Bosonic phases across the superconductor-insulator transition in infinite-layer samarium nickelate

This study demonstrates that spatially periodic network patterns in infinite-layer samarium nickelate films induce a superconductor-insulator transition driven by enhanced superconducting fluctuations, revealing direct evidence of 2e Cooper pairing and the emergence of two distinct anomalous metallic phases characterized by bosonic excitations and dynamic vortex roles.

The Gist

The Big Picture: A Dance of Electrons

Imagine a superconductor not as a wire, but as a massive, perfectly synchronized dance floor. In a normal metal, electrons are like a chaotic crowd of people bumping into each other, creating friction (resistance). In a superconductor, the electrons pair up (forming "Cooper pairs") and dance in perfect unison. Because they move as one giant team, they glide without any friction at all.

This paper is about what happens when you try to break that perfect dance floor into tiny islands and see how the dancers behave when they can't quite hold hands anymore.

The Experiment: Cutting the Dance Floor

The scientists took a special material called Nickelate (a new type of high-temperature superconductor that acts a bit like the famous Cuprate superconductors). They made a thin film of this material and then used a high-tech "laser scissors" to cut it into a honeycomb pattern.

Think of it like taking a solid sheet of ice and cutting it into a grid of tiny ice islands connected by very thin, fragile bridges.

• The Islands: These are the wide parts of the film where the electrons can still dance happily.
• The Bridges: These are the narrow connections. As they cut more and more, these bridges get weaker and weaker.

What They Found: The "Ghost" Dance

Usually, when you cut a superconductor enough, it stops conducting electricity entirely and becomes an insulator (a wall that blocks electricity). But the scientists found something weird happening in between.

1. The Magic Rhythm (h/2e Oscillations)
Even when the material was cut so much that it had zero superconductivity (no frictionless flow), they still saw a rhythmic pattern in the resistance when they applied a magnetic field.

• The Analogy: Imagine a drummer playing a beat. Even if the band stops playing music, you can still hear the drummer tapping a specific rhythm.
• The Meaning: This rhythm proved that the electrons were still pairing up (dancing in twos) even though the whole group had lost its synchronization. They were "ghost dancers"—paired up, but unable to move freely across the whole floor.

2. The "Anomalous Metal" (The Stubborn State)
This is the most exciting discovery. Usually, physics says that if you cool a material down to absolute zero, it should either be a perfect superconductor (zero resistance) or a perfect insulator (infinite resistance). There is no middle ground.

But these nickelate films found a "middle ground" state, which the authors call an Anomalous Metal.

• The Analogy: Imagine a car stuck in a traffic jam. It's not moving (superconductor), but it's not completely stopped either (insulator). It's just idling, vibrating, and refusing to go to zero speed, no matter how cold it gets.
• The Twist: They found two types of this stubborn state:
  • Type A: Happens when you push the system with a magnetic field. It's like the magnetic field is shaking the dance floor so hard the dancers can't sync up, but they keep jiggling in place.
  • Type B: Happens even without a magnetic field. This is stranger. It's like the dancers are so confused by the broken bridges that they just start vibrating in place on their own, creating a "strange metal" where resistance stays constant instead of dropping to zero.

3. The "Strange Metal"
In one specific state, the resistance didn't just stay constant; it changed in a straight line as the temperature changed.

• The Analogy: In normal physics, resistance usually changes in a curve (like a parabola). This "Strange Metal" is like a ruler: as you get colder, the resistance drops in a perfectly straight, predictable line. This is a behavior usually seen in the most complex, mysterious materials in the universe, and seeing it here in a simple grid of nickel is a big deal.

Why Does This Matter?

For years, scientists have been arguing about why high-temperature superconductors work. Is it because the electrons pair up first, or because they synchronize first?

This paper acts like a detective story. By breaking the material into a grid, they separated the "pairing" from the "synchronization."

• They proved that pairing happens first (the electrons are still dancing in twos even when the material is an insulator).
• They showed that synchronization is fragile (it breaks easily when the bridges are cut).

The Takeaway

The scientists discovered that by simply cutting a superconductor into a honeycomb pattern, they created a playground where electrons can exist in a "zombie state"—paired up but not flowing. They found new, weird states of matter (Anomalous Metals) that defy the usual rules of physics.

This suggests that Nickelates are a perfect new playground for studying these mysteries. It's like finding a new type of Lego set that allows you to build structures you didn't know were possible, giving us a better chance to understand how to make superconductors that work at room temperature in the future.

Technical Summary

1. Problem Statement

The study addresses fundamental questions regarding the nature of high-temperature superconductivity, specifically in the newly discovered infinite-layer nickelate superconductors (RNiO₂). While these materials share structural and electronic similarities with cuprates (e.g., low superfluid density and potential phase fluctuations), the role of superconducting fluctuations and the behavior of Cooper pairs in the absence of global phase coherence remain poorly understood.

Key open questions include:

• Do Cooper pairs persist in the insulating regime of nickelates, or does the superconductor-insulator transition (SIT) involve the breaking of pairs?
• What is the nature of the "anomalous metallic" (AM) state observed in 2D superconductors, where resistance saturates at finite values as temperature approaches zero?
• Can nickelates host "bosonic strange metal" states (characterized by linear-in-temperature resistance) similar to those seen in cuprates and iron-based superconductors?

2. Methodology

The authors employed a nanopatterning strategy to manipulate the phase coherence of Cooper pairs in thin films of Sm₀.₉₅₋ₓEuₓCa₀.₀₅NiO₂.

• Sample Fabrication:
  • Epitaxial films (~9 nm thick) were grown on (LaAlO₃)₀.₃(Sr₂TaAlO₆)₀.₇ substrates via Pulsed Laser Deposition (PLD) and subsequently reduced topotactically to the infinite-layer phase.
  • Nanopatterning: Anodized Aluminum Oxide (AAO) masks with a triangular array of holes (50 nm diameter, 100 nm pitch) were transferred onto the films.
  • Controlled Disorder: Reactive Ion Etching (RIE) was performed in incremental steps. This process progressively etched the film, breaking the continuous superconducting layer into a network of superconducting islands connected by weak links. This allowed for the systematic tuning of disorder and the suppression of global phase coherence without destroying the local pairing strength.
• Transport Measurements:
  • Electrical resistance ($R_s$) was measured as a function of temperature ($T$) and magnetic field ($H$) at various etching steps.
  • Measurements were conducted in cryostats with base temperatures down to 0.26 K.
  • Magnetoresistance (MR) oscillations were analyzed to determine the charge carrier pairing symmetry.

3. Key Contributions

• First Nanopatterned Nickelate Study: This work represents the first investigation of nanofabricated superconducting devices based on infinite-layer nickelates, establishing a platform to study bosonic phases in this material class.
• Direct Evidence of 2e Pairing: The authors provided unambiguous evidence that Cooper pairs (charge 2e) persist and participate in transport even in the insulating regime, evidenced by magnetoresistance oscillations with a period of $h/2e$.
• Discovery of Two Distinct AM States: The study identified two types of anomalous metallic states in nickelates:
  1. A field-induced AM state driven by quantum vortex creep.
  2. A zero-field AM state emerging from a bosonic strange metal phase, likely driven by Ohmic dissipation from boson-fermion coupling.
• Phase Diagram Construction: The authors constructed a comprehensive phase diagram mapping the evolution from a superconductor to a Cooper pair insulator, mediated by various bosonic metallic phases controlled by disorder and magnetic field.

4. Key Results

A. Superconductor-Insulator Transition (SIT) and Fluctuations

• As etching increased (increasing disorder), the sheet resistance rose, and the global superconducting transition broadened significantly.
• While zero resistance ($T_{c0}$) was suppressed rapidly, the onset of pairing ($T_{c, onset}$) remained relatively stable (dropping only from ~20 K to ~15 K despite a 20-fold increase in resistance).
• Conclusion: The etching primarily weakens the phase coupling between islands rather than the local pairing strength, confirming that superconducting fluctuations are enhanced in the disordered regime.

B. Magnetoresistance Oscillations ($h/2e$)

• In the insulating and metallic regimes, the authors observed resistance oscillations with a periodicity of $h/2e$ (one flux quantum per unit cell).
• Significance: This confirms that Cooper pairs (2e) are the charge carriers responsible for transport, even when global phase coherence is lost and zero resistance is absent.
• The oscillation amplitude was too large to be explained by the Little-Parks effect, suggesting the mechanism is analogous to Josephson Junction Arrays (JJA), where Cooper pair tunneling is modulated by the magnetic field.

C. Anomalous Metallic (AM) States

The study observed two distinct AM states where resistance saturates at finite values as $T \to 0$:

1. Field-Induced AM State (Sample S1#2):
   • Observed under finite magnetic fields.
   • Mechanism: Attributed to quantum creep of vortices. The resistance fits the quantum creep model, suggesting magnetic-field-driven vortex motion prevents the system from becoming a true insulator or superconductor.
2. Zero-Field AM State (Sample S1#3):
   • Observed in the absence of an external magnetic field.
   • Preceded by a Bosonic Strange Metal phase characterized by linear-in-temperature resistance ($R \propto T$) over a wide range (5 K to 1 K).
   • Mechanism: The transition to the AM state is attributed to Ohmic dissipation arising from the coupling between bosonic (Cooper pair) and fermionic modes. The resistance saturation is intrinsic, as it is suppressed by applying a magnetic field (ruling out Joule heating).

D. Phase Diagram

The resulting phase diagram (Fig. 5) illustrates a rich landscape:

• Low Disorder: Superconductor (zero resistance).
• Intermediate Disorder:
  • At 0 K: Transitions from Superconductor $\to$ Field-induced AM $\to$ Zero-field AM $\to$ Cooper Pair Insulator.
  • At 3 K: Thermal fluctuations dominate, showing thermally activated flux flow and a bosonic strange metal phase.
• High Disorder: Cooper Pair Insulator (where Cooper pairs exist but are localized).

5. Significance

• Validation of Bosonic Transport: The work confirms that nickelates, like cuprates, are systems where phase fluctuations are dominant and where Cooper pairs can exist as a distinct bosonic fluid even in the insulating state.
• Mechanism Constraints: The observation of $h/2e$ oscillations provides a critical constraint for theoretical models of nickelate superconductivity, confirming the $2e$ nature of the pairing.
• Universal Phenomena: The discovery of bosonic strange metals and AM states in nickelates suggests these are universal features of nanopatterned high-temperature superconductors, regardless of the specific material family (cuprates, iron-based, or nickelates).
• Vortex Dynamics: The distinction between the two types of AM states implies that vortex dynamics in nickelates may differ from other superconductors, potentially requiring material-specific microscopic models.
• Future Platform: This study establishes nanopatterned nickelates as a versatile platform for investigating pairing symmetry, quantum phase transitions, and the interplay between bosonic and fermionic degrees of freedom.