The stripe state at 1/8 Ba doping hosts optimal superconductivity in La-214 cuprates under low in-plane stress

By applying in-plane uniaxial stress to La$_{2-x}$Ba$_{x}$CuO$_{4}$ at the 1/8 doping level, researchers suppressed the competing LTT phase and static spin-stripe order volume, thereby unlocking a giant enhancement of bulk superconductivity with a transition temperature reaching 46 K, which reveals that while static stripes hinder phase coherence, stripe-related interactions actually strengthen the underlying pairing mechanism.

The Gist

The Big Picture: Unlocking a "Sleeping Giant"

Imagine a high-performance race car (a superconductor) that is stuck in a deep mud pit. It has a powerful engine, but it can't move because its wheels are locked together by a thick, sticky substance.

This is exactly what happens in a specific type of superconducting material called LBCO (Lanthanum Barium Copper Oxide) when it is doped with exactly 1/8th of the right amount of Barium. At this specific recipe, the material is famous for being a "bad" superconductor. Even though it has the ingredients to conduct electricity with zero resistance at high temperatures, it gets stuck at a very low temperature (about 5 Kelvin, or -268°C).

Why is it stuck?
Inside the material, the electrons and magnetic spins form a rigid, static pattern called "stripes." Think of these stripes like traffic jams on a highway. The cars (electrons) are lined up perfectly in lanes, but they are frozen in place. Because they are so rigid and organized, they can't flow freely to create a supercurrent. Furthermore, these stripes are arranged in a way that blocks the "traffic" from moving between the different layers of the car's engine (the crystal layers), preventing the whole system from working together.

The Experiment: The "Stress" Test

The scientists in this paper decided to try a new trick. Instead of trying to melt the ice or change the fuel, they applied uniaxial stress.

Imagine holding a block of Jell-O and gently squeezing it from the sides at a 45-degree angle. You aren't crushing it; you are just slightly warping its shape.

In the lab, they squeezed the crystal with a specific type of pressure (about 0.5 Gigapascals, which is like the pressure at the bottom of the ocean, but applied very precisely in one direction).

The Results: The Magic Transformation

When they applied this gentle squeeze, something miraculous happened:

1. The Traffic Jam Broke: The rigid "stripes" didn't disappear completely, but they stopped being frozen solid. They became dynamic (wiggly and moving). It's like the traffic jam turned into a flowing river. The cars could finally move.
2. The Layers Connected: Because the stripes were no longer rigidly blocking the path, the different layers of the material could finally "talk" to each other and work in unison.
3. The Temperature Skyrocketed: The temperature at which the material became a superconductor jumped from a chilly 5 K to a toasty 37 K (and the "onset" of superconductivity started as high as 46 K).

The Irony:
The most amazing part is that the material that was worst at being a superconductor at room pressure (the 1/8 doping) became the best under stress. It actually surpassed the performance of other famous superconductors in the same family.

The Key Takeaways (The "Why")

The paper teaches us three main lessons, explained through our analogy:

• Static vs. Dynamic: The problem wasn't the stripes themselves; it was that they were static (frozen). The material actually needs the stripe interactions to help pair up the electrons (the engine needs the fuel). But if the stripes are too rigid, they kill the flow. The stress turned the "frozen traffic" into "flowing traffic."
• Phase Coherence: The rigid stripes were like a wall preventing the different layers of the material from syncing up. By loosening the structure, the stress allowed the layers to synchronize, creating a strong, 3D superconducting state.
• The LTT Phase: The material has a specific crystal shape called the "LTT phase" that acts like a cage, locking the stripes in place. The stress broke this cage, allowing the material to shift into a more flexible shape (LTLO) where superconductivity can thrive.

The Conclusion

This research is like discovering that a car wasn't broken; it just needed a specific nudge to get out of the mud.

It proves that stripe order (the magnetic patterns) isn't the enemy of superconductivity. In fact, the interactions that create stripes might be the secret sauce for high-temperature superconductivity. The enemy is only the rigidity of those stripes.

By applying a tiny bit of "stress" (a squeeze), the scientists unlocked a hidden, high-performance state in a material that was previously thought to be a dead end. This gives us a huge clue about how to design better superconductors for the future: we don't need to eliminate the stripes; we just need to keep them wiggly and flexible!

Technical Summary

1. Problem Statement

The cuprate superconductor $\text{La}_{2-x}\text{Ba}_x\text{CuO}_4$ (LBCO) exhibits a complex phase diagram where superconductivity, charge order, and spin order compete. A long-standing anomaly occurs at the commensurate doping level $x=1/8$ (0.125). At this specific doping:

• Static Stripe Order: The system stabilizes a robust state of static spin and charge stripes.
• Suppressed Superconductivity: Despite the presence of strong two-dimensional (2D) superconducting correlations at higher temperatures, the bulk three-dimensional (3D) superconducting transition temperature ($T_c$) is drastically suppressed to approximately 3–5 K.
• Structural Pinning: This suppression is attributed to the Low-Temperature Tetragonal (LTT) structural phase, which pins the stripes and frustrates Josephson coupling between CuO$_2$ layers (often described as a Pair-Density-Wave or PDW state).

The Core Question: Can the suppression of 3D superconductivity at $x=1/8$ be reversed? Specifically, can symmetry-selective lattice tuning (uniaxial stress) destabilize the static stripe order and the LTT phase to unlock a high-$T_c$ state, and how does the $x=1/8$ composition compare to nearby dopings ($x=0.115, 0.135$)?

2. Methodology

The authors employed a multi-probe experimental approach on high-quality single crystals of LBCO with doping levels $x=0.115$, $0.125$, and $0.135$.

• Stress Application: In-plane uniaxial compressive stress was applied at an angle of $45^\circ$ to the Cu–O bond direction. This specific orientation is symmetry-selective, targeting the lattice distortions responsible for the LTT phase.
  • Stress Magnitude: Up to $\approx 0.5$ GPa (with specific measurements up to 0.32 GPa for $\mu$SR and higher for resistivity).
• Techniques:
  1. Muon-Spin Rotation ($\mu$SR): Performed on the $x=0.125$ sample to probe:
     • Static Magnetic Order: Zero-field (ZF) and weak transverse-field (wTF) measurements to determine the magnetic volume fraction ($V_M$) and the ordered moment size (via internal field $B_{int}$).
     • Spin-Stripe Temperature: Tracking the spin-ordering temperature ($T_{so}$).
  2. AC Susceptibility: Measured in situ under stress to determine the bulk 3D superconducting transition temperature ($T_{c,mid}$).
  3. Electrical Resistivity: Four-probe measurements on all three dopings to track:
     • The onset of zero resistance ($T_{c,zero}$), reflecting 2D superconductivity.
     • The resistivity peak associated with the LTT structural transition ($\Delta R_{LTT}$).

3. Key Contributions

• First Comprehensive Study at $x=1/8$: While previous studies focused on dopings near 1/8, this work provides the first detailed microscopic investigation (combining $\mu$SR, susceptibility, and resistivity) of the exact commensurate $x=0.125$ composition under uniaxial stress.
• Decoupling Static vs. Dynamic Stripes: The study demonstrates that static stripe order and superconductivity can be decoupled. It shows that suppressing the static volume fraction while retaining dynamic stripe correlations is the key to unlocking high-$T_c$.
• Reversal of the "1/8 Anomaly": The paper proves that the composition with the most robust stripe order and the lowest ambient-pressure $T_c$ can be transformed into the state with the highest $T_c$ in the 214 family under modest stress.

4. Key Results

A. Superconducting Transition Temperature ($T_c$) Enhancement

• Dramatic Increase: For the $x=0.125$ sample, the bulk $T_c$ (measured by susceptibility) increased from ~3–5 K (ambient pressure) to 35 K under 0.23 GPa, and the onset of the transition reached 37 K.
• Zero-Resistance State: Resistivity measurements showed a zero-resistance state ($T_{c,zero}$) at 37 K, with a superconducting transition onset as high as 46 K at 0.56 GPa.
• Comparison: This $T_c$ exceeds the optimal $T_c$ of nearby dopings ($x=0.115, 0.135$) under stress (which peak around 30–31 K) and slightly surpasses the optimal $T_c$ of the related LSCO system under ambient conditions.
• Pressure Efficiency: The critical pressure required to maximize $T_c$ for $x=0.125$ (0.5 GPa) is higher than for other dopings (0.15 GPa), consistent with the higher stability of stripes at 1/8, but the magnitude of the enhancement is unprecedented.

B. Suppression of Static Stripe Order and LTT Phase

• Magnetic Volume Fraction ($V_M$): $\mu$SR data revealed that while the spin-stripe ordering temperature ($T_{so}$) decreased only modestly (from ~40 K to ~33 K), the magnetic volume fraction ($V_M$) was reduced by a factor of ~2.5 (from ~100% to ~40%) at 0.23 GPa.
• Local Robustness: The internal magnetic field ($B_{int}$) and ordered moment size remained largely unchanged, indicating that the remaining stripes are locally robust; the stress primarily reduces the spatial extent of the static order, not its local strength.
• LTT Phase Suppression: The resistivity peak associated with the LTT structural transition was fully suppressed at the critical stress. This indicates a structural transition from the LTT phase to a Low-Temperature Less-Orthorhombic (LTLO) phase.

C. Correlation between Structure and Superconductivity

• Antagonistic Relationship: There is a direct correlation between the suppression of the LTT phase (disappearance of the resistivity peak) and the rise in $T_c$.
• Percolation Threshold: The data suggests an inhomogeneous state where LTLO domains (supporting dynamic stripes and uniform $d$-wave superconductivity) coexist with LTT domains (hosting static stripes). Optimal 3D superconductivity emerges only when the non-magnetic (LTLO) fraction reaches a percolation threshold (approx. 40–60%), allowing coherent interlayer coupling.

5. Significance and Implications

• Nature of Stripe-Superconductivity Competition: The results challenge the view that stripes are purely detrimental to superconductivity. Instead, they suggest that static stripe order competes with 3D superconductivity by frustrating interlayer Josephson coupling (via PDW formation), while dynamic stripe fluctuations may actually enhance pairing strength.
• Mechanism of High-$T_c$: Uniaxial stress acts as a "tuning knob" that converts a fully static stripe configuration into a mixed state of static and dynamic stripes. By destabilizing the LTT lattice pinning, it restores c-axis coherence, allowing a homogeneous $d$-wave superconducting state to emerge.
• Material Design: The finding that the $x=1/8$ composition can host the highest $T_c$ in the 214 family under stress implies that the electronic correlations driving stripe formation are intrinsically linked to the pairing mechanism. This suggests that high-$T_c$ superconductivity in cuprates may be maximized not by eliminating stripes, but by managing their static vs. dynamic nature through lattice symmetry control.

In conclusion, the paper establishes that modest in-plane uniaxial stress can unlock a "hidden" high-$T_c$ state in the most stripe-prone LBCO composition, proving that the suppression of static order and the LTT phase is the critical factor for realizing optimal bulk superconductivity.