Multimodal Terahertz Spectroscopy of the Pairing Symmetry and Normal-State Pseudogap in (La,Pr)$_3$Ni$_2$O$_7$ Films

This study employs multimodal terahertz spectroscopy to establish that compressively strained (La,Pr)$_3$Ni$_2$O$_7$ films are bulk superconductors with disordered $s_{\pm}$-wave pairing that coexists with a distinct correlated normal state exhibiting a pseudogap.

The Gist

Imagine you are trying to understand how a new, super-efficient engine works. You know it runs on a special fuel (electrons) and can reach incredible speeds (superconductivity) without friction. But you don't know how the engine parts are arranged, or if there are any hidden gears turning even when the engine is "off."

This paper is like a team of detectives using a special kind of "flashlight" (Terahertz light) to peek inside a brand-new type of engine made of a material called (La,Pr)₃Ni₂O₇. This material is a "nickelate," a cousin to the famous copper-based superconductors (cuprates) that scientists have been studying for decades.

Here is the story of what they found, explained simply:

1. The Mystery of the "Engine"

For a long time, scientists knew this nickel material could conduct electricity with zero resistance (superconductivity) if you squeezed it tight or made it very thin. But they were stuck on two big questions:

• How do the electrons pair up? (Do they dance in a circle, a square, or a weird zigzag?)
• What happens when the engine is "off"? (Is the material just a messy metal, or is there a secret order hiding even when it's not superconducting?)

2. The Special Flashlight (Terahertz Spectroscopy)

The researchers used two types of "flashlights" to look at the material:

• The Linear Flashlight: This shines a beam of light through the material to see how it absorbs energy. It's like shining a light through a foggy window to see how thick the fog is.
• The Non-Linear Flashlight: This shines a very strong beam to see how the material reacts when pushed hard. It's like tapping a glass to hear its ring; the way it rings tells you about its internal structure.

3. The Big Discovery: The "Messy Dance" (s± Pairing)

When they looked at the "Linear Flashlight" data, they saw something interesting.

• The Good News: The material is a true superconductor throughout its entire thickness, not just on the surface.
• The Bad News: It's a bit messy. About 65% of the electrons didn't join the superconducting "dance." They were left standing on the sidelines.
• The Analogy: Imagine a ballroom where most people are dancing in perfect pairs (superconductivity), but a huge crowd is just standing around, bumping into each other (disorder).
• The Conclusion: The electrons that did pair up are doing a "sign-changing dance" (s±). Imagine two groups of dancers: Group A holds hands with their left hand, and Group B holds hands with their right. They are partners, but their "signs" are opposite. This is a complex, high-tech dance move that suggests the material is very different from the simple dances seen in older superconductors.

4. The Secret "Ghost" in the Machine (The Pseudogap)

This is the most exciting part. When they used the "Non-Linear Flashlight" (the strong push), they found a surprise.

• Even when the temperature was above the point where the material becomes superconducting (when the engine is supposedly "off"), the material was still reacting strangely.
• The Analogy: Imagine a car that is parked. You expect it to be silent. But if you tap the hood, it hums with a specific rhythm. The researchers found that this nickel material has a "hum" (a pseudogap) starting way before it turns into a superconductor.
• The Meaning: There is a hidden, ordered state of matter that exists before the superconductivity kicks in. It's like a "pre-game" formation where the electrons are organizing themselves, waiting for the signal to start the superconducting dance. This "pseudogap" is a famous mystery in physics, usually seen in copper-based superconductors, and finding it here suggests these two families of materials might be related in a deeper way than we thought.

5. Why Does This Matter?

Think of high-temperature superconductors as the "Holy Grail" of energy. If we can make wires that carry electricity with zero loss, our power grid would be perfect, and we could build super-fast trains and computers.

• The Problem: We don't know the "recipe" for making these materials work perfectly.
• The Breakthrough: This paper shows that this new nickel material is a bulk superconductor (the whole thing works, not just the skin) with a specific, complex pairing style.
• The Future: By understanding that this material has a "messy" dance style and a "secret hum" before it starts, scientists can now try to clean up the mess (reduce the disorder) and control the secret hum. This brings us one step closer to designing a superconductor that works at room temperature, which would change the world.

In a nutshell: The scientists found a new superconductor that dances in a complex, sign-changing way, but it's a bit messy. Even more importantly, they found that this material has a secret, organized "pre-game" state that exists even when it's not superconducting, giving us a new clue on how to build better energy systems in the future.

Technical Summary

1. Problem Statement

The recent discovery of ambient-pressure superconductivity in compressively strained (La,Pr)₃Ni₂O₇ thin films has sparked intense interest in nickel-based Ruddlesden–Popper (RP) superconductors. However, critical questions regarding the nature of this superconductivity remain unresolved:

• Pairing Symmetry: Is the order parameter $s$-wave, $d$-wave, or sign-changing $s_{\pm}$?
• Normal State: What is the character of the normal state above the critical temperature ($T_c$)? Does it exhibit a pseudogap or strange-metal behavior similar to cuprates?
• Bulk vs. Surface: Previous studies relied heavily on surface-sensitive techniques (ARPES, STM). There is a lack of bulk-sensitive spectroscopic data to confirm intrinsic superconducting properties and the nature of the bulk normal state.

2. Methodology

The authors employed a multimodal terahertz (THz) spectroscopy approach combining linear and nonlinear techniques to probe 7-nm-thick (La,Pr)₃Ni₂O₇ films grown on SrLaAlO₄ (SLAO) substrates.

• Linear THz Time-Domain Spectroscopy (TDS):
  • Measured the complex optical conductivity $\sigma(\omega) = \sigma_1(\omega) + i\sigma_2(\omega)$ across a broad frequency range.
  • Used model-independent Fresnel analysis to extract bulk properties, specifically the London penetration depth ($\lambda_L$) and spectral weight redistribution.
  • Compared multiple sample batches (#1, #2, #3) with varying electrode geometries to distinguish intrinsic film responses from diffraction artifacts and sample inhomogeneity.
• Nonlinear THz Third-Harmonic Generation (THG):
  • Driven by intense, narrowband multi-cycle THz pulses (0.42–0.5 THz).
  • Measured the third-harmonic signal (1.26–1.5 THz) to probe collective excitations (Higgs mode), superconducting fluctuations, and nonlinearities in the normal state.
  • Analyzed the field-scaling exponent ($A_{THG} \propto E_{peak}^n$) and temperature dependence to distinguish between superconducting and normal-state contributions.
• Correlative Analysis:
  • Compared THz results with transport measurements (resistivity) and existing ARPES data on similarly grown films to identify characteristic temperature scales.

3. Key Contributions and Results

A. Evidence for Disordered $s_{\pm}$-Wave Superconductivity

• Bulk Superconducting Response: Linear THz spectroscopy revealed a suppression of low-frequency spectral weight below the onset temperature ($T_c^{onset} \approx 40$ K), confirming bulk superconductivity.
• Coherence Peak: A weak coherence peak was observed in the real part of conductivity ($\sigma_1$) just below $T_c$, a hallmark of $s$-wave-like pairing, though significantly broadened compared to clean superconductors.
• Anomalous Residual Conductivity: Unlike conventional fully gapped $s$-wave superconductors where $\sigma_1 \to 0$ as $T \to 0$, these films retained $\approx 65\%$ of the normal-state conductivity at 2 K.
• Large Penetration Depth: The London penetration depth was estimated at $\lambda_L \approx 620$ nm at 2 K. This is significantly larger than in cuprates ($\sim 200$ nm) and iron-based superconductors, indicating a strongly reduced superfluid density.
• Conclusion on Symmetry: The combination of a weak coherence peak, substantial residual conductivity, and reduced superfluid density is inconsistent with pure $s$-wave or $d$-wave scenarios. The authors attribute this to sign-changing $s_{\pm}$ pairing in the presence of strong disorder. In an $s_{\pm}$ state, interband impurity scattering acts as a pair-breaker (similar to magnetic impurities in $s$-wave), depleting the superfluid density and generating the observed residual absorption.

B. Anomalous Normal-State Nonlinearity and Pseudogap

• Persistence of THG Above $T_c$: The THG signal did not vanish at $T_c$ but persisted into the normal state up to temperatures exceeding 100 K.
• Distinct Kink at $\sim 100$ K: The temperature dependence of the normalized THG amplitude exhibited a reproducible kink (change in slope) near 98–100 K.
• Correlation with Pseudogap: This temperature scale ($T_{THG} \approx 100$ K) aligns with the pseudogap onset temperature identified by ARPES in similar films.
• Interpretation: The authors propose that the normal state hosts a distinct ordered phase, likely a pseudogap, which coexists with or competes with the superconducting state. The nonlinearity in this regime is attributed to either disorder-enhanced effects or the intrinsic nature of this pseudogap phase.
• Sample Dependence: The strength of the normal-state nonlinearity correlated with the robustness of the superconducting state. High-quality samples showed strong THG, while disordered samples showed negligible signals, suggesting the ordered phase requires a certain level of electronic coherence.

C. Microscopic Model

The authors propose a granular superconducting scenario where superconducting regions (condensed Cooper pairs) are embedded in a metallic normal-state background.

• The "beating" features in the THG waveform suggest interference between the superconducting response and the normal-state nonlinearity.
• The uncondensed carriers are likely due to pair-breaking scattering from intrinsic disorder and oxygen defects, which are inevitable in the current film growth process.

4. Significance

• Establishes Bulk Superconductivity: This work provides the first bulk-sensitive spectroscopic confirmation that (La,Pr)₃Ni₂O₇ films are intrinsic bulk superconductors, not just surface phenomena.
• Identifies Pairing Mechanism: The data strongly supports a sign-changing $s_{\pm}$ pairing symmetry, mediated likely by spin fluctuations, distinguishing RP nickelates from the nodal $d_{x^2-y^2}$ pairing of cuprates.
• Reveals a Pseudogap Phase: The discovery of a pseudogap-like state in the normal state of nickelates, identified via bulk nonlinear THz response, suggests that the phase diagram of RP nickelates shares deep similarities with cuprates, potentially involving intertwined orders.
• Platform for Future Research: The study highlights the critical role of disorder and inhomogeneity in these materials. It sets a benchmark for future growth improvements and theoretical modeling, narrowing the range of viable mechanisms for unconventional superconductivity beyond cuprates and pnictides.

5. Conclusion

By combining linear and nonlinear THz spectroscopy, the authors demonstrate that (La,Pr)₃Ni₂O₇ films exhibit bulk $s_{\pm}$-like superconductivity heavily influenced by disorder, coexisting with a distinct normal-state pseudogap phase. These findings position RP nickelates as a unique platform for exploring the interplay between disorder, pseudogaps, and unconventional superconductivity.