metal driven by quantum vortex tunneling.

B. Anomalous Reversal of Superconducting Anisotropy

• The Phenomenon: In the 10s- and 15s-etched Nd-based films, a striking reversal of the upper critical field anisotropy was observed at low temperatures: $B_{c\parallel} < B_{c\perp}$.
  • Normally, 2D superconductors exhibit $B_{c\parallel} \gg B_{c\perp}$ due to orbital pair-breaking effects.
  • Here, the superconductivity is more fragile to in-plane magnetic fields than out-of-plane fields.
• Control Experiments: This reversal was not observed in:
  • Unpatterned Nd-films (which show weak 2D anisotropy).
  • Nano-patterned La-based films (which maintain conventional 2D anisotropy).
• Mechanism: The authors attribute this to the intrinsic 3D character of Nd-nickelates, specifically the coupling between superconductivity and Nd 4f local moments.
  • The nano-patterning suppresses the dominant 2D orbital pair-breaking effect, revealing a hidden 3D pairing state.
  • The Nd 4f moments create a highly anisotropic effective g-factor ($g_\parallel > g_\perp$). An in-plane field polarizes these moments, generating an internal exchange-Zeeman field that annihilates singlet pairs, drastically reducing $B_{c\parallel}$. Out-of-plane fields couple weakly to these moments, preserving $B_{c\perp}$.

C. Quantum Phase Fluctuations and Coherence

• Quantum Oscillations: The observation of $h/2e$ oscillations confirms that phase coherence extends across the entire array, even in the presence of strong fluctuations.
• Tuning: By rotating the magnetic field near the in-plane direction ($\theta \approx 0^\circ$), the researchers decoupled the effects of thermal fluctuations (temperature) and quantum fluctuations (in-plane field component). They mapped a "quantum melting" boundary where inter-island coherence is destroyed by quantum fluctuations.

4. Significance

• Paradigm Shift: The study establishes nano-patterning as a powerful tool to "magnify" quantum fluctuations and uncover hidden intertwined orders (like magnetic coupling) that are masked by dominant geometric effects in bulk or pristine films.
• Mechanism of Nickelate Superconductivity: It provides strong evidence that Nd-based nickelates possess a complex dimensionality involving significant 3D character and strong coupling between superconductivity and rare-earth magnetism (4f electrons), distinguishing them fundamentally from La-based nickelates and cuprates.
• Anomalous Metal Physics: It offers a microscopic understanding of the anomalous metallic state, linking resistance saturation directly to the dephasing of Cooper pairs and quantum vortex tunneling.
• Future Applications: The ability to engineer phase coherence and manipulate the interplay between superconductivity and local moments opens new avenues for designing quantum devices and understanding high-$T_c$ mechanisms in strongly correlated systems.

In summary, this work demonstrates that by artificially engineering phase fluctuations in infinite-layer nickelates, one can reveal a hidden 3D superconducting state driven by rare-earth magnetism, leading to a reversal of magnetic anisotropy and the emergence of a robust bosonic anomalous metal.