Time-reversal symmetry breaking superconductivity with electronic glass in nickelate (La, Pr, Sm)3Ni2O7 films

This study reports the discovery of an unprecedented time-reversal symmetry breaking superconducting state accompanied by electronic glass dynamics in epitaxially strained (La, Pr, Sm)₃Ni₂O₇ bilayer nickelate films, evidenced by unconventional magnetoresistance hysteresis, zero-field non-reciprocity, and logarithmically slow resistance relaxations.

The Gist

Here is an explanation of the paper, translated into everyday language with creative analogies.

The Big Picture: A New Kind of Superconductor

Imagine you have a material that conducts electricity with zero resistance. This is a superconductor. Usually, when electricity flows through a superconductor, it's like a perfectly smooth highway where cars (electrons) can zoom forever without hitting a single bump or losing energy.

Scientists recently discovered a new family of superconductors made from nickel (nickelates) that work at relatively high temperatures (though still very cold by human standards). But in this new study, researchers found something even stranger happening inside these nickel films.

They discovered a state where the superconductor doesn't just let electricity flow; it develops a secret, invisible "glassy" memory that breaks the rules of time symmetry.

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The Three Weird Signs

The researchers found three specific "symptoms" that prove this strange new state exists. Think of it like a detective finding clues at a crime scene.

1. The "Magnetic Hangover" (Hysteresis)

The Analogy: Imagine you are walking through a field of tall grass. If you walk forward, the grass bends one way. If you turn around and walk back, the grass doesn't snap back instantly; it stays bent for a while. The path you take depends on where you came from.

The Science: In normal materials, if you apply a magnetic field and then remove it, the material returns to exactly how it was. But in these nickel films, when they applied a magnetic field and then swept it back to zero, the electrical resistance didn't go back to the same spot. It took a "detour."

• Why it matters: This proves the material has "forgotten" its original state. It remembers the magnetic field it just saw. This is called Time-Reversal Symmetry Breaking. In simple terms: Time has a direction here. If you played the movie of the electrons moving backward, it wouldn't look the same as the movie playing forward.

2. The "One-Way Street" (Non-Reciprocity)

The Analogy: Imagine a hallway where it is easy to walk from the kitchen to the living room, but walking from the living room to the kitchen is much harder. You have to push harder to get the same result.

The Science: The researchers sent electricity through the film in two directions: forward and backward. They found that the material resisted the current differently depending on which way it was flowing, even when there was no magnetic field applied.

• Why it matters: This is like a "Superconducting Diode." It's a one-way street for electricity that appears spontaneously. This confirms that the material has an internal magnetic structure that is breaking the symmetry of space and time.

3. The "Slow-Motion Glass" (Glassy Dynamics)

The Analogy: Think of honey. If you stir honey and then stop, it doesn't stop moving instantly. It slowly, slowly trickles to a halt over a long time. Now imagine the honey is made of tiny magnets that are all fighting each other, getting stuck in a messy, frozen mess.

The Science: When they turned off the magnetic field, the electrical resistance didn't settle down immediately. It kept changing very slowly for hours, following a "logarithmic" pattern (slowing down but never quite stopping).

• Why it matters: This is the hallmark of an Electronic Glass. In a normal crystal, atoms are neat and orderly. In a "glass," they are disordered and stuck. Here, the electrons themselves are stuck in a disordered, frozen state, acting like a glass.

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The "Magic Ingredient": Oxygen

The researchers played a trick on the material: they slowly removed oxygen atoms from the film.

• The Result: As they took away oxygen, both the superconductivity (the zero-resistance highway) and the "weird glassy behavior" (the magnetic hangover) got weaker and eventually disappeared.
• The Conclusion: This tells us that the "glassy" state and the superconductivity are best friends. They are linked to the same specific electrons (orbitals) in the nickel atoms. If you mess with the oxygen, you break the bond between the superconductivity and this new glassy state.

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Why is this a Big Deal?

For decades, scientists have been trying to understand High-Temperature Superconductors (like the copper-based ones discovered in the 80s). They suspect that "magnetism" and "superconductivity" are fighting a war inside these materials.

• The Old Theory: In copper superconductors, magnetism usually gets in the way and kills the superconductivity.
• The New Discovery: In these nickel films, it looks like the "glassy" magnetic state might actually be helping the superconductivity happen. It's as if the electrons need to get stuck in a messy, frozen "glass" state to allow the superconducting traffic to flow smoothly.

The Takeaway

This paper reports the discovery of a new state of matter: a Superconducting Electronic Glass.

It's a material that conducts electricity perfectly, but inside, the electrons are frozen in a disordered, time-breaking, one-way street mess. It's like finding a highway where the cars drive perfectly fast, but the road itself is made of a strange, sticky jelly that remembers every turn the cars ever took.

This discovery gives scientists a new puzzle piece to solve the mystery of how to make superconductors work at room temperature, which would revolutionize our power grids, computers, and transportation.

Technical Summary

Here is a detailed technical summary of the paper "Time-reversal symmetry breaking superconductivity with electronic glass in nickelate (La, Pr, Sm)3Ni2O7 films."

1. Problem and Motivation

The discovery of high-transition temperature ($T_c$) superconductivity in Ruddlesden-Popper (R-P) nickelates under high pressure has opened a new frontier in condensed matter physics. Recently, ambient-pressure superconductivity was achieved in bilayer R-P nickelate thin films (e.g., $(La, Pr)_{3}Ni_{2}O_{7}$) via epitaxial compressive strain. However, the fundamental nature of this unconventional superconducting state remains elusive. Specifically, there is a lack of understanding regarding:

• The microscopic mechanisms driving the superconducting pairing in these multi-orbital systems.
• The existence of exotic phases, such as time-reversal symmetry (TRS) breaking or glassy states, which are often associated with unconventional superconductivity in cuprates but have not been definitively identified in ambient-pressure nickelates.
• The role of electronic orbitals ($3d_{x^2-y^2}$vs.$3d_{z^2}$) and magnetic correlations in stabilizing the zero-resistance state.

2. Methodology

The researchers employed a comprehensive suite of electrical transport measurements on high-quality, single-crystalline thin films of bilayer nickelates with varying compositions:

• Sample Synthesis: Films of $La_{1.95}Pr_{1.05}Ni_{2}O_{7}$, $La_{2.85}Pr_{0.15}Ni_{2}O_{7}$, and $La_{2.46}Pr_{0.24}Sm_{0.3}Ni_{2}O_{7}$ were grown on $(001)$-oriented $SrLaAlO_{4}$ substrates using gigantic-oxidative atomic-layer-by-layer epitaxy (GAE). This ensured precise stoichiometry and coherent compressive strain (~2%).
• Transport Measurements: Standard Hall bar geometry was used to measure sheet resistance ($R_S$) and Hall coefficient ($R_H$) as a function of temperature ($T$), magnetic field ($B$), and current ($I$).
• Key Experimental Techniques:
  • Magnetoresistance Hysteresis: $R_S(B)$ was measured by sweeping magnetic fields in opposite directions (up/down) to detect hysteresis loops.
  • Non-reciprocal Transport: Current-voltage ($I-V$) characteristics were measured for positive ($I^+$) and negative ($I^-$) currents to detect non-reciprocity (superconducting diode effect) in zero magnetic field.
  • Time-Dependent Relaxation: After polarizing the sample with a magnetic field and removing it, the time-dependent resistance $R_S(\tau)$ was monitored to detect glassy dynamics (aging effects).
  • Oxygen Tuning: The oxygen content ($p$) was modulated in situ to study the correlation between superconductivity, orbital occupancy, and the observed exotic phenomena.
  • Field Calibration: High-resolution InAs Hall sensors were used to calibrate magnetic fields, ruling out remnant field artifacts.

3. Key Contributions and Results

The study reports the discovery of an unprecedented superconducting state characterized by spontaneous Time-Reversal Symmetry (TRS) breaking and electronic glassy dynamics, emerging in the lower-temperature regime of the superconducting transition (approaching the zero-resistance state).

A. Unconventional Magnetoresistance Hysteresis

• Observation: In the low-temperature regime (below ~26 K), the magnetoresistance curves exhibit a distinct hysteresis loop when the magnetic field is swept in opposite directions.
• Characteristics:
  • The hysteresis is robust under both out-of-plane ($B_{\perp}$) and in-plane ($B_{\parallel}$) fields.
  • Crucially, the resistance minima at zero field coalesce (merge into a single minimum) rather than splitting into two distinct minima. This rules out trapped vortices or long-range ferromagnetic order (which typically show split minima due to coercivity).
  • The hysteresis vanishes above a critical temperature ($T^* \approx 26$ K), well below the onset $T_c$ but within the superconducting transition regime.

B. Zero-Field Non-Reciprocity (Superconducting Diode Effect)

• Observation: The current-voltage ($I-V$) curves show non-reciprocity ($V(I^+) \neq |V(I^-)|$) even at zero magnetic field.
• History Dependence: The polarity of the non-reciprocity is reversible and controllable by the history of the applied magnetic field (e.g., sweeping from +3 T vs. -3 T before returning to zero field).
• Significance: This confirms spontaneous TRS breaking and the existence of a "magnetic memory" effect intrinsic to the superconducting state, distinct from extrinsic thermal gradients.

C. Logarithmically Slow Resistance Relaxation (Glassy Dynamics)

• Observation: Upon removing a polarizing magnetic field, the sheet resistance relaxes logarithmically over time ($R_S \propto -\beta \log \tau$) for over 200 minutes without saturation.
• Significance: This "aging" behavior is the hallmark of a glassy phase. The relaxation exponent $\beta$ is non-zero only below ~28 K, correlating with the onset of TRS breaking. This indicates the freezing of low-energy magnetic fluctuations into a disordered glass state.

D. Orbital and Oxygen Dependence

• Correlation: Systematic reduction of oxygen content simultaneously suppresses the global superconductivity ($T_c$) and the TRS-breaking hysteresis amplitude.
• Mechanism: Recent studies suggest oxygen reduction enhances the $Ni-3d_{z^2}$ orbital weight while suppressing $Ni-3d_{x^2-y^2}$. The observed correlation implies that the TRS-breaking glassy state is predominantly driven by the $Ni-3d_{x^2-y^2}$ orbital, distinguishing it from the infinite-layer nickelates where $d_{z^2}$ plays a larger role.

4. Exclusion of Extrinsic Mechanisms

The authors rigorously ruled out alternative explanations:

• Remnant Magnetic Fields: Excluded via Hall sensor calibration and control measurements on a conventional Nb superconductor (which showed no hysteresis).
• Trapped Vortices: Excluded because hysteresis persists under in-plane fields (where vortices are suppressed by 2D confinement) and because the zero-field minima coalesce rather than split.
• Thermal/Heating Effects: Excluded by verifying the independence of results on current magnitude and sweep rates.
• Magnetic Impurities: Unlikely given the non-magnetic nature of all substrates and electrodes, and the fact that the effect is confined strictly to the low-temperature SC regime.

5. Significance and Implications

• New State of Matter: The paper identifies a novel "TRS-breaking electronic glass superconducting state" in ambient-pressure nickelates. This state is distinct from the long-range ordered magnetic phases seen in some cuprates or the vortex glass states in conventional superconductors.
• Microscopic Insight: The findings suggest that short-range magnetic correlations (likely a spin-glass phase involving $Ni-3d_{x^2-y^2}$ spins) freeze into a disordered state at low temperatures. This glassy state appears to be intimately linked to the stabilization of the zero-resistance superconducting state, contrasting with cuprates where spin-glass phases often compete with or fade away as superconductivity sets in.
• Multi-Orbital Physics: The results highlight the critical role of multi-orbital physics ($d_{x^2-y^2}$ and $d_{z^2}$) and interlayer coupling in bilayer nickelates, offering a new perspective on the mechanism of high-$T_c$ superconductivity.
• Future Directions: This discovery provides a new phenomenological framework for investigating unconventional superconductivity, suggesting that low-energy spin fluctuations and their freezing into glassy states may be a universal feature in high-$T_c$ materials that warrants further theoretical and experimental exploration.

In summary, this work uncovers a complex interplay between superconductivity, broken time-reversal symmetry, and glassy dynamics in bilayer nickelates, fundamentally advancing the understanding of the electronic ground state in these promising high-$T_c$ materials.