Fermi-liquid transport beyond the upper critical field in superconducting La$_2$PrNi$_2$O$_7$ thin films

This study demonstrates that superconducting La$_2$PrNi$_2$O$_7$ thin films exhibit a highly renormalized Fermi-liquid normal state characterized by $T^2$ resistivity and Kohler scaling, with a quasiparticle effective mass of approximately 10, thereby confirming their adherence to the universal $T_{\rm c}/T_{\rm F}$ scaling observed in strongly correlated superconductors.

The Gist

Imagine you are trying to understand how a superconductor works. Superconductors are special materials that conduct electricity with zero resistance, but usually only when they are incredibly cold. Scientists have recently discovered a new family of these materials (nickelates) that can superconduct at relatively "warm" temperatures (around 40°C to 80°C, which is hot for a superconductor!).

However, there was a big mystery: What does the material look like before it becomes a superconductor?

Think of the material as a busy highway.

• In some versions of this material (thick crystals under high pressure), the traffic is chaotic and unpredictable, like a "strange metal" where cars (electrons) move in a weird, linear pattern.
• In the version studied in this paper (a very thin film stretched tight like a drum), the traffic is orderly.

Here is the simple breakdown of what the researchers found, using some everyday analogies:

1. The "Stretched" Material

The scientists took a thin slice of a material called La2PrNi2O7 and stretched it slightly (like stretching a rubber band). This stretching changed how the atoms are arranged, allowing the material to become a superconductor at about 40 Kelvin (very cold, but not as cold as liquid helium).

2. The "Traffic Jam" Test (Magnetotransport)

To see how the electrons move inside this material, the researchers turned up the "pressure" by blasting it with massive magnetic fields (up to 64 Tesla—about a million times stronger than a fridge magnet). This force is so strong it breaks the superconducting state, forcing the electrons back into their normal, non-superconducting mode so they can study them.

They looked at three main things:

• Resistivity (Traffic Congestion): They measured how hard it is for electricity to flow as they changed the temperature.
• Hall Effect (Lane Changing): They measured how the electrons swerve when pushed by a magnetic field.
• Magnetoresistance (The Curve): They saw how the resistance changed as they turned up the magnetic field.

3. The Big Discovery: It's a "Fermi Liquid"

In the world of physics, there are two main ways electrons behave in metals:

• Strange Metal: Like a chaotic mosh pit where everyone bumps into each other randomly. The resistance goes up in a straight line as it gets hotter.
• Fermi Liquid: Like a well-organized dance floor. The electrons move in a coordinated way, bumping into each other in a predictable pattern. The resistance goes up with the square of the temperature (if you double the heat, the resistance quadruples).

The Finding: The thin film in this study behaved exactly like the Fermi Liquid.

• The resistance followed a perfect "square" curve ($T^2$).
• The way the electrons swerved (Hall angle) also followed a perfect "square" curve.
• The magnetic resistance followed a rule called "Kohler scaling," which is like a universal law that only orderly traffic follows.

Why is this cool? Usually, scientists think high-temperature superconductivity comes from the "chaotic mosh pit" (strange metal) state. This paper shows that you can actually get high-temperature superconductivity coming from a very orderly, "Fermi liquid" state. It's like discovering that a symphony orchestra can produce a rock-and-roll hit.

4. The "Heavy" Electrons

The researchers calculated that the electrons in this material act as if they are 10 times heavier than normal electrons.

• Analogy: Imagine a normal electron is a ping-pong ball. In this material, the electrons are like bowling balls. They move slowly and sluggishly because they are interacting so strongly with each other. This "heaviness" (effective mass) is a sign that the material is highly "correlated"—the electrons are all talking to each other constantly.

5. The Universal Rule

Finally, the team looked at the relationship between the temperature at which the material becomes a superconductor ($T_c$) and the "Fermi temperature" (a measure of how energetic the electrons are).

• They found a ratio of about 1%.
• The Analogy: It's like saying that no matter what kind of car you drive (a Ferrari, a truck, or a bicycle), if it's a "super-car," it always uses about 1% of its total engine power to break the sound barrier.
• This suggests that all high-temperature superconductors, whether they are copper-based, iron-based, or this new nickel-based one, follow the same universal rulebook.

Summary

This paper is like a detective story where the scientists used giant magnets to "wake up" a superconductor and see what it looks like when it's sleeping. They found that, contrary to expectations, this specific material is a very orderly, "heavy" dancer (Fermi liquid) rather than a chaotic brawler (strange metal). This discovery helps us understand that high-temperature superconductivity might be more flexible than we thought, emerging from different types of electronic "personalities," and that there is a universal rule governing how hot these materials can get.

Technical Summary

1. Problem Statement and Motivation

The discovery of high-temperature superconductivity ($T_c > 80$ K) in bulk $(La,Pr)_3Ni_2O_7$ under high pressure and $T_c \approx 40$ K in epitaxially strained thin films has established bilayer Ruddlesden-Popper (RP) nickelates as a new platform for studying unconventional superconductivity. However, a fundamental understanding of the normal electronic ground state from which superconductivity emerges remains elusive due to conflicting observations:

• Bulk crystals under high pressure exhibit strange-metal behavior (linear-in-$T$ resistivity, $\rho \propto T$).
• Thin films under compressive strain exhibit Fermi-liquid behavior (quadratic-in-$T$ resistivity, $\rho \propto T^2$).

Resolving this dichotomy is critical because the nature of the normal state dictates the mechanism of electron pairing. Furthermore, key parameters characterizing the superconducting state, such as the upper critical field ($H_{c2}$) and quasiparticle effective mass ($m^*$), are difficult to extract in bulk samples due to the high-pressure constraints. The authors aim to characterize the normal-state transport and superconducting parameters of $La_2PrNi_2O_7$ (LPNO) thin films using high magnetic fields to suppress superconductivity and access the normal state.

2. Methodology

• Sample Preparation: High-quality $La_2PrNi_2O_7$ thin films ($\approx 5$ nm thick) with a $SrTiO_3$ capping layer were grown on $SrLaAlO_4(001)$ substrates via pulsed-layer deposition. The films exhibit high crystallinity with a residual resistivity ratio (RRR) of $\approx 8$.
• Experimental Setup:
  • Magnetotransport: Measurements were conducted under pulsed magnetic fields up to 64 T (at the International MegaGauss Science Laboratory and Dresden High Magnetic Field Laboratory) to fully suppress superconductivity and access the low-temperature normal state.
  • Temperature Range: 1.5 K to 300 K.
  • Configurations: Measurements were taken with magnetic fields applied both parallel to the $c$-axis ($H \parallel c$) and parallel to the $ab$-plane ($H \parallel ab$).
• Data Analysis Techniques:
  • Parallel Resistor Model (PRF): Used to model the total resistivity above $T_c$ and extrapolate the zero-field normal-state resistivity below $T_c$.
  • Kohler Scaling: Analyzed magnetoresistance (MR) to determine if transport is governed by a single scattering time.
  • Kadowaki-Woods Ratio: Used to estimate the quasiparticle effective mass ($m^*$) by relating the $T^2$ resistivity coefficient ($A_2$) to the electronic specific heat coefficient ($\gamma_0$).
  • Ginzburg-Landau & Tinkham Models: Used to extract $H_{c2}$, coherence length ($\xi_{ab}$), and anisotropy ($\gamma$).

3. Key Contributions and Results

A. Confirmation of Fermi-Liquid Ground State

The study provides definitive evidence that the normal state of compressively strained LPNO thin films is a Fermi liquid, characterized by:

1. Resistivity: The in-plane resistivity $\rho_{xx}(T)$ follows a $T^2$ dependence as $T \to 0$ in the field-induced normal state. This holds even when extrapolated to zero field.
2. Hall Angle: The Hall angle ($\cot \theta_H$) exhibits a $T^2$ temperature dependence, consistent with standard Fermi-liquid theory where longitudinal and Hall transports are governed by a single quasiparticle lifetime.
3. Magnetoresistance (MR): The MR follows a $H^2$ dependence and obeys Kohler scaling ($\Delta\rho/\rho_0 \propto (\mu_0 H / \rho_0)^2$). This indicates a single dominant scattering mechanism, contrasting with the complex scattering seen in strange metals.
4. Anisotropy: Negligible MR was observed when $H \parallel ab$, further distinguishing this system from high-$T_c$ cuprates in the strange-metal regime.

B. Superconducting Parameters and Anisotropy

• Upper Critical Field ($H_{c2}$):
  • $H \parallel c$: $\mu_0 H_{c2, \perp}(0) \approx 42.8$ T.
  • $H \parallel ab$: $\mu_0 H_{c2, \parallel}(0) \approx 106$ T.
  • Anisotropy Factor: $\gamma = H_{c2, \parallel} / H_{c2, \perp} \approx 2.5$. This value is comparable to optimally doped YBCO cuprates, suggesting similar electronic anisotropy.
• Coherence Length and Thickness:
  • In-plane coherence length: $\xi_{ab}(0) \approx 2.76$ nm.
  • Effective superconducting thickness: $d_{sc} \approx 3.88$ nm (consistent with the 5 nm film thickness), indicating bulk-like superconductivity rather than purely 2D behavior.
• Superconducting Gap: An order-of-magnitude estimate of the gap magnitude is $\Delta_0 \approx 6.3$ meV.

C. Quasiparticle Effective Mass and Scaling Laws

• Effective Mass: Using the Kadowaki-Woods ratio ($A_2/\gamma_0^2 \approx 10 \mu\Omega\text{cm mol}^2\text{K}^2\text{J}^{-2}$) and the measured $A_2 = 8.1 \text{ n}\Omega\text{cm K}^{-2}$, the authors estimate the electronic specific heat $\gamma_0 \approx 28 \text{ mJ mol}^{-1}\text{K}^{-2}$. This yields an average quasiparticle effective mass of $m^* \approx 10 m_e$.
• Universal Scaling: The study calculates the ratio of the critical temperature to the effective Fermi temperature ($T_c/T_F$).
  • $T_c \approx 40$ K.
  • $T_F \approx 2330$ K.
  • Ratio: $T_c/T_F \approx 0.01$.
  • This ratio aligns with a universal scaling law observed across diverse strongly correlated superconductors (cuprates, iron-based, heavy fermions), suggesting a universal principle governing $T_c$ in unconventional superconductors.

4. Significance and Discussion

• Resolution of the Dichotomy: The paper clarifies that the difference between the strange-metal behavior in bulk crystals and Fermi-liquid behavior in thin films is likely due to effective carrier doping and strain anisotropy. The thin films appear to reside in an "overdoped" regime of the superconducting dome where $T^2$ resistivity dominates, whereas bulk crystals may be near optimal doping.
• Dominant Electron-Electron Interactions: The persistence of $T^2$ resistivity up to 300 K (room temperature) implies that electron-electron interactions dominate over electron-phonon coupling, a rare feature in conventional metals. This suggests that the high-$T_c$ superconductivity in these nickelates emerges from a highly renormalized Fermi liquid.
• Future Directions: The identification of the Fermi-liquid ground state in strained films suggests that $T_c$ could potentially be further optimized by tuning the system back toward the optimal doping regime (where strange-metal behavior might emerge), provided a suitable doping strategy (beyond simple oxygen deficiency) is found.

Conclusion

This work establishes the normal-state transport properties of epitaxially strained $La_2PrNi_2O_7$ thin films, demonstrating they are a highly renormalized Fermi liquid with an effective mass of $\sim 10 m_e$. The findings confirm that the superconductivity in these materials follows the universal $T_c/T_F \approx 0.01$ scaling law seen in other unconventional superconductors, providing a crucial benchmark for theoretical models of high-$T_c$ nickelate superconductivity.